Solutions Manual
FINANCIAL
MANAGEMENT
Principles and Practice
Sixth Edition
Timothy J. Gallagher
Colorado State University
 2013 Textbook Media, Madison Wisconsin
(Insert publication data on this page)
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Solutions Manual
to accompany
Financial Management: Principles and Practice
6th Edition
by Timothy J. Gallagher
This solutions manual provides the answers to all the review questions and end-of-chapter problems
in Financial Management: Principles and Practice, by Timothy Gallagher. The answers and the steps taken
to obtain the answers are shown.
Readers are reminded that in finance there is often more than one answer to a question or to a
problem, depending on one’s viewpoint and assumptions. One answer is provided here to each question and
one approach is shown for solving each problem. Other answers and approaches may be equally valid, or
judged even better according to each individual’s preference.
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TABLE OF CONTENTS
Chapter 1 Solutions ...................................................................................................................5
Chapter 2 Solutions ...................................................................................................................9
Chapter 3 Solutions .................................................................................................................13
Chapter 4 Solutions .................................................................................................................16
Chapter 5 Solutions .................................................................................................................24
Chapter 6 Solutions .................................................................................................................35
Chapter 7 Solutions .................................................................................................................42
Chapter 8 Solutions .................................................................................................................54
Chapter 9 Solutions .................................................................................................................62
Chapter 10 Solutions ...............................................................................................................68
Chapter 11 Solutions ...............................................................................................................80
Chapter 12 Solutions ...............................................................................................................94
Chapter 13 Solutions .............................................................................................................104
Chapter 14 Solutions .............................................................................................................114
Chapter 15 Solutions .............................................................................................................121
Chapter 16 Solutions .............................................................................................................125
Chapter 17 Solutions .............................................................................................................132
Chapter 18 Solutions .............................................................................................................139
Chapter 19 Solutions .............................................................................................................148
Chapter 20 Solutions .............................................................................................................164
Chapter 21 Solutions .............................................................................................................168
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Chapter 1 Solutions
Answers to Review Questions
1.
How is finance related to the disciplines of accounting and economics?
Financial management is essentially a combination of accounting and economics. First, financial
managers use accounting information—balance sheets, income statements, and so on—to analyze,
plan, and allocate financial resources for business firms. Second, financial managers use economic
principles to guide them in making financial decisions that are in the best interest of the firm. In other
words, finance is an applied area of economics that relies on accounting for input.
2.
List and describe the three career opportunities in the field of finance.
Finance has three main career paths: financial management, financial markets and institutions, and
investments.
Financial management involves managing the finances of a business. Financial managers—people
who manage a business firm's finances—perform a number of tasks. They analyze and forecast a
firm's finances; assess risk, evaluate investment opportunities, decide when and where to find money
sources and how much money to raise, and decide how much money to return to the firm's investors.
Bankers, stockbrokers, and others who work in financial markets and institutions focus on the flow of
money through financial institutions and the markets in which financial assets are exchanged. They
track the impact of interest rates on the flow of that money.
People who work in the field of investments locate, select, and manage income-producing assets. For
instance, security analysts and mutual fund managers both operate in the investment field.
3.
Describe the duties of the financial manager in a business firm.
Financial managers measure the firm's performance, determine what the financial consequences will
be if the firm maintains its present course or changes it, and recommend how the firm should use its
assets. Financial managers also locate external financing sources and recommend the most beneficial
mix of financing sources, and they determine the financial expectations of the firm's owners.
All financial managers must be able to communicate, analyze, and make decisions based on
information from many sources. To do this, they need to be able to analyze financial statements,
forecast and plan, and determine the effect of size, risk, and timing of cash flows.
4.
What is the basic goal of a business?
The primary financial goal of the business firm is to maximize the wealth of the firm's owners.
Wealth, in turn, refers to value. If a group of people owns a business firm, the contribution that firm
makes to that group's wealth is determined by the market value of that firm.
5
5.
List and explain the three financial factors that influence the value of a business.
The three factors that affect the value of a firm's stock price are cash flow, timing, and risk.
The Importance of Cash Flow: In business, cash is what pays the bills. It is also what the firm
receives in exchange for its products and services. Cash is therefore of ultimate importance, and the
expectation that the firm will generate cash in the future is one of the factors that gives the firm its
value.
The Effect of Timing on Cash Flows: Owners and potential investors look at when firms can expect
to receive cash and when they can expect to pay out cash. All other factors being equal, the sooner
companies expect to receive cash and the later they expect to pay out cash, the more valuable the
firm and the higher its stock price will be.
The Influence of Risk: Risk affects value because the less certain owners and investors are about a
firm's expected future cash flows, the lower they will value the company. The more certain owners
and investors are about a firm's expected future cash flows, the higher they will value the company.
In short, companies whose expected future cash flows are doubtful will have lower values than
companies whose expected future cash flows are virtually certain.
6.
Explain why accounting profits and cash flows are not the same thing.
Stock value depends on future cash flows, their timing, and their riskiness. Profit calculations do not
consider these three factors. Profit, as defined in accounting, is simply the difference between sales
revenue and expenses. It is true that more profits are generally better than less profits, but when the
pursuit of short-term profits adversely affects the size of future cash flows, their timing, or their
riskiness, then these profit maximization efforts are detrimental to the firm.
7.
What is an agent? What are the responsibilities of an agent?
An agent is a person who has the implied or actual authority to act on behalf of another. The owners
whom the agents represent are the principals. Agents have a legal and ethical responsibility to make
decisions that further the interests of the principals.
8.
Describe how society's interests can influence financial managers.
Sometimes the interests of a business firm's owners are not the same as the interests of society. For
instance, the cost of properly disposing of toxic waste can be so high that companies may be tempted
to simply dump their waste in nearby rivers. In so doing, the companies can keep costs low and
profits high, and drive their stock prices higher (if they are not caught). However, many people
suffer from the polluted environment. This is why we have environmental and other similar laws:
So that society's best interests take precedence over the interests of individual company owners.
When businesses take a long-term view, the interests of the owners and society often (but not always)
coincide. When companies encourage recycling, sponsor programs for disadvantaged young people,
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run media campaigns promoting the responsible use of alcohol, and contribute money to worthwhile
civic causes, the goodwill generated as a result of these activities causes long-term increases in the
firm's sales and cash flows, which translate into additional wealth for the firm's owners.
9.
Briefly define the terms proprietorship, partnership, and corporation.
A proprietorship is a business owned by one person.
Two or more people who join together to form a business make up a partnership. This can be done on
an informal basis without a written partnership agreement, or a contract can spell out the rights and
responsibilities of each partner.
A limited liability company is a hybrid between a partnership and a corporation. Profits and losses
pass through to the members. Members generally enjoy limited liability.
Corporations are legal entities separate from their owners. To form a corporation, the owners specify
the governing rules for the running of the business in a contract known as the articles of
incorporation. They submit the articles to the government of the state in which the corporation is
formed, and the state issues a charter that creates the separate legal entity.
10.
Compare and contrast the potential liability of owners of proprietorships, partnerships (general
partners), and corporations.
The sole proprietor has unlimited liability for matters relating to the business. This means that the
sole proprietor is responsible for all the obligations of the business, even if those obligations exceed
the amount the proprietor has invested in the business.
Each partner in a partnership is usually liable for the activities of the partnership as a whole. Even if
there are a hundred partners, each one is technically responsible for all the debts of the partnership.
If ninety-nine partners declare personal bankruptcy, the hundredth partner still is responsible for all
the partnership's debts.
A corporation is a legal entity that is liable for its own activities. Stockholders, the corporation's
owners, have limited liability for the corporation's activities. They cannot lose more than the amount
they paid to buy the corporation’s stock.
Answers to End-of-Chapter Problems
1.
An accountant prepares financial statements while a financial analyst interprets them.
2.
A financial manager’s role in a publicly traded company is to make financial decisions so as to
best serve the principal stockholders.
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3.
a. The value of the firm would go down due to the increase in the amount of time it takes to
receive the cash inflows.
b. The value of the firm would go up due to the increase in expected cash inflows.
c. If expected future cash flows do not change the value of the firm would go down due to the
increased riskiness of the firm.
4.
This practice obviously takes advantage of people who are in a difficult financial situation. This
transaction is voluntary, however, and high risk loans have high interest rates.
5.
LLCs have a small number of members like partnerships and each of these members is likely to
have an active voice in the company like a partnership. The LLC is taxed like a partnership.
Unlike a partnership, and more like a corporation, the owners generally enjoy limited liability.
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Chapter 2 Solutions
Answers to Review Questions
1.
What are financial markets? Why do they exist?
Financial markets are where financial securities are bought and sold. They exist primarily to bring
deficit economic units (those needing money) and surplus economic units (those having extra money)
together.
2.
What is a security?
Securities are claims on financial assets. They can be described as “claim checks” that give their
owners the right to receive funds in the future. Securities are traded in both the money and capital
markets. Money market securities include Treasury bills, negotiable certificates of deposit,
commercial paper, and banker’s acceptances. Capital market securities include bonds and stock.
3.
What are the characteristics of an efficient market?
The term market efficiency refers to the ease, speed, and cost of trading securities. In an efficient
market, securities can be traded easily, quickly, and at low cost. Markets lacking these qualities are
considered to be inefficient.
4.
How are financial trades made on an organized exchange?
Each exchange-listed security is traded at a specified location on the trading floor called the post. The
trading is supervised by specialists who act either as brokers (bringing together buyers and sellers) or
as dealers (buying or selling the stock themselves). Prominent international securities exchanges
include the New York Stock Exchange (NYSE) and major exchanges in Tokyo, London,
Amsterdam, Frankfurt, Paris, Hong Kong, and Mexico.
5.
How are financial trades made in an over-the-counter market? Discuss the role of a dealer in the OTC
market.
In contrast to the organized exchanges, which have physical locations, the over-the-counter market
has no fixed location, or more correctly, it is everywhere. The over-the-counter market, or OTC, is
a network of dealers around the world who maintain inventories of securities for sale. If you wanted
to buy a security that is traded OTC, you would call your broker, who would then shop among
competing dealers who have the security in their inventory. After locating the dealer with the best
price, your broker would buy the security on your behalf.
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The role of dealers: Dealers make their living buying securities and reselling them to others. They
operate just like car dealers who buy cars from manufacturers for resale to others. Dealers make
money by buying securities for one price (called the bid price) and selling them for a higher price,
(called the ask price). The difference, or spread, between the bid price and the ask price represents
the dealer’s fee.
6.
What is the role of a broker in security transactions? How are brokers compensated?
Brokers handle orders to buy or sell securities. Brokers are agents who work on behalf of an investor.
When investors call with an order, brokers work on their behalf to find someone to take the other side
of the proposed trade. If investors want to buy, brokers find sellers. If investors want to sell, brokers
find buyers. Brokers are compensated for their services when the person whom they represent, the
investor, pays them a commission on the sale or purchase of securities.
7.
What is a Treasury bill? How risky is it?
Treasury bills are short-term debt instruments issued by the U.S. Treasury that are sold at a discount
and pay face value at maturity. They are very nearly risk-free as they are backed by the U.S.
Government which could, if need by, print money to pay their holders at maturity.
8.
Would there be positive interest rates on bonds in a world with absolutely no risk (no default risk,
maturity risk, and so on)? Why would a lender demand, and a borrower be willing to pay, a positive
interest rate in such a no-risk world?
Yes, there would be a positive rate of interest in a risk-free world. This is because regardless of risk,
lenders of money must postpone spending during the time the money is loaned. Lenders, then, lose
the opportunity to invest their money for that period of time. To compensate for the cost of losing
investment opportunities while they postpone their spending, lenders demand, and borrowers pay, a
basic rate of return, the real rate of interest.
Answers to End of Chapter Problems
2-1.
a. Surplus economic units have income that exceeds their expenditures. Wealthy families in the
household sector and most states (which have balanced budget requirements) are surplus economic
units.
b. Deficit economic units have expenditures that exceed their incomes. Home buyers and college
students are likely to be deficit economic units.
2.2.
a. false
b. false
c. false
d. false
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2-3.
a. 2 3 4 1
b. The money market is dominated by large institutional traders and there is much competition. The
New York Stock Exchange tends to have larger more actively traded stocks. The over-the-counter
market tends to have smaller less actively traded securities. The real estate market has very high
transaction costs and trades take months.
2.4.
a. A money market security is short term and actively traded.
b. Treasury bills and commercial paper are both traded in the money market.
2-5.
$66.25/$1,000 = 6 5/8 % coupon rate
2-6. The yield on a Bonds-R-Us bond:
Real rate of interest......................
Inflation premium........................
Default risk premium...................
Illiquidity risk premium...............
Maturity risk premium.................
2%
3%
1%
1%
1%
Total yield on Bonds-R-Us Bond: 8%
(reference figure 2-2)
2-7. Treasury Yield Curve:
Given:
Treasury Security Yields:
Three-month T-bills
Six-month T-bills
One-year T-notes
Two-year T-notes
Three-year T-bonds
Five-year T-bonds
Ten-year T-bonds
Thirty-year T-bonds
4.50%
4.75%
5.00%
5.25%
5.50%
5.75%
6.00%
6.50%
Chart: (see next page)
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Maturity in Years (for Chart)
0.25
0.5
1
2
3
5
10
30
Implications:
a. For borrowers: Borrowers tend to look for the low point of the curve, which indicates the least
expensive loan maturity. In this case the low point is 3 months, leading the borrower to seek a shortterm loan. However, if a firm borrows long-term and obtains the higher interest rate, that rate is
locked in for the life of the loan (30 years in this case). If interest rates rise the borrower may be glad
he/she locked in the long-term rate.
b. Lenders face the opposite situation. Granting short-term-term loans at relatively low interest rates
may look unattractive now; but if short-term rates rise, the lenders will be able to roll over
investments at higher and higher rates.
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Chapter 3 Solutions
Answers to Review Questions
1.
Define intermediation.
The financial system makes it possible for surplus and deficit economic units to come together,
exchanging funds for securities, to their mutual benefit. When funds flow from surplus economic
units to a financial institution to a deficit economic unit, the process is known as intermediation. The
financial institution acts as an intermediary between the two economic units.
2.
What can a financial institution often do for a surplus economic unit that it would have difficulty
doing for itself if the surplus economic unit (SEU) were to deal directly with a deficit economic unit
(DEU)?
Surplus economic units do not usually have the expertise to determine whether deficit economic units
can and will make good on their obligations, so it is difficult for them to predict when a would-be
deficit economic unit will fail to pay what it owes. Such a failure is likely to be devastating to a
surplus economic unit that has lent a proportionately large amount of money. In contrast, a financial
institution is in a better position to predict who will pay and who won't. It is also in a better position,
having greater financial resources, to occasionally absorb a loss when someone fails to pay. (This is
just one example of the beneficial things financial institutions do for SEUs)
3.
What can a financial institution often do for a deficit economic unit (DEU)that it would have
difficulty doing for itself if the DEU were to deal directly with an SEU?
SEUs typically want to supply a small amount of funds, while DEUs typically want to obtain a large
amount of funds. Thus it is often difficult for surplus and deficit economic units to come together on
their own to arrange a mutually beneficial exchange of funds for securities. A financial institution
can step in and save the day. A bank, savings and loan, or insurance company can take in small
amounts of funds from many individuals, form a large pool of funds, and then use that large pool to
purchase securities from individual businesses and governments. (This is just one example of the
beneficial things financial institutions do for DEUs)
4.
What are a bank's primary reserves? When the Fed sets reserve requirements, what is its primary
goal?
Vault cash and deposits in the bank's account at the Fed are used to satisfy these reserve
requirements; they are called primary reserves. These primary reserves are non-interest-earning
assets held by financial institutions.
The Federal Reserve requires all commercial banks to keep a minimum amount of reserves on hand
to meet the withdrawal demands of its depositors and to pay other obligations as they come due.
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Many would argue, however, that the reserve requirement is set more with monetary policy in mind
than to ensure that banks meet their depositors' withdrawal requests.
5.
Compare and contrast mutual and stockholder-owned savings and loan associations.
Some savings and loan associations are owned by stockholders, just as commercial banks and other
corporations are owned by their stockholders. Other S&Ls, called mutuals, are owned by their
depositors. When a person deposits money in an account at a mutual S&L, that person becomes a
part owner of the firm. The mutual S&L's profits (if any) are put into a special reserve account from
which dividends are paid from time to time to the owner/depositors.
6.
Who owns a credit union? Explain.
Credit unions are owned by their members. When credit union members put money in their credit
union, they are not technically "depositing" the money. Instead, they are purchasing shares of the
credit union. In general, credit unions exist to pay interest on shares bought by, and collect interest
on loans made to, the members.
7.
Which type of insurance company generally takes on the greater risks: a life insurance company or a
property and casualty insurance company?
The risks protected against by property and casualty companies are much less predictable than are the
risks insured by life insurance companies. Hurricanes, fires, floods, and trial judgments are all much
more difficult to predict than the number of sixty-year-old females who will die this year among a
large number in this risk class. This means that property and casualty insurance companies must
keep more liquid assets than do life insurance companies.
8.
Compare and contrast a defined benefit and a defined contribution pension plan.
In a defined benefit plan, retirement benefits are determined by a formula that usually considers the
worker's age, salary, and years of service. The employee and/or the firm contribute the amounts
necessary to reach the goal. In a defined contribution plan, the contributions to be made by the
employee and/or employer are spelled out, but retirement benefits depend on the total accumulation
in the individual's account at the retirement date.
9.
Special security software is used such that customers who enter their identification and password
information can keep sensitive information out of the hands of hackers.
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Answers to End-of-Chapter Problems
3-1.
a) If there were no financial institutions the SEUs and the DEUs would find that the amount of
money needed by a given DEU did not match the amount of money available by a given SEU. The
money available would not be put to work and the economic activity that would have otherwise taken
place would not.
b) If financial institutions were available in this society they could position themselves between the
SEUs and DEUs. The financial institution could pool the $1,000 available (100 SEUs times $10
each) and pass that money along in $100 increments to the DEUs. This could be done via either a
debt or equity claim that the financial institution would accept from the DEU in return for the money.
3-2.
a) .10 rate on loans made - .05 rate paid to depositors = .05 = 5% interest rate spread
b) (.5 x .10) + (.5 x .12) = .11 = 11% weighted average loan rate
(.5 x .05) + (.5 x .07) = .06 = 6% weighted average deposit rate
11% - 6% = 5% interest rate spread
3-3.
($60M-$11.5M)*.03) +$20M*0.0+$10M*0.0 = $1,455,000
3-4.
a) The FOMC should buy government securities in the open market. This would increase the
reserves of the banking system and would put downward pressure on the federal funds rate.
b) The Fed’s trader at the New York Federal Reserve Bank would contact various government
securities dealers and would buy the Treasury securities from them. Payment would be made by
crediting the accounts at the Fed of these dealers. This would make more funds available and would
tend to put downward pressure on the cost of these funds, the federal funds rate.
3-5.
a) ($1,000,000 x .08) – ($1,000,000 x .07) = $10,000 a profit of $10,000
b) ($1,000,000 x .08) – ($1,000,000 x .09) = -$10,000 a loss of $10,000
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Chapter 4 Solutions
Answers to Review Questions
1.
Why do total assets equal the sum of total liabilities and equity? Explain.
Assets = Liabilities + Equity
Assets are the items of value a business owns. Liabilities are claims on the business by non-owners,
and equity is the owners' claim on the business. The sum of the liabilities and equity is the total
capital contributed to the business, which, by definition, equals the total value of the assets.
2.
What are the time dimensions of the income statement, the balance sheet, and the statement of cash
flows? Hint: Are they videos or still pictures? Explain.
The income statement is like a video: It measures a firm's profitability over a period of time (which
can be a week, a month, a year, or any other time period).
The balance sheet is like a still photograph. The balance sheet shows the firm's assets, liabilities, and
equity at a given point in time.
This cash flow statement like the income statement, can be compared to a video: It shows how cash
flows into and out of a company over a given period of time.
3.
Define depreciation expense as it appears on the income statement. How does depreciation affect
cash flow?
Accounting depreciation is the allocation of an asset's initial cost over time. Depreciation expense on
an income statement is the amount of the asset=s initial cost allocated to the period covered by the
income statement.
Depreciation expense is not a cash flow. Depreciation as an expense category affects cash flow,
however, because it is tax-deductible. Depreciation expense lowers a company’s taxable income
and, therefore its income tax liability. In this way depreciation reduces cash outflows..
4.
What are retained earnings? Why are they important?
Retained earnings represents the sum of all the earnings available to common stockholders of a
business during its entire history, minus the sum of all the common stock dividends which it has ever
paid. Those earnings that were not paid out were, by definition, retained.
Retained earnings are important because they represent amounts reinvested in a company on behalf
of the company’s owners instead of being paid out in the form of dividends.
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5.
Explain how earnings available to common stockholders and common stock dividends paid from the
current income statement affect the balance sheet item retained earnings.
The change in the retained earnings account from one balance sheet to the next equals net income
less preferred stock dividends (which is the amount of earnings available to common stockholders)
less common stock dividends.
6.
What is accumulated depreciation?
Depreciation is the allocation of an asset's initial cost over time. Accumulated depreciation is the
total of all the depreciation expense that has been recognized to date.
7.
What are the three major sections of the statement of cash flows?
Cash flows from Operations
Cash flows from investing activities
Cash flows from financing activities
Net change in cash balance
Cash balance at beginning of period
Cash balance at end of period
8.
How do financial managers calculate the average tax rate?
Average tax rates are calculated by dividing tax dollars paid by earnings before taxes (EBT).
9.
Why do financial managers calculate the marginal tax rate?
Financial managers use marginal tax rates to estimate the future after-tax cash flows from
investments. Since they are interested in how much of the next dollar earned from new investments
will have to be paid in taxes, they use the marginal tax rate (rather than the average tax rate) to
calculate the tax liability.
10.
Identify whether the following items belong on the income statement or the balance sheet.
a. Interest Expense IS
b. Preferred Stock Dividends Paid IS
c. Plant and Equipment BS
d. Sales IS
e. Notes Payable BS
f. Common Stock BS
g. Accounts Receivable BS
h. Accrued Expenses BS
i. Cost of Goods Sold IS
j. Preferred Stock BS
k. Long-Term Debt BS
l. Cash BS
m. Capital in Excess of Par BS
n. Operating Income IS
o. Depreciation Expense IS
p. Marketable Securities BS
q. Accounts Payable BS
r. Prepaid Expenses BS
s. Inventory BS
t. Net Income IS
u. Retained Earnings BS
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11.
Indicate in which section the following balance items belong (current assets, fixed assets, current
liabilities, long-term liabilities, or equity).
a. Cash CA
b. Notes Payable CL
c. Common Stock EQ
d. Accounts Receivable CA
e. Accrued Expenses CL
f. Preferred Stock EQ
g. Plant and Equipment FA
h. Capital in Excess of Par EQ
i. Marketable Securities CA
j. Accounts Payable CL
k. Prepaid Expenses CA
l. Inventory CA
m. Retained Earnings EQ
Answers to End-of-Chapter Problems
4-1.
Revenues
Expenses
Net Income
Retained Earnings, Jan 1
Dividends Paid
Retained Earnings, Dec 31
Current Assets, Dec 31
Non-current Assets, Dec 31
Total Assets, Dec 31
Current Liabilities, Dec 31
Non-current Liabilities, Dec 31
Total Liabilities, Dec 31
CS & Cap. in Excess of Par, Dec 31
Total Stockholders’ Equity, Dec 31
CASE A
200,000
160,000
40,000
300,000
70,000
270,000
80,000
850,000
930,000
40,000
100,000
140,000
520,000
790,000
CASE B
110,000
70,000
40,000
100,000
30,000
110,000
230,000
180,000
410,000
60,000
140,000
200,000
100,000
210,000
Sales
COGS
Gross Profit
Operating Expenses
Operating Income (EBIT)
Interest Expense
Earnings Before Taxes (EBT)
Tax Expense (40%)
Net Income
CASE A
500,000
200,000
300,000
60,000
240,000
10,000
230,000
92,000
138,000
CASE B
250,000
100,000
150,000
60,000
90,000
10,000
80,000
32,000
48,000
4-2.
4-3.
a) 15%; $48,000 X 0.15 = $7,200
b) $7,200/$48,000 = 0.15 or 15%
18
4-4.
a) Tax = $50,000 X 0.15 + $25,000 X 0.25 + $25,000 X 0.34 + $50,000 X 0.39
= $41,750
b) Effective tax rate = $41,750/$150,000 = 0.2783 or 27.83%
4-5.
The marginal tax rate is the tax rate applied to the next dollar of income. Therefore, the marginal tax
rate is 34%.
The average tax rate is 34%
50,000 X .15 = 7,500
25,000 X .25 = 6,250
25,000 X .34 = 8,500
235,000 X .39 = 91,650
2,865,000 X .34 = 974,100
∑ = $1,088,000
$1,088,000/$3,200,000 = 34%
4-6.
$1 + $400,000/200,000 = $3.00 per share
4-7.
Sales
$10,000,000
- Operating Costs
5,200,000
- Interest Expense
200,000
= EBT
$4,600,000
- Taxes (40%)
1,840,000
Net after-tax income
$2,760,000
Simon’s net after-tax income was $2,760,000 for the year.
4-8.
Depreciation expense in 2012 = $70,000 - $60,000 = $10,000.
4-9
a) Cash + Marketable Securities + Inventory + Accounts Receivable + Prepaid expenses.
(11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) = 35,000,000
Current Assets = $35,000,000
b) Fixed assets – depreciation
30,000,000 – 8,000,000 = 22,000,000
Net Fixed Assets = $22,000,000
c) Notes Payable + Accrued Expenses
4,000,000 + 2,000,000 = 6,000,000
Current Liabilities = $6,000,000
19
d) Current Assets – Current Liabilities
(11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) – (4,000,000 + 2,000,000)
35,000,000 – 6,000,000 = 29,000,000
Net Working Capital = $29,000,000
4-10.
a)
b)
c)
d)
e)
Gross Profit
$440,000 - $200,000 = $240,000
Operating Income (EBIT) $240,000 - $40,000 - 85,000 = $115,000
Earning Before Taxes (EBT)
$ 115,000 - $40,000 = $75,000
Income Taxes
$ 75,000 X 0.4 = $30,000
Net Income
$75,000 - $30,000 = $45,000
4-11
$1,500,000 – $200,000 = $1,300,000
Simon and Pieman had a net worth of $1,300,000 at the end of the year.
4-12
a ) 2012 Depreciation Expense for this process line
($131,000 + $12,000) X (0.245) = $35,035
b ) Amount of tax savings due to this investment.
$35,035 X 0.4 = $14,014
4-13.
Operating Income (EBIT) = $768,000
+ Depreciation
= $42,000
+ Amortization
= $15,000
$825,000
Target Telecom’s EBITDA = $825,000.
4-14
a ) The company's 2012 taxable income =
($400,000 - $130,000 X 0.2)
=
$374,000
b ) Income tax = $374,000 X 0.34 = $127,160
4-15.
a) Earnings = [($600,000 - 50,000) X (1 - .34) - $63,000] = $300,000
Earnings per share = $300,000 / 100,000 = $3 per share
b) Addition to Retained Earnings = $300,000 - 100,000 = $200,000
20
4-16.
a ) Current Assets:
b ) Total Assets:
c ) Current Liabilities:
d ) Total Liabilities:
e ) Total Stockholders' Equity:
4-17.
2011: $5,534 + 14,745 + 10,733 + 952 + 3,234 = $35,198
2012: $9,037 + 15,943 + 11,574 + 1,801 + 2,357=$40,712
2011: $35,198+(57,340 - 29,080)+1,010+2,503 = $66,971
2012: $40,712+(60,374 - 32,478)+1,007+4,743 = $74,358
2011: $3,253 + 6,821 = $10,074
2012: $2,450 + 7,330 = $9,780
2011: $10,074 + 2,389 = $12,463
2012: $9,780 + 2,112 = $11,892
2011: $8,549 + 45,959 = $54,508
2012: $10,879 + 51,587 = $62,466
2011: $12,463 TL + $54,508 EQ = $66,971 TA
2012: $11,892 TL + $62,466 EQ = $74,358 TA
4-18.
a ) Accumulated Depreciation
b ) Accounts Receivable (net)
c ) Inventories
d ) Prepaid Expenses
e ) Accounts Payable
f ) Accrued Expenses
g ) Plant and Equipment (gross)
h ) Marketable Securities
i ) Land
j ) Long Term Investments
k ) Common Stock
l ) Bonds Payable
4-19.
Operations:
Add:
(Dollars)
Inflow
Outflow
Outflow
Inflow
Outflow
Inflow
Outflow
Outflow
Inflow
Outflow
Inflow
Outflow
3,398
1,198
841
877
803
509
3,034
849
3
2,240
2,330
277
Pinewood Company and Subsidiaries
Statement of Cash Flows
For the year 2012
Net Income
Depreciation Exp.
Decrease in Prepaid Expenses
Increase in Accrued Expenses
Less: Increase in A/C Receivable
Increase in Marketable Securities
Increase in Inventories
Decrease in A/C Payable
Total Cash Flow from Operations
Investments:
Add: Decrease in Land
Less: Increase in Plant and Equipment
Increase in Long Term Investment
Total Cash Flow from Investments
10,628
3,398
877
509
(1,198)
( 849)
( 841)
( 803)
$11,721
3
(3,034)
(2,240)
($5,271)
21
Financing:
Add:
Less:
Increase in Common Stock
Common Stock Dividends
Decrease in Bonds Payable
Cash Flow from Financing
2,330
(5,000)
( 277)
($2,947)
Net Cash Flow
$3,503
4-20. $3,503 = $9,037 end of ‘09 cash - $5,534 end of ‘08 cash ∴ Yes, the net cash flow figure from
problem #16 gives the same answer as calculating the change in the cash figures from the end of 2011 to the
end of 2012 balance sheets.
4-21.
Sales
COGS
Gross Profit
Operating Expenses
Operating Income (EBIT)
Interest Expense
Income before taxes (EBT)
Tax Expense (30%)
Net Income
900,000
300,000
600,000
200,000
400,000
100,000
300,000
90,000
$210,000
4-22.
Retained Earnings end of 2012
$8,700,000
Retained Earnings end of 2011
8,000,000
Addition to Retained Earnings 2012
700,000
Net Income
$1,500,000
-Addition to Retained Earnings
-700,000
Dividends paid to Common Stockholders 2012 = $ 800,000
4-23.
Year
1
2
3
4
5
6
7
8
9
10
11
Deprec. % X Depreciable Base = Depreciation
$38,500
10%
$385,000
18%
$385,000
$69,300
14.4%
$385,000
$55,440
11.5%
$385,000
$44,275
9.2%
$385,000
$35,420
7.4%
$385,000
$28,490
6.6%
$385,000
$25,410
6.6%
$385,000
$25,410
6.5%
$385,000
$25,025
6.5%
$385,000
$25,025
3.3%
$385,000
$12,705
22
4-24.
Basis = $1,000,000 + $100,000 + $50,000 = $1,150,000
Year 3 depreciation = $1,150,000 X .148 = $170,200
4-25.
Year 1 $7,000,000 X .1 = $700,000
Year 2 $7,000,000 X .18 = $1,260,000
Year 3 $7,000,000 X .144 = $1,008,000
Year 4 $7,000,000 X .115 = $805,000
Year 5 $7,000,000 X .092 = $644,000
Year 6 $7,000,000 X.074 = $518,000
Year 7 $7,000,000 X .066 = $462,000
Year 8 $7,000,000 X .066 = $462,000
Year 9 $7,000,000 X .065 = $455,000
Year 10 $7,000,000 X .065 = $455,000
Year 11 $7,000,000 X .033 = $231,000
23
Chapter 5 Solutions
Answers to Review Questions
1.
What is a financial ratio?
A financial ratio is a number that expresses the value of one financial variable relative to another.
Put more simply, a financial ratio is the result you get when you divide one financial number by
another. Calculating an individual ratio is simple, but each ratio must be analyzed carefully to
effectively measure a firm's performance.
2.
Why do analysts calculate financial ratios?
Ratios are comparative measures. Because the ratios show relative value, they allow financial
analysts to compare information that could not be compared in its raw form. For example, ratios may
be used to compare one ratio to a related ratio, a firm's performance to management's goals, a firm's
past and present performance, or a firm's performance to similar firms
3.
Which ratios would a banker be most interested in when considering whether to approve an
application for a short-term business loan? Explain.
Bankers and other lenders use liquidity ratios to see whether to extend short-term credit to a firm.
Liquidity ratios measure the ability of a firm to meet its short-term obligations. These ratios are
important because failure to pay such obligations can lead to bankruptcy. Generally, the higher the
liquidity ratio, the more able a firm is to pay its short-term obligations.
4.
Which ratios would a potential long-term bond investor be most interested in? Explain.
Current and potential lenders of long-term funds, such as banks and bondholders, are interested in
debt ratios. When a business's debt ratios increase significantly, bondholder and lender risk increases
because more creditors compete for that firm's resources if the company runs into financial trouble.
5.
Under what circumstances would market to book value ratios be misleading? Explain.
The Market to Book ratio is useful, but it is only a rough approximation of how liquidation and going
concern values compare. This is because the Market to Book ratio uses accounting-based book
values. The actual liquidation value of a firm is likely to be different than the book value. For
instance, the assets of a firm may be worth more or less than the value at which they are currently
carried on the company's balance sheet. In addition, the current market price of the company's bonds
and preferred stock may also differ from the accounting value of these claims.
24
6.
Why would an analyst use the Modified Du Pont system to calculate ROE when ROE may be
calculated more simply? Explain.
Actually, an analyst would not use the Modified Du Pont equation to calculate ROE for precisely the
reason stated above. What an analyst would use the Modified Du Pont equation for is to help analyze
the factors that contribute to a firm's ROE. In other words, analysts use the Modified Du Pont system
to “take apart” ROE to see what factors are influencing it.
7.
Why are trend analysis and industry comparison important to financial ratio analysis?
Trend analysis helps financial managers and analysts see whether a company's current financial
situation is improving or deteriorating.
Cross-sectional analysis, or industry comparison, allows analysts to put the value of a firm's ratios in
the context of its industry.
Answers to End-of-Chapter Problems
5-1.
a) Gross Profit Margin = Gross Profit/Sales
20,000,000/35,000,000 = .5714
Gross Profit margin = 57.14%
b) Operating Profit Margin = EBIT/Sales
16,000,000/35,000,000 = .4571
Operating Profit Margin = 45.71%
c) Net Profit Margin = Net Income/Sales
8,100,000/35,000,000 = .2314
Net Profit Margin = 23.14%
5-2.
Current Ratio = Total Current Assets/Total Current Liabilities
(5,000) / (500 +850 + 600) = 2.56
Current Ratio = 2.56
Quick Ratio = (Total Current Assets - Inventory)/Total Current Liabilities
(5,000 – 900)/(500 + 850 + 600) = 2.10
Quick Ratio = 2.10
5-3.
Average Daily Credit Sales = Annual credit sales/365
5,000,000/365 = $13,698.63
Average Collection Period = Accounts Receivable/Average Daily Credit Sales
$500,000/13,698.63 = 36.5
Average Collection Period = 36.5 days
25
5-4.
Inventory Turnover = Sales/Inventory
35,000,000/2,400,000 = 14.58
Inventory Turnover = 14.58 X
Total Asset Turnover = Sales/Total Assets
35,000,000/(15,000,000 + 20,000,000) = 1
Total Asset Turnover = 1 X
5-5.
a) Book Value per share
Book price per share = Common Stock Equity/Number of shares Outstanding
$4,500,000/650,000 =$6.92
BPS = $6.92
b) Market to Book Value ratio
Market to book value ratio = Market price per share/Book value per share
$25.00/$6.92 = 3.61
Market to book value ratio = 3.61
5-6.
a)
b)
c)
d)
e)
Gross Profit Margin:
Operating Profit Margin
Net Profit Margin
Return on Assets
Return on Equity
$47,378/$94,001
$12,941/$94,001
$8,620/$94,001
$8,620/$66,971
$8,620/$54,508
=
=
=
=
=
50.40%
13.77%
9.17%
12.87%
15.81%
While the Net Profit Margin is higher than the industry average, the Return on Assets is lower.
may consider increasing its debt to leverage profits.
5-7.
a) Current Assets = $5,534 + $14,745 + $10,733 + $952 + $3,234 = $35,198
Current Ratio = $35,198/$10,074 = 3.494
b) Quick Ratio = ($35,198 - $10,733)/$10,074 = 2.429
Pinewood seems highly capable of paying off short-term debts.
5-8.
a) Total Debt = $3,253 + $6,821 + $2,389 = $12,463
Debt to Total Assets = $12,463/$66,971 = 18.61%
b) Times Interest Earned = $12,941/$48 = 270 times
Pinewood
Yes. The Pinewood has very low debt and its earnings are extremely high compared to its interest
expense.
5-9.
a. Average Collection Period
b. Inventory Turnover
c. Total Asset Turnover
$14,745/($94,001 / 365) = 57.25 days
$94,001/$10,733 = 8.76
$94,001/$66,971 = 1.404
We would need to know the industry averages for these figures, and also know about Pinewood’s
credit and inventory management practices to comment meaningfully on the above figures.
26
5-10. Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity
= 0.0917 X 1.404 X $66,971/$54,508 = 15.82%
5-11.
a) EVA = EBIT (1- tax rate) – (invested capital X investor’s required rate of return)
EVA = $12,941,000 X (1 - 0.35) – ($77,389,000 X 0.10) = $672,750
b) Pinewood has a true economic profit of $672,750. This is the amount by which its
earnings exceed the returned expected by the firm’s investors.
c) MVA = Total market value – invested capital
MVA = ($75,000,000 + $2,389,000) – ($54,508,000 + $2,389,000) = $20,492,000
d) Pinewood has a total market value that is $20,492,000 greater that the amount of capital
invested in the firm.
5-12.
a) EVA = EBIT (1 – Tax Rate) – (invested capital X investors required rate of return)
EVA = $8,000 (.65) – ($33,000 X .12)
= $5,200 – $3,960
EVA = $1,240
b) The economic value is positive; therefore, Eversharp earned a sufficient amount during the
year to provide more than the expected rate of return from the investors and lenders who
contributed to the capital of the company.
c) MVA = Total market value – invested capital
MVA = $33,000 - $21,000 = $12,000
d) Eversharp’s total market value exceeds its invested capital by $12,000.
5-13.
EVA & MVA Calculation:
Income tax rate
Cost of Capital
Stock Price (ref)
Number of shares outstanding (ref)
Market Value of Common Equity (ref)
Book Value of Common Equity
Debt Capital (ref)
Total Invested Capital (ref)
EVA
MVA
a. EVA
35%
12% Ka
$9
3,000
$27,000
$15,210
$6,630 (Notes payable + Long-Term Debt )
$33,630 (Debt + Common)
$189
EBIT(1-Tr) - (Invested Capital X Ka)
b. Comment on EVA: This year T & J earned enough to exceed the return expected by the
contributors of the firm's capital by $189.
27
5-14.
a. Du Pont:
ROA
Modified Du Pont:
ROE
= Net Profit Margin X Total Asset Turnover
= (80/1,000) X (1,000/500) = 16%
= Net Profit Margin X Total Asset Turnover X Assets over Equity
= ($80/$1,000) X ($1,000/$500) X (1/(1-0.5) = 32%
b. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.7) = 53.3%
c. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.9) = 160%
d. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.1) = 17.78%
5-15.
Assets
Cash
Accounts Receivable
Inventory
Prepaid Expenses
Total Current Assets
Fixed Assets
Total Assets
$6,000
15,068
6,667
282
28,017
34,483
$62,500
Liabilities + Equity
Accounts Payable
Notes Payable
Accrued Expenses
Total Current Liabilities
Bonds Payable
Common Stock
Retained Earnings
Total Liabilities + Equity
$6,000
2,739
600
9,339
15,661
16,000
21,500
$62,500
Total Assets = Sales / Total Asset Turnover = $100,000/1.6 = $62,500
Fixed Assets = Sales / Fixed Asset Turnover = $100,000/2.9 = $34,483
Total Current Assets = $62,500 - $34,483 = $28,017
Accounts Receivable = Sales/day X Ave. Collection Period = ($100,000/365) X 55 = $15,068
Inventory = Sales / Inventory Turnover = $100,000/15 = $6,667
Prepaid Expenses = $28,017 - ($15,068 + $6,667 + $6,000) = $282
Total Debt = Total Assets X Debt to Asset Ratio = $62,500 X 0.4 = $25,000
Total Current Liabilities = Total Current Assets / Current Ratio = $28,017/3 = $9,339
Bonds Payable = Total Debt - Total Current Liabilities = $25,000 - $9,339 = $15,661
Retained Earnings = $62,500 - ($16,000 + $25,000) = $21,500
Notes Payable = $9,339 - ($600 + $6,000) = $2,739
5-16.
NI/$5,000 = 0.10
NI = $500
TE = TA - TL = $10,000 - $6,000 = $4,000
ROE = $500/$4,000 = .125 = 12.5%
5-17.
Current Liability = $20,000 - $18,000 = $2,000
Current Ratio = $5,000/$2,000 = 2.5 times
5-18.
Return on Assets = Net Profit Margin X Total Asset Turnover
0.12 = 0.04 X Total Asset Turnover
Total Asset Turnover = 0.12/0.04 = 3
28
5-19.
Gross Profit = 0.50 X $5,000,000 = $2,500,000
5-20.
EBIT = $2,500,000 - $200,000 - $50,000 = $2,250,000
Operating Profit Margin = $2,250,000/$5,000,000 = .45 = 45%
5-21.
Net Income = 0.20 X $5,000,000 = $1,000,000
5-22.
Net Income = 0.20 X $5,000,000 = $1,000,000
ROA = $1,000,000/$20,000,000 = .05 = 5%
5-23.
Net Income = 0.10 X $15,000,000 = $1,500,000
5-24.
Current Ratio = (20,000,000 - 2,000,000)/4,000,000 = 4.5
5-25.
Quick Ratio = ($20,000,000 - $2,000,000 - $3,000,000)/$4,000,000 = 3.75 times
5-26.
Total Debt = 0.30 X $20,000,000 = $6,000,000
Debt to Equity ratio = $6,000,000/$14,000,000 = 0.43
5-27.
Inventory Turnover = 5,000,000/3,000,000 = 1.67
5-28.
Return on Assets = 0.20 X 0.25 = 0.05 = 5%
5-29. a) Du Pont:
ROA
= Net Profit Margin X Total Asset Turnover
= ($200/$2,000) X ($2,000/$1,000) = .20 = 20%
Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity
= ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.6)) = .50 = 50%
b)
ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.8)) = 100%
c)
ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.2)) = 25%
5-30.
Notoriously Niagara
Niagara’s Notions
a)
NPM = $100,000/$500,000 = 0.20
NPM = $10,000/$500,000 = 0.02
b)
TATO = $500,000/$5,000,000 = 0.10
TATO = $500,000/$500,000 = 1.0
c)
ROA = 0.20 X 0.10 = 0.02
ROA = 0.02 X 1.0 = 0.02
29
d)
Notoriously Niagara must have a higher net profit margin because their asset turnover is low
compared to that of Niagara’s Notions even though they have the same ROA. Niagra’s Notions has a high
asset turnover but a low net profit margin.
5-31.
a)
b)
c)
d)
e)
$2,250,000/1,750,000=$1.29
$40/$1.29 = 31
$15,000,000/1,750,000 = $8.57
$40/$8.57 = 4.67
Yes, the market seems to believe that the company has going-concern value as evidenced by
the market to book ratio greater than 1.
5-32.
Net Profit Margin Current Ratio
NI/Sales
CA/CL
Year
2010
2011
2012
Golden Products
Industry averages:
Total Asset Turnover
Sales/TA
10.00%
9.44%
9.36%
.94
1.02
1.08
1.05
1.15
1.18
9.42%
1.13
2.00
The NPM is about average, although it is deteriorating. The liquidity, as measured by the current
ratio, is below average but improving. Asset utilization, as measured by the total asset turnover is way below
average.
5-33.
The Industry averages are:
Fixed Asset Turnover
1.33
YEAR
2010
2011
2012
Return on Assets
Debt to Assets Ratio
11.00%
PM
10.00%
9.44%
9.36%
CR
0.94
1.02
1.08
Return on equity
0.60
TATO
1.05
1.15
1.18
FATO
1.21
1.33
1.36
26%
ROA
10.53%
10.90%
11.00%
D/A
0.68
0.64
0.60
ROE
33.33%
30.36%
27.50%
Golden Products has an improving ROA that now equals that of the industry norm. The ROE has
slipped a little, but is still above the industry norm in spite of the fact that Golden has a little less debt
in its capital structure in 2012. Overall, Johnny should be pleased.
5-34. ( Figures in $ '000)
NPM
ROA
Mining Smelting Rolling Extrusion
3.3%
8.7%
11.7%
10.0%
4.2%
10.4%
17.9%
13.9%
30
Whole Company
9.7%
13.4%
5-35.
National Glass Company
Income Statement (in $ 000's)
2012
Sales
Cost of Goods Sold
Gross Profit
Selling and Admin Expenses
Depreciation
Operating Income
Interest Expense
Earnings Before Tax
Income Taxes
Net Income
Ratios:
$45,000
23,000
22,000
13,000
3,000
6,000
200
5,800
2,320
$3,480
Balance Sheet (in $ 000's)
As of Dec 31
2012
Assets
Current Assets:
Cash
Accounts Receivable
Inventory
Total Current Assets
Plant & Equipment, Net
Land
Total Assets
Liabilities & Equity
Current Liabilities:
Accounts Payable
Notes Payable
Accrued Expenses
Total Current Liabilities
Bonds Payable
Total Liabilities
Common Stock
Retained Earnings
Total Stockholders' Equity
Total Liabilities & Equity
$2,000
6,000
5,000
13,000
16,000
1,000
$30,000
$2,000
3,000
3,000
8,000
4,000
12,000
4,000
14,000
18,000
$30,000
31
ACP
Inventory Turnover
Debt to Assets
Current Ratio
Total Asset turnover
Fixed Asset Turnover
Return on Equity
Return on Assets
Operating Profit Margin
Gross Profit Margin
48.7 days
9X
40%
1.6250
1.50
2.6471
19.33%
11.6%
13.33%
48.89%
5-36.
a.)
(Industry)
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
x.
xi.
xii.
Kingston, 2012
Gross Profit Margin (50%)
Operating Profit Margin (15%)
Net Profit Margin (8%)
Return on Assets (10%)
Return on Equity (20%)
Current Ratio (1.5)
Quick Ratio (1.0)
Debt to Total Asset (0.5)
Times Interest Earned (25)
Average Collection Period (45 days)
Inventory Turnover (8)
Total Asset Turnover (1.6)
Kingston, 2013
48.9%
15.1%
8.5%
11.56%
19.3%
1.63
1.00
.4
15.5X
53.5days
8.18X
1.4X
48.9%
13.3%
7.5%
9.97%
16.3%
1.62
1.04
.39
14.6X
61.6days
8.62X
1.3X
b.) Kingston has about the same net profit margin and return on equity as the industry norm. The return on
assets ratio for Kingston is about the same as than the industry norm.
c.) Determine the sources and uses of funds and prepare a statement of cash flows for 2013.
(1) Sources and Uses of Funds:
Change,
2012 to 2013
Balance SheetSources
Net Income
Dividends paid
Depreciation
Cash
Accounts Receivable, Net
Inventory
Property, Plant & Equipment, Gross
Land
Accounts Payable
Notes Payable
Accrued expenses
Bonds Payable
Common Stock
Totals
Uses
$3,353
$733
$3,000
($200) $200
$1,600
$1,600
$220
$220
$5,000
$5,000
$0
$600 $600
$300 $300
$100 $100
$0
$0
$7,553 $7,553
(2) Statement of Cash Flows:
Kingston Tool Company
Statement of Cash Flows for the year 2013
( in $ 000s)
Cash Flows from Operations:
Net Income $3,353
Depreciation 3,000
Decrease(Increase) in Accounts Receivable (1,600)
Decrease(Increase) in Inventory (220)
Increase(Decrease) in Accounts Payable
600
Increase(Decrease) in Notes Payable
300
Increase(Decrease) in Accrued Expenses
100
32
Total Cash Flows from Operations
Cash Flows from Investments:
Total Cash Flows from Investments
Cash Flows from Financing:
$5,533
New Property, Plant, & Equipment($5,000)
($5,000)
Dividends Paid ($733)
(733)
($200)
Total Cash Flows from Financing
Net Cash Flow
Beginning Cash Balance
Ending Cash Balance
$2,000
$1,800
d.) Profit margins are eroding and generally a little below the industry norm. Liquidity is about average.
Debt is low, but interest coverage is below the industry norm in spite of the low debt load. Inventory
turnover is way below average. The negative cash flow of $200,000 came mainly from the buildup of
accounts receivable and plant & equipment.
e.) The current ratio, quick ratio, and times interest earned would get the most scrutiny from loan officers.
5-36b. EVA = EBIT X (1 – tax rate) – (invested capital X investor’s required rate of return)
EVA = ($4,000 X 0.60) – ($60,000 X 0.10) = -$3,600
EVA = -$3,600
MVA = Total market value – invested capital
MVA = $50,000 - $60,000 = -$10,000
MVA = -$10,000
5.37.
a) Accounts Receivable/Average Daily Credit Sales
$564,000.00 / ($3,814,000 / 365)= 53.71 = 54 days
b) Super Dot Com was more profitable in 2012 than it was in 2010.
2010
$519,000/$2,100,000
Net Profit Margin
24.71%
2012_________
$1,115,000/$3,814,000
29.23%
$519,000/$2,859,000
Return on Assets
18.15%
$1,115,000/$5,316,000
20.97%
Both the NPM and ROA ratios were better in 2012.
33
c) Super Dot Com was less liquid at the end of 2012 than it was at the end of 2011.
Current Ratio
2010
$981,000/$245,000
4.00
2012_________
$1,720,000/$623,000
2.76
Quick Ratio
($981,000 - $307,000)/$245,000
2.75
34
($1,720,000 - $960,000)/$623,000
1.22
Chapter 6 Solutions
Answers to Review Questions
1.
Why do businesses spend time, effort, and money to produce forecasts? Explain.
Businesses succeed or fail depending on how well prepared they are to deal with the situations they
confront in the future. Therefore they expend considerable sums making estimates (forecasts) of
what the future situation is likely to be. Businesses develop new products, set production quotas, and
select financing sources based on forecasts about the future economic environment and the firm's
condition. If economists predict interest rates will be relatively high, for example, firms may plan to
limit borrowing and defer expansion plans.
2.
What is the primary assumption behind the experience approach to forecasting?
The experience approach to forecasting is based on the assumption that things will happen a certain
way in the future because they happened that way in the past. For instance, if it has always taken you
fifteen minutes to drive to the grocery store, then you will probably assume that it will take you about
fifteen minutes the next time you drive to the store. Similarly, financial managers often assume sales,
expenses, or earnings will grow at certain rates in the future because they grew at that rate in the past.
3.
Describe the sales forecasting process.
Sales forecasting is a group effort. Sales and marketing personnel usually provide assessments of
demand and the competition. Production personnel usually provide estimates of manufacturing
capacity and other production constraints. Top management will make strategic decisions affecting
the firm as a whole. Financial managers coordinate, collect, and analyze the sales forecasting
information. Figure 6-1 in the text shows a diagram of the process.
4.
Explain how the cash budget and the capital budget relate to pro forma financial statements.
The cash budget shows the projected flow of cash in and out of the firm for specified time periods.
The capital budget shows planned expenditures for major asset acquisitions. Forecasters incorporate
data from these budgets into pro forma financial statements under the assumption that the budget
figures will, in fact, occur.
5.
Explain how management goals are incorporated into pro forma financial statements.
Management sets a target goal, and forecasters produce pro forma financial statements under the
assumption that the goal will be reached. For example, if management’s goal is to pay off all shortterm notes during the coming year, forecasters would incorporate this into the pro forma balance
sheet by setting Notes Payable to zero.
35
6.
Explain the significance of the term additional funds needed.
When the pro forma balance sheet is completed, total assets and total liabilities and equity will rarely
match. The discrepancy between forecasted assets and forecasted liabilities and equity results when
either too little or too much financing is projected for the amount of asset growth expected. The
discrepancy is called additional funds needed (AFN) when forecast assets exceed forecast liabilities
and equity, and excess financing when forecast liabilities and equity exceed forecast assets.
7.
What do financial managers look for when they analyze pro forma financial statements?
After the pro forma financial statements are complete, financial managers analyze the forecast to
determine (1) what current trends suggest what will happen to the firm in the future, (2) what effect
management's current plans and budgets will have on the firm, and (3) what actions to take to avoid
problems revealed in the pro forma statements
8.
What action(s) should be taken if analysis of pro forma financial statements reveals positive trends?
Negative trends?
When analyzing the pro forma statements, managers often see signs of emerging positive or negative
conditions. If forecasters discover positive indicators, they will recommend that current plans be
continued. If forecasters see negative indicators, they will recommend corrective action.
Answers to End-of-Chapter Problems
6-1.
Sales Record for The Miniver Corporation
Sales in 2013 is expected to be approximately $215,000 following the trend of the last six years as shown
above.
$250,000
$200,000
$150,000
$100,000
$50,000
$0
2007
2008
2009
2010
36
2011
2012
2013
6-2.
This year
Next Year
Forecasting Assumption
100
50
40
10
120
60
40
20
Sales will grow 20% (100 X 1.2)
Constant % of Sales (120 X 0.5)
Remains same
(120 - 60 - 40)
5
10
Keep 50% Payout Ratio(20 X 0.5)
Current Assets
Fixed Assets
Total Assets
60
100
160
72
100
172
Constant % of sales(120 X 0.6)
Remains same
(100 + 72)
Current Liabs.
Long-term Debt
Common Stock
Retained Earns.
Tot Liabs & Eq
20
20
20
100
160
24
20
20
110
174
Constant % of sales (120 X 0.2)
Remains same
Remains same
(100+20-10)
Sales
- Variable Costs
- Fixed Costs
= Net Income
Dividends
AFN = 172-174= -2 (Negative AFN means there are excess funds.)
6-3.
Jolly Joe's Pizza, Inc.
Financial Status and Forecast
2012
Est. for 2013
$10,000
4,000
6,000
3,000
3,000
1,000
$2,000
20,000
8,000
12,000
3,000
9,000
3,000
6,000
$0
0
Current Assets
Net Fixed Assets
Total Assets
$25,000
15,000
$40,000
50,000
15,000
65,000
Current Liabilities
Long-term debt
Common Stock
Retained Earnings
Total Liabs & Eq
$17,000
3,000
7,000
13,000
$40,000
34,000
3,000
7,000
19,000
63,000
Sales
COGS
Gross Profit
Fixed Expenses
Before-Tax Profit
Tax @ 33.33%
Net Profit
Dividends
Joe will need $2,000 in additional funds in 2013 ($65,000 - $63,000).
37
6-4.
Sugar Cane Alley
Financial Status and Forecast
2012
Sales
$90,000
COGS
48,000
Gross Profit
42,000
Selling and
marketing expenses
13,000
General and administrative expenses
5,000
Depreciation Expense 2,000
Operating Income
Interest Expense
EBT
Tax @ 30%
Net Profit
Est. for 2013
110,000
58,667
51,333
15,889
5,000
2,000
22,000
28,444
800
27,644
8,293
19,351
Dividends
10,000
Addition to RE
9,351
6-5.
a)
Cash
.111111 X $110,000 = $12,222
Accounts Receivable .024667 X $110,000 = $2,713
Inventory
.088889 X $110,000 = $9,778
b)
Property and Equipment, gross $25,000
Accumulated Depreciation
$6,000
Property and Equipment, net $19,000
Total Assets $19,000 + $12,222 + $2,713 + $9,778 = $43,713
c)
Accounts Payable
d)
Total Liabilities = $8,000 + $1,687 = $9,687
e)
Total Liabilities and Equity
= $50,878
f)
Total Assets = $12,222 + $2,713 + $9,778 + $19,000 = $43,713
AFN = $43,713 - $50,878 = -$7,165
There are excess funds of $7,165.
g)
2012: Net Profit Margin = $14,840/$90,000 = 16.49%
2013: Net Profit Margin = $19,351/$110,000 = 17.6%
.015333 X $110,000 = $1,687
= $9,687 + $9,351 + $5,000 + $26,840
38
6-6.
Assets
2012
2013
Liabilities
Cash
$10,000 $12,500
Acct Rec.
25,000 31,250
Inventory
20,000 25,000
Prepaid Exp
2,000
2,500
Total Current
Assets
57,000 71,250
Fixed Assets 32,000 32,000
Depreciation
4,000
4,000
Total Assets
85,000 $99,250
Accounts Payable
Notes Payable
Accrued Expenses
Long Term Debt
Common Equity
Total Liabilities
Equity
2012
2013
$10,500
10,000
11,000
15,000
38,500
$13,125
12,500
13,750
15,000
38,500
85,000
$92,875
*Net Sales for 2013 = $150 million X 1.25 = $187.5 million
Additional funds needed = $99,250 - $92,875 = $6,375
6-7.
2012
Sales
Variable Costs
Fixed Costs
Net Income
Dividends
6-8.
2013
1,250
562.50
160
527.50
290.13
1,000
500
160
340
136
Pro Forma Balance Sheets
End of Year
Assets
2012
2013
Cash
$4,000
4,400
Accounts Rec 10,000 11,000
Inventory
13,000 14,300
Prepaid Exp
400
440
Current Assets27,400
30,140
Fixed Assets 11,000 11,000
Total Assets
$38,400 $41,140
Liabilities + Equity
2012
2013
Accounts Payable
$4,400
4,840
Notes Payable
4,000
4,400
Accrued Expenses
5,000
5,500
Tot.Current Liabilities13,400
14,740
Bonds Payable
6,000
6,000
Common Equity
19,000 21,468
Tot.Liab. + Equity
$38,400 $42,208
In 2013 there would be $1,068 ($42,208-$41,140) in excess funds. This assumes, as the problem states, that
notes payable would increase by 10% along with other current liabilities. Notes payable usually does not
increase with sales.
Year
2013
Total Sales
$85,000 X 1.1
= $93,500
PBT
NI
Addition to RE
$93,500 X .11 $10,285 X .6 $6,171 X .40
= $10,285
= $6,171
= $2,468
39
6-9.
Compute the following ratios for 2012 and 2013:
2012
2013
Current Ratio
3
3
Debt to Assets Ratio 25%
25.3%
Sales to Assets Ratio 62.5%
66.27%
Net Profit Margin
10%
13.64%
Return on Assets
6.25%
9.04%
Return on Equity
8.33%
12.10%
Liquidity seems strong and stable. Debt is modest and stable. Asset utilization is improving slightly while
all the profit margins calculated show marked improvement.
6-10.
BRIGHT FUTURE CORPORATION
Historical and Projected Income Statements
Historical
2012
Sales
Cost of goods Sold
Gross Profit
Selling & Admin. Expenses
Depreciation Expense
Operating Income (EBIT)
Interest Expenses
Earnings Before Tax (EBT)
Income Tax (40%)
Net Income (NI)
Projected
2013
$10,000,000 $12,000,000
$4,000,000 $4,800,000
$6,000,000 $7,200,000
$800,000
$960,000
$2,000,000 $2,000,000
$3,200,000 $4,240,000
$1,350,000 $1,350,000
$1,850,000 $2,890,000
$740,000 $1,156,000
$1,110,000 $1,734,000
Common Stock Dividends paid
Addition to Retained earnings
Earnings per Share (1,000,000 shares)
$400,000
$710,000
$1.11
$400,000
$1,334,000
$1.73
BRIGHT FUTURE CORPORATION
Historical and Projected Balance Sheets
Projection with AFN
Historical
Projected
Excess Financing
Dec 31, 2012 Dec 31, 2013
Incorporated
ASSETS
Current Assets:
Cash
Marketable Securities
Accounts Receivable (Net)
Inventory
Prepaid Expenses
Total Current Assets
Plant and Equipment (gross)
Less: Accumulated Depreciation
Plant and equipment (net)
TOTAL ASSETS
$9,000,000
$8,000,000
$1,000,000
$20,000,000
$1,000,000
$39,000,000
$20,000,000
$9,000,000
$11,000,000
$50,000,000
$10,800,000
$9,600,000
$1,200,000
$24,000,000
$1,200,000
$46,800,000
$20,000,000
$11,000,000
$9,000,000
$55,800,000
$10,800,000
$9,600,000
$1,200,000
$24,000,000
$1,200,000
$46,800,000
$20,000,000
$11,000,000
$9,000,000
$55,800,000
LIABILITIES AND EQUITY
Current Liabilities:
Accounts payable
Notes Payable
Accrued Expenses
Total Current Liabilities
$12,000,000 $14,400,000
$5,000,000 $5,000,000
$3,000,000 $3,600,000
$20,000,000 $23,000,000
$14,400,000
$5,000,000
$3,600,000
$23,000,000
40
L-T Debt (Bonds Payable, 5%, due 2015)
Total Liabilities
Common Stock (1,000,000 shares, $1 par)
Capital in Excess of Par
Retained Earnings
Total Equity
TOTAL LIABILITIES AND EQUITY
$20,000,000
$40,000,000
$1,000,000
$4,000,000
$5,000,000
$10,000,000
$50,000,000
$20,000,000
$43,000,000
$1,000,000
$4,000,000
$6,334,000
$11,334,000
$54,334,000
Question 2a. Excess Financing (Additional Funds Needed)
$1,466,000
$21,466,000
$44,466,000
$1,000,000
$4,000,000
$6,334,000
$11,334,000
$55,800,000
AFN is incorporated in L-T debt. If $1,466,000 of new L-T debt is issued the financing need will be met.
Other financing sources could be used but we chose new L-T debt in this illustration.
Question 2, Ratios:
2012
2013
b. Current Ratio
1.95
2.03
c. Total Asset Turnover
Inventory Turnover
0.20
0.50
0.22
0.50
d. Total Debt to Assets
0.80
0.77
e. Net Profit Margin
Return on Assets
Return on Equity
11.10% 14.45%
2.22% 3.11%
11.10% 15.30%
Question 3, Comments on liquidity, asset productivity, debt management, and profitability:
Liquidity is improving. Debt is high but stable. Inventory and overall asset utilization are stable. The net
profit margin appears healthy. The return on assets ratio is much lower than the net profit margin because of
the low asset turnover. The return on equity ratio is much higher than the return on assets because of the
high debt load.
Question 4, Recommendations:
A 20% projected increase in sales is quite impressive. Management should prepare now, however, to raise
the $1,466,000 that will be needed in 2013 to support the necessary new investments if the projected sales
increase is to be achieved.
41
Chapter 7 Solutions
Answers to Review Questions
1.
What is risk aversion? If common stockholders are risk averse, how do you explain the fact that they
often invest in very risky companies?
Risk aversion is the tendency to avoid additional risk. Risk-averse people will avoid risk if they can,
unless they receive additional compensation for assuming that risk. In finance, the added
compensation is a higher expected rate of return.
People are not all are equally risk averse. For example, some people are willing to buy risky stocks,
while others are not. The ones that do, however, almost always demand an appropriately high
expected rate of return for taking on the additional risk.
2.
Explain the risk–return relationship.
The relationship between risk and required rate of return is known as the risk–return relationship. It
is a positive relationship because the more risk assumed, the higher the required rate of return most
people will demand.
Risk aversion explains the positive risk–return relationship. It explains why risky junk bonds carry a
higher market interest rate than essentially risk-free U.S. Treasury bonds.
3.
Why is the coefficient of variation often a better risk measure when comparing different projects than
the standard deviation?
Whenever we want to compare the risk of investments that have different means, we use the
coefficient of variation (CV). The CV represents the standard deviation's percentage of the mean.
Because the CV is a ratio, it adjusts for differences in means, while the standard deviation does not.
therefore the CV provides a standardized measure of the degree of risk that can be used to compare
alternatives.
4.
What is the difference between business risk and financial risk?
Business risk refers to the uncertainty a company has with regard to its operating income (also
known as earnings before interest and taxes or EBIT). Business risk is brought on by sales volatility
and intensified by the presence of fixed operating costs.
Financial risk is the additional volatility of net income caused by the presence of interest expense.
Firms that have only equity financing have no financial risk because they have no debt on which to
make fixed interest payments. Conversely, firms that operate primarily on borrowed money are
exposed to a high degree of financial risk.
42
5.
Why does the riskiness of portfolios have to be looked at differently than the riskiness of individual
assets?
The riskiness of portfolios has to be looked at differently than the riskiness of individual assets
because the weighted average of the standard deviations of returns of individual assets does not result
in the standard deviation of a portfolio containing the assets. There is a reduction in the fluctuations
of the returns of portfolios which is called the diversification effect.
6.
What happens to the riskiness of a portfolio if assets with very low correlations (even negative
correlations) are combined?
How successfully diversification reduces risk depends on the degree of correlation between the two
variables in question. When assets with very low or negative correlations are combined in portfolios,
the riskiness of the portfolios (as measured by the coefficient of variation) is greatly reduced.
7.
What does it mean when we say that the correlation coefficient for two variables is -1? What does it
mean if this value were zero? What does it mean if it were +1?
Correlation is measured by the correlation coefficient, represented by the letter r. The correlation
coefficient can take on values between +1.0 (perfect positive correlation) to -1.0 (perfect negative
correlation). The closer r is to +1.0, the more the two variables will tend to move with each other at
the same time. The closer r is to -1.0, the more the two variables will tend to move opposite each
other at the same time. An r value of zero indicates that the variables’ values aren't related at all.
This is known as statistical independence.
8.
What is nondiversifiable risk? How is it measured?
Unless the returns of one-half the assets in a portfolio are perfectly negatively correlated with the
other half—which is extremely unlikely—some risk will remain after assets are combined into a
portfolio. The degree of risk that remains is nondiversifiable risk, the part of a portfolio's total risk
that can't be eliminated by diversifying.
Nondiversifiable risk is measured by a term called beta (β). The ultimate group of diversified assets,
the market, has a beta of 1.0. The betas of portfolios, and individual assets, relate their returns to
those of the overall stock market. Portfolios with betas higher than 1.0 are relatively more risky than
the market. Portfolios with betas less than 1.0 are relatively less risky than the market. (Risk-free
portfolios have a beta of zero.)
9.
Compare diversifiable and nondiversifiable risk. Which do you think is more important to financial
managers in business firms?
Diversifiable risk can be dealt with by, of course, diversifying. Nondiversifiable risk is generally
compensated for by raising one’s required rate of return. Both types of risk are important to financial
managers.
43
10.
How do risk-averse investors compensate for risk when they take on investment projects?
Because of risk aversion, people demand higher rates of return for taking on higher-risk projects.
11.
Given that risk-averse investors demand more return for taking on more risk when they invest, how
much more return is appropriate for, say, a share of common stock, than is appropriate for a Treasury
bill?
Although we know that the risk–return relationship is positive, the question of much return is
appropriate for a given degree of risk is especially difficult. Unfortunately, no one knows the answer
for sure. One well-known model used to calculate the required rate of return of an investment, given
its degree of risk, is the Capital Asset Pricing Model (CAPM).
12.
Discuss risk from the perspective of the Capital Asset Pricing Model (CAPM).
The Capital Asset Pricing Model, or CAPM, can be used to calculate the appropriate required rate of
return for an investment project given its degree of risk as measured by beta (β). A project's beta
represents its degree of risk relative to the overall stock market. In the CAPM, when the beta term is
multiplied by the market risk premium term, the result is the additional return over the risk-free rate
that investors demand from that individual project. High-risk (high-beta) projects have high required
rates of return, and low-risk (low-beta) projects have low required rates of return.
Answers to End-of-Chapter Problems
7-1.
Cash Flow
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
$10,000
5.00%
$500
$13,000
10.00%
$16,000
20.00%
$19,000
30.00%
$5,700
$0
$0
$0
$22,000
20.00%
$4,400
$3,000
$9,000,000
$1,800,000
$25,000
10.00%
$2,500
$6,000
$36,000,000
$3,600,000
$28,000
5.00%
$1,400
$9,000
$81,000,000
$4,050,000
Sum of (R x P) = mean:
$19,000
Sum of P x (CF- mean) = variance:
Square root of variance = standard deviation of the variance:
$18,900,000
$4,347
2
2
($9,000)
$81,000,000
$4,050,000
$1,300
($6,000)
$36,000,000
$3,600,000
$3,200
($3,000)
$9,000,000
$1,800,000
2
Coefficient of Variation = std.dev./mean =
44
(CF - mean) P x (CF - mean)
22.88%
7-2.
EXPECTED VALUE, STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF OPERATING INCOME
Operating
Sales Variable
Fixed
Estimate Expenses Expenses
Income
Prob.
Estimate
of Occurrence
CF
$500
$250
$250
$0
P CF x P
2.00%
CF - mean
(CF - mean)
2
Px(CF - mean
2
$0
($350)
$122,500
$2,450
$700
$350
$250
$100
8.00%
$8
($250)
$62,500
$5,000
$1,200
$600
$250
$350
80.00%
$280
$0
$0
$0
$1,700
$850
$250
$600
8.00%
$48
$250
$62,500
$5,000
$1,900
$950
$250
$700
2.00%
$14
$350
$350
$122,500
$2,450
b.
Sum of (CF- mean) x P= variance
Square root of variance = standard deviation:
$14,900
$122
c.
Coeff. of Variation = std.dev/mean:
34.88%
a.
Sum of (R x P) = mean:
2
d. New expected value, standard deviation, and coefficient of variation based on revised sales forecast:
Operating
Sales Variable
Fixed
Estimate Expenses Expenses
Income
Probability
Estimate
of Occurrence
CF
P CF x P
CF - mean
(CF - mean)
2
Px(CF - mean)
2
$500
$250
$250
$0
10.00%
$0
($350)
$122,500
$12,250
$700
$350
$250
$100
15.00%
$15
($250)
$62,500
$9,375
$1,200
$600
$250
$350
50.00%
$175
$0
$0
$0
$1,700
$850
$250
$600
15.00%
$90
$250
$62,500
$9,375
$1,900
$950
$250
$700
10.00%
$70
$350
$350
Sum of (R x P) = mean:
2
Sum of P x (CF - mean) = variance:
$122,500
$12,250
a.
b. Square root of variance = standard deviation:
c.
e. Comments:
7-3.
Coeff. of Variation = std. dev./mean:
$43,250
$208
59.43%
Note how the increased possibilities that sales will be other than $1,200 caused the standard deviation
and coefficient of variation of operating income to nearly double.
Mean:
.10(1,000) + .2(5,000) + .45(10,000) + .15(15,000) + .10(20,000) =
100 + 1,000 + 4,500 + 2,250 + 2,000
Mean = $9,850
Standard Deviation:
ơ 2 = .1(1,000 – 9,850)2 + .2(5,000 – 9,850)2 + .45(10,000 – 9,850)2 + .15(15,000 – 9,850)2 +
.1(20,000 – 9,850)2
ơ 2 = 7,832,250 + 4,704,500 + 10,125 + 3,978,375 + 10,302,250
ơ 2 = 26,827,500
ơ = √ 26,827,500
ơ = 5,179.53
Standard deviation = 5,179.53
45
7-4.
I. EQUITY EDDIE'S COMPANY:
Operating
Income
Interest
Before-Tax
Estimate Expense
Income
Net
Taxes
Probability
Income of Occurrence
2
2
($216)
$46,656
$2,333
CF
P
CF x P
CF - mean
$28
$72
5.00%
$4
(CF - mean) Px(CF - mean)
$100
$0
$100
$200
$0
$200
$56
$144
10.00%
$14
($144)
$20,736
$2,074
$400
$0
$400
$112
$288
70.00%
$202
$0
$0
$0
$600
$0
$600
$168
$432
10.00%
$43
$144
$20,736
$2,074
$700
$0
$700
$196
$504
5.00%
$25
$216
$46,656
$2,333
Sum of (R x P) = mean:
$288
a.
2
Sum of P x (CF - mean) =
variance:
$8,813
$94
b. Square root of variance = standard deviation:
c. Coeff. of Variation = std. dev./mean:
32.60%
II. BARRY BORROWER'S COMPANY:
Operating
Income
Interest
Before-Tax
Estimate Expense
Income
Net
Taxes
Probability
Income of Occurrence
CF
P
CF x P
CF - mean
2
2
(CF - mean) Px(CF - mean)
$110
$40
$70
$19.6
$50.4
5.00%
$2.52
($237.60)
$56,453.76
$2,822.69
$220
$40
$180
$50.4
$129.6
10.00%
$12.96
($158.40)
$25,090.56
$2,509.06
$440
$40
$400 $112.0
$288.0
70.00%
$201.60
$0.00
$0.00
$0.00
$660
$40
$620 $173.6
$446.4
10.00%
$44.64
$158.40
$25,090.56
$2,509.06
$770
$40
$730 $204.4
$525.6
5.00%
$26.28
$288.00
$237.60
$56,453.76
$2,822.69
a.
Sum of (R x P) = mean:
2
Sum of P x (CF - mean) =
variance:
Square
root of variance = standard deviation=
b.
$10,663.49
$103.26
c. Coeff. of Variation = std. dev./ mean:
e. Comments:
35.86%
Note how Barry Borrower's use of debt financing causes his company to have a higher
standard deviation and coefficient of variation of net income than Equity Eddie's.
7-5.
STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF CASH FLOWS FOR THE GO-RILLA PROJECT
Cash Flow
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
(CF - mean)
2
P x (CF - mean)
2
$20,000
1.00%
$200
($6,000)
$36,000,000
$360,000
$22,000
12.00%
$2,640
($4,000)
$16,000,000
$1,920,000
$24,000
23.00%
$5,520
($2,000)
$4,000,000
$920,000
$26,000
28.00%
$7,280
$0
$0
$0
$28,000
23.00%
$6,440
$2,000
$4,000,000
$920,000
46
$30,000
12.00%
$3,600
$4,000
$16,000,000
$1,920,000
$32,000
1.00%
$320
$26,000
$6,000
$36,000,000
$360,000
Sum of (R x P) = mean:
2
Sum of P x (CF - mean) =
variance:
$6,400,000
a. Square root of variance = standard deviation:
$2,530
b. Coefficient of Variation = std. dev./mean:
9.73%
c. Comment:
Given that the average coefficient of variation of George's other product lines is 12%, we would
say that the Go-Rilla project is LESS risky than average
7-6.
Effect of Adding Asset B to Existing Portfolio A
Correlation coefficient r between existing portfolio A and new asset B:
0
Amount invested in Portfolio A:
$700,000
Amount invested in Asset B:
$200,000
Total value of combined portfolio:
$900,000
Weight of existing assets in combined portfolio:
77.8%
Weight of new asset B in combined portfolio:
22.2%
Expected Return of existing portfolio A:
Standard deviation of existing portfolio A:
9.00%
3.00%
Coefficient of variation of existing portfolio A:
33.33%
Expected Return of new asset B:
12.00%
Standard deviation of new asset B:
Coefficient of variation of new asset B:
4.00%
33.33%
Expected Return of combined portfolio per equation 7-1:
9.67%
Standard deviation of combined portfolio per equation 7-5:
2.50%
Coefficient of Variation of combined portfolio:
25.83%
a. Comparison of standard deviations of existing portfolio A and the new combined portfolio:
Standard deviation of existing portfolio A:
3.00%
Standard deviation of combined portfolio:
2.50%
a. Comparison of coefficients of variation of existing portfolio A and the new combined portfolio:
Coefficient of variation of existing portfolio A:
33.33%
Coefficient of variation of combined portfolio:
25.83%
47
7-7.
Coefficient of variation (CV) = Standard Deviation/Mean
288/1,200 = .24
CVzazzle = 24%
7-8.
Total Portfolio = $10,000
Weights: Stock A: 4,000/10,000 = .4
Stock B: 6,000/10,000 = .6
.4(13) + .6(9) = 10.6%
Expected Rate of Return = 10.6%
7-9.
ơp = √ (0.3)2 X (0.05)2 + (0.7)2 X (0.02)2 + ( 2 X 0.3 X 0.7 X 0.6 X 0.05 X 0.02)
ơp = √0.000673
ơp = 0.0259
ơp = 2.59%
7-10.
Effect of Adding PROJ1 to Existing Portfolio
Expected Return of existing portfolio:
11.00%
Standard deviation of existing portfolio:
Coefficient of variation of existing portfolio:
4.00%
36.36%
Expected Return of new PROJ1:
13.00%
Standard deviation of new PROJ1:
Coefficient of variation of new PROJ1:
5.00%
38.46%
Amount invested in existing portfolio:
$820,000
Amount invested in PROJ1:
$194,000
Total value of combined portfolio:
$1,014,000
c.
Weight of existing assets in combined portfolio:
80.9%
d.
Weight of new PROJ1 in combined portfolio:
19.1%
Correlation coefficient r between existing portfolio and new PROJ1:
0
Standard deviation of combined portfolio:
3.37%
(lower than existing portfolio)
Expected Return of combined portfolio per equation 7-1
f.:
Coefficient of Variation of combined portfolio
11.38%
29.63%
a.
b.
e.
:
(lower than existing portfolio)
g. Firm's risk decreases with the addition of PROJ1 to the portfolio
48
7-11.
Required Rate of Return per the CAPM
Risk free rate (kRF)
Expected rate of return on the market (km)
5.0%
15.0%
Beta
Required rate of return on stock per the CAPM:
1.2
17.0%
(equation 7-6)
7-12.
kl = 4.5 + .5(12.5) = 10.75%
ka = 4.5 + 1.0(12.5) = 17%
kh = 4.5 + 1.6(12.5) = 24.5%
7-13.
Effect on CAPM Required Rate of Return of Adding a New Project
Risk free rate (kRF)
5.0%
Expected rate of return on the market (km)
15.0%
Existing firm's Beta
1.5
New Project's Beta
0.8
a. Required rate of return on company per the CAPM:
20.0%
b. Required rate of return on new project per the CAPM:
13.0%
c.
Weight of new project in firm's portfolio:
20.0%
Weight of firm's other assets:
80.0%
1.36
Beta of firm with new project
7-14.
STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF PSC SALES REVENUE
Sales
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
$800
2.00%
$16
2
2
($1,200)
$1,440,000
$28,800
(CF - mean) P x (CF - mean)
$1,000
8.00%
$80
($1,000)
$1,000,000
$80,000
$1,400
20.00%
$280
($600)
$360,000
$72,000
$2,000
40.00%
$800
$0
$0
$0
$2,600
20.00%
$520
$600
$360,000
$72,000
$3,000
8.00%
$240
$1,000
$1,000,000
$80,000
$3,200
2.00%
Sum of (R x P) = exp val:
$64
$2,000
$1,200
$1,440,000
$28,800
49
2
Sum of P x (CF - mean) = variance:
$361,600
Square root of variance = standard deviation:
$601
Coefficient of Variation = std. dev./mean:
30.07%
7-15.
COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME
Operating
Sales Variable
Estimate
Fixed
Expenses
Expenses
Income
Probability
Estimate
of Occurrence
CF
P
CF x P
2
CF - mean (CF - mean) Px(CF - mean)
2
$800
$480
$0
$320
2.00%
$6
($480)
$230,400
$4,608
$1,000
$600
$0
$400
8.00%
$32
($400)
$160,000
$12,800
$1,400
$840
$0
$560
20.00%
$112
($240)
$57,600
$11,520
$2,000
$1,200
$0
$800
40.00%
$320
$0
$0
$0
$2,600
$1,560
$0
$1,040
20.00%
$208
$240
$57,600
$11,520
$3,000
$1,800
$0
$1,200
8.00%
$96
$400
$160,000
$12,800
$3,200
$1,920
$0
$1,280
2.00%
$26
$800
$480
$230,400
$4,608
Sum of (R x P) = mean:
2
Sum of P x (CF - mean) = variance:
$57,856
Square root of variance = standard deviation:
$241
Coefficient of Variation = std. dev./mean:
30.07%
7-16.
COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME
Operating
Sales Variable
Estimate
Fixed
Expenses Expenses
Income
Probability
Estimate
of Occurrence
CF
P
CF x P
CF - mean
(CF - mean)
2
Px(CF - mean)
2
$800
$480
$400
($80)
2.00%
($2)
($480)
$230,400
$4,608
$1,000
$600
$400
$0
8.00%
$0
($400)
$160,000
$12,800
$1,400
$840
$400
$160
20.00%
$32
($240)
$57,600
$11,520
$2,000
$1,200
$400
$400
40.00%
$160
$0
$0
$0
$2,600
$1,560
$400
$640
20.00%
$128
$240
$57,600
$11,520
$3,000
$1,800
$400
$800
8.00%
$64
$400
$160,000
$12,800
$3,200
$1,920
$400
$880
2.00%
$18
$480
$230,400
$4,608
Sum of (R x P) = mean:
$400
50
2
Sum of P x (CF - mean) = variance:
$57,856
Square root of variance = standard
deviation:
$241
Coefficient of Variation = std.
dev./mean:
60.13%
Note how the addition of fixed costs caused the coefficient of variation of PSC's operating income to
double from what it was in problem 7-10
Comment:
7-17.
MEASURING PSC'S FINANCIAL RISK
I. Expected value, standard deviation, and coefficient of variation of PSC's net income when no interest expense is
present
Sales
Operating Interest BeforeTax
Estimate Expenses Expenses Income Expense Income Taxes
$800
$1,000
$1,400
$2,000
$2,600
$3,000
$3,200
Variable
$480
$600
$840
$1,200
$1,560
$1,800
$1,920
Fixed
$400
$400
$400
$400
$400
$400
$400
-$80
$0
$160
$400
$640
$800
$880
$0
$0
$0
$0
$0
$0
$0
Probability of
Net
Occurrence
Income
NI
P
NI X P NI - mean (NI 2
mean)
($80) ($24)
($56) 2%
$0
$0
$0 8%
$160 $48
$112 20%
$400 $120
$280 40%
$640 $192
$448 20%
$800 $240
$560 8%
$880 $264
$616 2%
Sum of (NI X P) = mean
-$1
$0
$22
$112
$90
$45
$12
$ 280
($336) $112,896
($280) $78,400
($168) $28,224
$0
$0
$168 $28,224
$280 $78,400
$336 $112,896
2
Sum of P X (CF - mean) = variance:
Square root of variance = standard deviation:
Coefficient of Variation = std. dev./mean:
P X (NI 2
mean)
$2,258
$6,272
$5,645
$0
$5,645
$6,272
$2,258
$28,349
$168
60.1%
II. Expected value, standard deviation, and coefficient of variation of PSC's net income when interest expense is
present
Sales Variable
Operating Interest BeforeTax
Estimate Expenses Expenses Income Expense Income
$800
$1,000
$1,400
$2,000
$2,600
$3,000
$3,200
$480
$600
$840
$1,200
$1,560
$1,800
$1,920
Fixed
$400
$400
$400
$400
$400
$400
$400
($80)
$0
$160
$400
$640
$800
$880
$60
$60
$60
$60
$60
$60
$60
Probability of
Taxes Net
Income
NI
Occurrence
P
($140) ($42)
($98) 2%
($60) ($18)
($42) 8%
$100 $30
$70 20%
$340 $102
$238 40%
$580 $174
$406 20%
$740 $222
$518 8%
$820 $246
$574 2%
Sum of (R X P) = mean =
NI X P NI - mean (NI 2
mean)
($2)
($3)
$14
$95
$81
$41
$11
$ 238
($336) $112,896
($280) $78,400
($168) $28,224
$0
$0
$168 $28,224
$280 $78,400
$336 $112,896
2
Sum of P X (CF - mean) = variance =
Square root of variance = standard deviation =
51
P X (NI 2
mean)
$2,258
$6,272
$5,645
$0
$5,645
$6,272
$2,258
$28,349
$168
Coefficient of variation equals std. dev./mean =
70.7%
7-18.
I. New coefficient of variation of PSC's operating income:
Operating
Sales
Variable
Fixed
Income Probability of
Estimate Expenses Expenses Estimate Occurrence
EBIT
P
EBIT X EBIT - (EBIT 2
P
mean mean)
$800
$1,000
$1,400
$2,000
$2,600
$3,000
$3,200
$480
$600
$840
$1,200
$1,560
$1,800
$1,920
$250
$70
1%
$250
$150
6%
$250
$310
13%
$250
$550
60%
$250
$790
13%
$250
$950
6%
$250
$1,030
1%
Sum of (EBIT X P) = mean =
P X (EBIT - mean)
$0.70 ($480) $230,400
$9.00 ($400) $160,000
$40.30 ($240) $57,600
$330.00
$0
$0
$102.70 $240 $57,600
$57.00 $400 $160,000
$10.30 $480 $230,400
$550.00
2
$2,304
$9,600
$7,488
$0
$7,488
$9,600
$2,304
2
Sum of P X (CF - mean) = variance =
Square root of variance = standard deviation =
Coefficient of Variation = std. dev./mean =
$38,784
$197
35.8%
II. New coefficient of variation of PSC's net income when no interest expense is present
Sales
Variable
Fixed
Operating
Estimate Expenses Expenses Income
$800
$1,000
$1,400
$2,000
$2,600
$3,000
$3,200
$480
$600
$840
$1,200
$1,560
$1,800
$1,920
$250
$250
$250
$250
$250
$250
$250
$70
$150
$310
$550
$790
$950
$1,030
Interest
BeforeTax
Expense Income Taxes
$0
$70
$0
$150
$0
$310
$0
$550
$0
$790
$0
$950
$0 $1,030
$21
$45
$93
$165
$237
$285
$309
Net
Probability of
Income Occurrence
NI
P
$49
1%
$105
6%
$217
13%
$385
60%
$553
13%
$665
6%
$721
1%
Sum of (NI X P) = mean =
NI X (NI 2
P mean)
P X (NI
2
mean)
$0 $112,896 $1,129
$6 $78,400 $4,704
$28 $28,224 $3,669
$231
$0
$0
$72 $28,224 $3,669
$40 $78,400 $4,704
$7 $112,896 $1,129
$385
2
Sum of P X (CF - mean) = variance = $19,004
Square root of variance = standard deviation =
$138
Coefficient of Variation = std. dev./mean = 35.8%
III. New coefficient of variation of PSC's net income when interest expense is present
Sales
Variable
Fixed Operating Interest
Estimate Expenses Expenses Income
Expense
$800
$1,000
$1,400
$2,000
$2,600
$3,000
$3,200
$480
$600
$840
$1,200
$1,560
$1,800
$1,920
$250
$250
$250
$250
$250
$250
$250
$70
$150
$310
$550
$790
$950
$1,030
$40
$40
$40
$40
$40
$40
$40
B-T
Income Taxes
$30
$110
$270
$510
$750
$910
$990
52
$9
$33
$81
$153
$225
$273
$297
Net
Probability of
Income Occurrence
NI
P
$21
1%
$77
6%
$189
13%
$357
60%
$525
13%
$637
6%
$693
1%
Sum of (NI X P) = mean =
NI X (NI 2
P mean)
P X (NI
2
mean)
$0 $112,896 $1,129
$5 $78,400 $4,704
$25 $28,224 $3,669
$214
$0
$0
$68 $28,224 $3,669
$38 $78,400 $4,704
$7 $112,896 $1,129
$357
2
Sum of P X (CF - mean) = variance = $19,004
Square root of variance = standard deviation =
$138
Coefficient of Variation = std. dev./mean = 38.62%
Summary:
Old Coefficient of variation of operating income (business risk) 60.13%
New coefficient of variation of operating income (business risk) 35.81%
Old difference between the coefficient of variation of net income with and without interest expense
(financial risk)
New difference between the coefficient of variation of net income with and without interest expense
(financial risk)
-10.6%
-2.8%
Comments: The effect of PSC's risk reduction measures was to lower business risk substantially, but
financial risk increased slightly. Managers must evaluate this trade-off and proceed accordingly.
53
Chapter 8 Solutions
Answers to Review Questions
1.
What is the time value of money?
The time value of money means that money you hold in your hand today is worth more than money
you expect to receive in the future. Similarly, money you must pay out today is a greater burden than
the same amount paid in the future.
2.
Why does money have time value?
Positive interest rates indicate that money has time value. When one person lets another borrow
money, the first person requires compensation in exchange for reducing current consumption. The
person who borrows the money is willing to pay to increase current consumption. The required rate
of return on an investment reflects the pure time value of money, an adjustment for expected
inflation, and any risk premiums present.
3.
What is compound interest? Compare compound interest to discounting.
Compound interest occurs when interest is earned on interest and on the original principal of an
investment. Discounting is the inverse of compounding. Compound interest causes the value of a
beginning amount to increase at an increasing rate. Discounting causes the present value of a future
amount to decrease at a decreasing rate.
4.
How is present value affected by a change in the discount rate?
Present value is inversely related to the discount rate. In other words, present value moves in the
opposite direction of the discount rate. If the discount rate increases, present value decreases. If the
discount rate decreases, present value increases.
5.
What is an annuity?
An annuity is a series of equal cash flows, spaced evenly over time.
6.
Suppose you are planning to make regular contributions in equal payments to an investment fund for
your retirement. Which formula would you use to figure out how much your investments will be
worth at retirement time, given an assumed rate of return on your investments?
To figure out how much your investments will be worth at retirement time, given an assumed rate of
return on your investments, you would use the future value of an annuity formula:
54
Future Value of an Annuity Formula
 (1 + k ) n − 1
FVA = PMT 

k


where:
7.
FVA = Future Value of an Annuity
PMT = Amount of each annuity payment
k = Interest rate per time period
n = Number of annuity payments
How does continuous compounding benefit an investor?
The effect of increasing the number of compounding periods per year is to increase the future value
of the investment. The more frequently interest is compounded, the greater the future value. The
smallest compounding period is used when we do continuous compounding--compounding that
occurs every tiny unit of time (the smallest unit of time imaginable).
8.
If you are doing PVA and FVA problems, what difference does it make if the annuities are "ordinary
annuities" or "annuities due"?
In FVA or a PVA of annuity due problems, annuity payments earning interest one period sooner than
in ordinary annuity problems. So, higher FVA and PVA values result with an annuity due. The first
payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due
problems, each annuity payment occurs one period sooner, so the payments are discounted less
severely.
9.
Which formula would you use to solve for the payment required for a car loan if you know the
interest rate, length of the loan, and the borrowed amount? Explain.
To solve for k when the known values are PVA, n, and PMT, start with the present value of an
annuity formula, Equation 8-3b, as follows:
Present Value of an Annuity Formula, Table Method
PVA = PMT X (PVIFAk,n)
Next, rearrange terms and solve for (PVIFAk, n) as follows
PVA / PMT = (PVIFAk,n)
Now refer to the PVIFA values in the text, Table IV. You know n, so find the n row corresponding
to the number of periods in your problem on the left hand side of the table. You have also determined
the PVIFA, so move across the n row until you find (or come close to) the value of PVIFA that you
have solved for. The percent column in which the value is located is the interest rate.
55
Answers to End-of-Chapter Problems
8-1.
$1,000 X (1 + 0.04)5 = $1,216.65
8-2.
a) 0%
b) 5%
c) 10%
d) 20%
8-3.
$5,000 X (1 + 0.06)10 = $8,954.24
8-4.
a) 3%
b) 6%
c) 9%
d) 12%
$50,000 X (1 + 0.03)15 = $77,898.37
$50,000 X (1 + 0.06)15 = $119,827.91
$50,000 X (1 + 0.09)15 = $182,124.12
$50,000 X (1 + 0.12)15 = $273,678.29
8-5
a) 50,000
b) 75,000
c) 100,000
d) 125,000
$50,000 X (1 + 0.04)25 = $133,291.82
$75,000 X (1 + 0.04)25 = $199,937.72
$100,000 X (1 + 0.04)25 = $266,583.63
$125,000 X (1 + 0.04)25 = $333,229.54
8-6
a) 5 years
b) 10 years
c) 15 years
d) 20 years
$60,000 X (1 + 0.05)5 = $76,576.89
$60,000 X (1 + 0.05)10 = $97,733.68
$60,000 X (1 + 0.05)15 = $124,735.69
$60,000 X (1 + 0.05)20 = $159,197.86
8-7.
PV = $20,000 X [1/(1 + .07)10] = $10,166.99
8-8.
a) 0%
b) 5%
c) 10%
d) 20%
8-9
$9,000 X [1/(1+0.06)4] = $7,128.84
8-10
a) 3%
b) 6%
c) 9%
d) 12%
$20,000 X (1 + 0.00)10 = $20,000.00
$20,000 X (1 + 0.05)10 = $32,577.89
$20,000 X (1 + 0.10)10 = $51,874.85
$20,000 X (1 + 0.20)10 = $123,834.73
$20,000 X [1/(1+0.00)20] = $20,000.00
$20,000 X [1/(1+0.05)20] = $7,537.79
$20,000 X [1/(1+0.10)20] = $2,972.87
$20,000 X [1/(1+0.20)20] = $521.68
$15,000 X [1/(1 + 0.03)10] = $11,161.41
$15,000 X [1/(1 + 0.06)10] = $8,375.92
$15,000 X [1/(1 + 0.09)10] = $6,336.16
$15,000 X [1/(1 + 0.12)10] = $4,829.60
56
8-11.
a)$50,000
b)$75,000
c)$100,000
d)$125,000
$50,000 X [1/(1 + 0.04)15 = $27,763.23
$75,000 X [1/(1 + 0.04)15 = $41,644.84
$100,000 X [1/(1 + 0.04)15 = $55,526.45
$125,000 X [1/(1 + 0.04)15 = $69,408.06
8-12.
a) 5 years
b) 10 years
c) 15 years
d) 20 years
$80,000 X [1/(1 + 0.05)5] = $62,682.09
$80,000 X [1/(1 + 0.05)10] = $49,113.06
$80,000 X [1/(1 + 0.05)15] = $38,481.37
$80,000 X [1/(1 + 0.05)20] = $30,151.16
8-13.
PVA = $500 X [(1-1/1.0410)/0.06] = $4,055.45
8-14.
a) 0% $15,000 X 30 = $450,000
b) 10% $15,000 X [(1-1/1.1030)/0.10] = $141,403.72
c) 20% $15,000 X [(1-1/1.2030)/0.20] = $74,684.05
d) 50% $15,000 X [(1-1/1.5030)/0.50] = $29,999.84
8-15.
$20,000 X [(1-1/1.0410)/0.07] = $162,217.92
8-16.
a)
b)
c)
d)
8-17.
FVA = $300 X [(1.095-1)/.09] = $1,795.41
8-18.
a) 0%
b) 2%
c) 10%
d) 20%
8-19.
$5,000 X [(1.0410 – 1)/0.04] = $60,030.54
8-20.
$5,000 X [(1.078 – 1)/0.07] = $51,299.01
8-21.
a) $1,000
b) $10,000
c) $75,000
d) $125,000
9%
13%
15%
21%
$10,000 X [(1-1/1.094)/0.09] = $32,397.20
$10,000 X [(1-1/1.134)/0.13] = $29,744.71
$10,000 X [(1-1/1.154)/0.15] = $28,549.78
$10,000 X [(1-1/1.214)/0.21] = $25,404.41
$8,000 X 12 = $96,000.00
$8,000 X [(1.0212-1)/0.02] = $107,296.72
$8,000 X [(1.1012-1)/0.10] = $171,074.27
$8,000 X [(1.2012-1)/0.20] = $316,644.02
$5,523.63
$1,000 X [(1.055 – 1)/0.05] =
5
$10,000 X [(1.05 – 1)/0.05] = $55,256.31
$75,000 X [(1.055 – 1)/0.05] = $414,422.34
$125,000 X [(1.055 – 1)/0.05] = $690,703.91
57
8-22.
$5,000 X [(1.1240 – 1)/.12] X 1.12 = $4,295,711.95
8-23.
$500 X [(1.045 – 1)/0.04] X 1.04 = $2,816.49
8-24.
$54,163.23 X 1.04 = $56,329.76
8-25.
$80 X [(1-1/1.0620)/.06] X 1.06 = $972.65
8-26.
$30,000 X [(1-1/1.0725)/0.07] X 1.07 = $374,080.02
8-27.
$1,300 X [(1-1/1.005180)/0.005] X 1.005 = $154,824.84
8-28.
$118,368 = FVIF10,k% X $50,000
FVIF10,k% = 2.3674; from Table I, k = 9%
8-29.
$1,000 X (1 + k)5 = $815.37
(1 + k)5 = $815.37/$1,000
(1 + k)5 = .81537
1+k
= .95999
k = -.04 = -4%
8-30.
$50,000 X (1 + k)10 = $118,368
(1 + k)10 = $118,368/$50,000
(1 + k)10 = 2.36736
1 + k = 1.089999
k = .09 = 9%
8-31.
PVA = $50/0.04 = $1,250
8-32.
$70/0.09 = $777.78
8-33.
$65/0.085 = $764.71
8-34.
PVA = PMT X PVIFA k,n
$24,000 = $3,576.71 X PVIFA k,10
6.7101 = PVIFA k,10
k = 8%
58
8-35
PVA = PMT X PVIFA k,n
$200,000 = $898.09 X PVIFA k,360
222.6948 = PVIFA k,360
k = .2917% per month X 12 = 3.5% annual rate
8-36.
a ) 5 years?
b ) 10 years?
c ) 20 years?
8-37.
PV = $16,850.58 X [1/(1+.06)5]
PV = $12,591.30
8-38.
a ) FV = $35,000 X (1 + .05)7 = $49,248.51
b ) FV = $35,000 X (1 + .07)10 = $68,850.30
8-39.
$55.00 = $490.39 X [PVIFk%, 12 years ]
.1122 = PVIFk%, 12 years; k = 20.00%
8-40.
$1,000 = $4,321.94 X [PVIF5%, ?];
.2314 = PVIF5%,?; ? = 30 semi-annual periods, so it will take 15 years.
8-41.
PVA = 50,000 X [(1-1/1.0615)/0.06] = $485,612.45
8-42.
$4,000 X [(1.0720 –1)/0.07] X 1.07 = $175,460.71
8-43.
$250 X [(1.0220 –1)/0.02] = $6,074.34
8-44.
$2,000 X [((1+.06)10 - 1)/.06] = $2,000 X 13.18079494 = $26,361.59
8-45.
a ) $450 X [((1+.02)120 - 1)/.02] = $219,716.17
$10,000/(1+.03)5 = $8,626.09
$10,000/(1+.03)10 = $7,440.94
$10,000/(1+.03)20 = $5,536.76
b ) $219,716.17 = $6,000 X [PVIFA2%, n quarters ]
PVIFA2%, n quarters = 36.6194; n = 66.57 quarters or 16.64 years
8-46.
$30,000 = PMT X [(1-1/(1+0.04)7)/0.04];
$30,000 = PMT X 6.00205467; PMT = $4,998.29
59
8-47.
$1,000 X e.04x15 = $1,822.12
8-48.
$10,000/.05 = $200,000.00
8-49.
FV = $1,000 X e.05 x 23 = $3,158.19
8-50.
FVIF k=8%, n=? = 3
n = 14.27 years
8-51.
PVA = PMT X PVIFA k,n
$4,000 = $250 X PVIFA k=.195/12, n=?
16 = PVIFA k=.01625, n=?
n = 18.68 months
8-52.
$16,936.06 = $5,000 X [PVIFAk%,4 years], assuming payments start one year from the date of
borrowing
[PVIFAk%,4 years] = 3.3872; k = 7%
8-53.
a) FVA = $1,000 X [[(1+.01)60 - 1]/.01] = $81,669.67
b) $81,669.67 = $6,000 X PVIFA1%, n quarters
PVIFA1%, n quarters = 13.6116; n = 14.70 quarters = 3.68 years
8-54.
Option 1)
PV = $5,650
Option 2)
PV = $6,750 X [1/1.0158] = $5,992.05
Option 3)
PV = $800 X [(1-(1/(1+.015)8)/.015] = $5,988.74
Option 4)
PV = $1,000 + $5,250 X (1/(1+.015)8) = $5,660.48
Option 1 is the one with lowest cost to Jack.
8-55.
n = 30 X 12 = 360
k = .06/12 =0 .005 or 0.5%
$250,000 = PMT X [(1-1/1.005360)/0.005]
PMT = $250,000/166.7916144 = $1,498.88
8-56.
PVA = PMT [(1-1/1.005 240)/.005]
$250,000 = PMT X 139.5807717
PMT = $1,791.08
8-57.
a) n = 4 X 12 = 48
k = .06/12 =0 .005 or 0.5%
60
$28,000 = PMT X [(1-1/1.00548)/0.005]
PMT = $28,000/42.58031778 = $657.58
b) n = 6 X 12 = 72
k = .06/12 =0 .005 or 0.5%
$28,000 = PMT X [(1-1/1.00572)/0.005]
PMT = $28,000/60.33951394 = $464.04
8-58. Missing Cash Flow Problem
I. Given Information:
Discount Rate 10%
Known Cash Flows
Time
0
Time
1 $100
Time
2 $150
Time
3
Time
4 $100
Total Present Value of all Cash Flows, including the missing cash flow
II. Solution: The value of the missing cash flow at Time 3:
Known Cash Flows
End of Year
End of Year
End of Year
End of Year
1
2
3
4
$90.9091
$123.9669
$100
$68.3013
Future Value of Missing Cash Flow at End of Year 3
a) n = 5X12 = 60
k = .06/12 = .005
$22,000 = PMT X [1-1/1.00560)/0.005]
$22,000 = PMT X 51.72556075
PMT = $22,000/51.72556075 = $425.32
61
Present Value of Known Cash Flows
$100
$150
Total Present Value of all Cash Flows, including the missing cash flow
Total present value of known cash flows only
Difference (Present Value of missing cash flow)
8-59.
$471.01
$471.01 (given)
$283.1774
$187.8326
$250
Chapter 9 Solutions
Answers to Review Questions
1.
Which is lower for a given company: the cost of debt or the cost of equity? Explain. Ignore taxes in
your answer.
The cost of debt is always less than the cost of equity for a given firm. This is because the debt
investor is taking a lower risk than the equity investor and therefore the required rate of return is
lower.
2.
When a company issues new securities, how do flotation costs affect the cost of raising that capital?
When a company issues new securities flotation costs increase the cost of raising the capital. The
company receives a smaller amount of the proceeds from the new issues, the greater the flotation
costs.
3.
What does the “weight” refer to in the weighted average cost of capital?
The weight referred to in weighted average cost of capital refers to the portion of the total capital
raised by the firm that comes from a given source such as debt, preferred stock or equity.
4.
How do tax considerations affect the cost of debt and the cost of equity?
Because interest on debt is tax deductible to the issuing firm, the higher the tax rate the lower the
after tax cost of debt financing. Tax considerations do not enter into the cost of equity calculation
since dividends paid to stockholders are not tax deductible to the firm.
5.
If dividends paid to common stockholders are not legal obligations of a corporation, is the cost of
equity zero? Explain your answer.
Although common stockholders do not have a contractual claim on dividends the funds supplied by
stockholders definitely have a cost. Equity investors are paid last and so they are taking the greatest
risk among all the suppliers of capital. If the company does not earn a higher rate of return on equity
funds to compensate for the higher risk taken by equity investors, the price of the stock will fall and
therefore the value of the firm.
6.
What is the investment opportunity schedule (IOS)? How does it help financial managers make
business decisions?
62
The investment opportunity schedule shows graphically proposed capital budgeting projects
depicting the IRR and dollar amount of investment for each project. This helps the financial manager
make business decisions since the investment opportunity schedule and the marginal cost of capital
schedule can be plotted together, with those projects on the IOS schedule above the MCC being
acceptable.
7.
What is a marginal cost of capital schedule (MCC)? Is the schedule always a horizontal line?
Explain.
The marginal cost of capital schedule is a graphic depiction of the weighted average cost of capital at
different levels of financing. The MCC schedule is not always a horizontal line. For many firms the
MCC schedule increases, usually at discreet intervals, as the amount of funds to be raised increases.
8.
For a given IOS and MCC, how do financial managers decide which proposed capital budgeting
projects to accept, and which to reject?
For a given IOS and MCC, all independent projects that plot on the IOS above the MCC are
accepted. Those projects on the IOS below the MCC are rejected.
Answers to End-of-Chapter Problems
9-1.
9-2.
9-3.
a)
(i) YTM = 7%
(ii) YTM = 11%
(iii) YTM = 13%
AT kd = .07(1-.40) = 4.2%
AT kd = .11(1-.40) = 6.6%
AT kd = .13(1-.40) = 7.8%
b)
(i) YTM = 7%
(ii) YTM = 11%
(iii) YTM = 13%
AT kd = .07(1-.34) = 4.62%
AT kd = .11(1-.34) = 7.26%
AT kd = .13(1-.34) = 8.58%
a)
AT kd = .10(1-.00) = 10.0%
b)
AT kd = .10(1-.22) = 7.8%
c)
AT kd = .10(1-.34) = 6.6%
Company
A
B
C
YTM
8%
11%
14%
Tax Rate(%)
34%
40%
30%
AT kd
0.8(1-.34) = 5.28%
0.11(1-.40) = 6.60%
0.14(1-.30) = 9.80%
63
9-4.
YTM
AT kd
T=40%
0.08(1-.40) = 4.80%
0.14(1-.40) = 8.40%
0.16(1-.40) = 9.60%
8%
14%
16%
9-5.
a)
kd = 13%
b)
AT kd = .13(1-.40) = 7.8%
9-6.
kd = .095 X (1 - .35) = .06175 = 6.2%
9-7.
kp = $2/($26 - $0.75) = $2/$25.25 = 7.92%
9-8.
kp = $8.00/($61.00 - $1.00) = 13.3%
AT kd = .11(1-.40) = 6.6%
Leo is correct. The cost of debt is lower.
9-9.
kp = $6/($50 - $2.25) = 12.57%
9-10.
kp = $100 X 0.12/($89 - ($89 X 0.05))
= $12/($89 - $4.45) = 14.19%
9-11.
kp = $0.75/($27 - $1) = 2.88%
9-12.
a)
b)
AT kd
T=34%
0.08(1-.34) = 5.28%
0.14(1-.34) = 9.24%
0.16(1-.34) = 10.56%
ks = ($7/$143) + 0. 13 = 17.90%
kn = ($7/($143 - $4) + 0. 13 = 18.04%
9-13. AT kd = 0.14(1-.30) = 9.80%
ks = ($1.50/$39.00) + 0.04 = 7.85%
The cost of the company's retained earnings is lower. This would lead you to reevaluate the
estimated numbers, or question the applicability of the valuation models used here, since ks cannot be
lower than AT kd for a given company.
9-14.
ks = .045 + 1.4(.12 - .045) = 15%
9-15.
a)
ks = ($7/$65) + 0.10 = 20.77%
64
b)
kn = ($7/($65 - $3)) + 0.10 =21.29%
Yes. Floatation costs make cost of capital from new common stock higher.
9-16.
ks = kRF + (kM - kRF) X β
= .03 + (.11 - .03) X 1.6 = 15.8%
9-17. a )
9-18.
ks = ($2 X 1.05)/$30 + .05 = 12.0%
b)
kn = ($2 X 1.05)/($30-$2) + .05 = 12.5%
c)
ks = .03 + (.12 - .03) x 1.4 = 15.6%
AT kd = 0.10(1-0.4) = 6%
kp = $2/($31 - $1) = 6.67%
kn = $4/($100 -$4) + .06 = 10.17%
ka = (0.3)(6) + (0.15)(6.67) + (0.55)(10.17) = 8.394%
9-19. AT kd = 0.11(1-0.4) = 6.60%
kp = $2/($26 - $0.75) = 7.92%
kn = $7/($143 - $4) + .13 = 18.04%
ka = (300,000/600,000)(0.066) + (100,000/600,000)(0.0792) +
(200,000/600,000)(0.1804) = 10.63%
9-20. ka = (600/1250)(0.12(1-0.4)) + (250/1250)(0.14) + (400/1250)(0.16)
= (.48 X .072) + (.20 X .14) + (.32 X .16)
= .03456 + .028 + .0512 = 11.38%
9-21. AT kd = .10(1-.35) = 6.5%
kp = $2/($25 - $1.00) = $2/$24 = 8.33%
kn = ($5/($140 - $4) + 0.10 = 13.68%
ka = (300,000/1,000,000)(0.065) + (100,000/1,000,000)(0.0833) +(600,000/1,000,000)(0.1368) =
10.99%
= minimum expected rate of return needed to satisfy the suppliers of capital.
9-22.
0.60(0.05) + 0.10(0.08) + 0.30(0.12) = 0.074 = 7.4%
9-23.
kd = .095(1 - 0.35) = .06175 = 6.2%
kp = $10/$50 = 0.20 = 20%
ks = 0.04 + 1.1(0.12 – 0.04) = 12.8%
Weight:
65
Debt = 230,000/430,000 = 0.54
Preferred Stock = 100,000/430,000 = 0.23
Common Equity = 100,000/430,000 = 0.23
WACC = .54(0.062) + .23(0.20) + .23(0.128) = .10892 = 10.892%
9-24.
a ) $200,000/0.40 = $500,000 equity break-point
b ) $500,000/0.60 = $833,333 debt break-point
9-25. $1,000,000/.4 = $2,500,000 total capital raised before BPd1 is reached.
$2,000,000/.4 = $5,000,000 total capital raised before BPd2 is reached.
$2,750,000/.5 = $5,500,000 total capital raised before BPe is reached.
a)
ka = (0.40)(0.11(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 10.34%
b)
ka = (0.40)(0.13(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 10.82%
c)
ka = (0.40)(0.15(1 - 0.40)) + (0.5)(0.13) + (0.1)(0.12) = 11.30%
9-26.
OPTIMAL CAPITAL STRUCTURE: DEBT
35.00%
TAX RATE
40.00%
NET INCOME NEXT YEAR:
$1,200,000
ADDITION TO RETAINED EARNINGS $1,000,000
LOAN INTEREST RATE
10.00%
12.00%
COMMON STOCK PRICE PER SHARE
$50
DIVIDEND PER SHARE
$5
GROWTH RATE
9.00%
FLOATATION COST
8.00%
a. COST OF NEW EQUITY
COST OF RETAINED EARNINGS
AT COST OF DEBT
b. EQUITY BREAK POINT
DEBT
DEBT BREAK POINT
DEBT
TOTAL EQUITY
INVESTMENT OPPORTUNITIES
PROJECT INVESTMENT
RETURN
EQUITY 65.00%
A
$500,000
0.16
B
$1,600,000
0.12
C
$600,000
0.15
D
$1,500,000
0.18
FOR LOAN UPTO $750,000
$4,200,000
FOR LOAN ABOVE $750,000
19.87%
19.00%
6.00% FOR LOAN UPTO $750,000
7.20% FOR LOAN ABOVE $750,000
$1,538,462
$538,462
$2,142,857
$750,000
$1,392,857
c. MCC UPTO TOTAL CAPITAL OF $1,538,462 =
14.45%
MCC BETWEEN $1,538,462 AND $2,142,857 15.02%
MCC ABOVE $2,142,857
d.
15.44%
INVESTMENT OPPORTUNITY SCHEDULE
66
PROJECT
D
A
C
INVESTMENT
$1,500,000
$500,000
$600,000
RETURN
0.18
0.16
0.15
B $1,600,000
0.12
e.
MCC/IOS Schedule
Costs of Capital and IRRs
Stone Wood Products
19.00%
Project D
18.00%
17.00%
A
C
16.00%
15.00%
14.00%
13.00%
12.00%
B
11.00%
$0
$500
$1,000 $1,500 $2,000 $2,500 $3,000 $3,500 $4,000 $4,500
Capital Budget Size ($000s)
MCC
IOS
f. Only Projects D and A would be chosen. They are the ones with IRR values on the IOS schedule that
plot above the MCC schedule.
67
Chapter 10 Solutions
Answers to Review Questions
1.
How do we calculate the payback period for a proposed capital budgeting project? What are the
main criticisms of the payback method?
We calculate the payback period for a proposed project by adding a project’s positive cash flows, one
period at a time, until the sum equals the initial investment. The number of time periods it takes to
cover this investment is the payback period. The main criticisms of the payback method are that cash
flows after the payback period are ignored and the time value of money is not considered.
2.
How does the net present value relate to the value of the firm?
The net present value is the dollar amount of the change to the value of the firm if the project under
consideration is accepted.
3.
What are the advantages and disadvantages of the internal rate of return method?
The internal rate of return method is a discounted cash flow method and a number expressed as a
percentage. These are typically seen as advantages. The main disadvantage of the internal rate of
return is that it is somewhat more difficult to calculate, although this is less true with the ready
availability of financial calculators.
4.
Provide three examples of mutually exclusive projects.
Mutually exclusive projects are projects that compete against each other for our selection. If a firm
were considering the purchase of a new computer, needing only one computer, then the proposals
made by the sales reps from Hewlett-Packard, Compaq, and Toshiba would be mutually exclusive
projects vying for our selection.
5.
What is the decision rule for accepting or rejecting proposed projects when using net present value?
When using the net present value decision rule any project with a net present value greater than or
equal to zero would be acceptable. Any project with a negative net present value would be rejected.
6.
What is the decision rule for accepting or rejecting proposed projects when using internal rate of
return?
Whenever the internal rate of return is greater than or equal to the required rate of return, the hurdle
rate, the project is accepted. When the internal rate of return is less than this required rate of return,
the project is rejected.
68
7.
What is capital rationing? Should a firm practice capital rationing? Why?
Capital rationing is the practice of setting dollar limits on what will be invested in new capital
budgeting projects. Proprietorships, partnerships and private corporations are in a position to do
whatever the owners wish. It can be argued, however, that for a publicly traded corporation capital
rationing may not be consistent with maximizing the value of the firm. This is because some value
adding projects may be rejected if they would cause the firm to exceed its self imposed capital
rationing limit.
8.
Explain how to resolve a “ranking conflict” between the net present value and the internal rate of
return. Why should the conflict be resolved as you explained?
Whenever there is a ranking conflict between net present value and internal rate of return we
generally suggest that the project with the highest net present value be chosen. This is because the
net present value method ties more directly with the primary financial goal of the firm, to maximize
firm value.
9.
Explain how to measure the firm risk of a capital budgeting project.
The firm risk of a capital budgeting project measures the impact of adding a new project to the
existing projects of the firm.
10.
Why is the coefficient of variation a better risk measure to use than the standard deviation when
evaluating the risk of capital budgeting projects?
The coefficient of variation is a better risk measure than the standard deviation alone because the CV
adjusts for the size of the project. The CV measures the standard deviation divided by the mean and
therefore puts the standard deviation into context. For example, a standard deviation of .05 may be
considered large relative to a mean of .02 but would be considered a small value relative to a mean
value of 8.
11.
Explain why we measure a project’s risk as the change in the CV.
We measure a project’s risk as the change in the coefficient of variation because this focuses on the
change in the riskiness of the firm’s existing portfolio.
12.
Explain how using a risk-adjusted discount rate improves capital budgeting decision making
compared to using a single discount rate for all projects?
The risk-adjusted discount rate improves capital budgeting decision making compared to the single
discount rate approach because the RADR allows us to set a higher hurdle for the high risk project
and a lower hurdle for the low risk project thus aligning our capital budgeting decision making
process more closely with the goal of maximizing the value of the firm.
69
Answers to End-of-Chapter Problems
10-1.
Zombiebook: (5 mil) + 2mil + 2 mil + 2 mil + 2 mil -- 2.5 years
Angry Rabbits: (5mil) + 1 mil + 1 mil + 1 mil + 20 mil -- 3.05 years
Zombie has the lower payback period, 2.5 years versus 3.05 years so if we base our decision on the
basis of payback (choose the project with the lower payback) we would choose Zombiebook over
Angry Rabbits. Making this choice, however, is cause for concern. Because the very large $20
million positive cash flow in year 5 for Angry Rabbit occurs after the payback it is ignored when
applying the payback decision rule. It doesn’t seem right to ignore such a large positive cash flow.
Ignoring this large cash flow after the payback period points out on out one of the weaknesses of the
payback decision rule. NPV, IRR, and MIRR would not ignore this cash flow.
10-2.
CF0 = -80,000,000
CF1 = 0
CF2 = 0
CF3 = 0
CF4-23 = 5,000,000
I = 10%
NPV = -$48,018,167.84
IRR = 1.70%
10-3.
a)
Peter: (10,000) + 4,000 + 4,000 + 4,000 ----> 2.5 years
Paul: (10,000) + 2,000 +8,000 + 2,000 ----> 2.0 years
Mary: (10,000) + 10,000 + 1,000 + 1,000 ----> 1 year
b)
Mary's project is most liquid using payback as the liquidity measure.
10-4.
CF0 = -20,000,000
CF1-25 = $2,000,000
I = 8%
NPV = $1,349,552
10-5.
IRR = 8.78%
10-6.
CF0 = -20,000,000
CF25 = 146, 211,879.90
MIRR = 8.28%
10-7.
Expected Cash Flows
Year
Weights Cum. CF
0
-$200,000
(200,000)
Waters
Cum. CF
-$300,000
(300,000)
70
1
2
3
4
100,000
75,000
50,000
100,000
(100,000)
(25,000)
25,000
125,000
200,000
150,000
150,000
150,000
(100,000)
50,000
200,000
350,000
Project Weights: 2.5 years
Project Waters: 1.67 years
Project Waters is the better project according to payback because it recoups its investment in a shorter time.
10-8.
Year
0
1
2
3
4
Expected Cash Flows
Weights
Waters
-$200,000
-$300,000
100,000
200,000
75,000
150,000
50,000
150,000
100,000
150,000
k= 8%
NPVweights (k = 8%) = $70,087.60
NPVwaters (k= 8%) = $243,115.32
10-9.
a)
NPV = (17,291.42) + 5,000[1/1.091] + 8,000[1/1.092] + 10,000[1/1.093] =
$1,751.01
b)
NPV = (17,291.42) + 5,000[1/(1+k)1] + 8,000[1/(1+k)2] + 10,000[1/(1+k)3] = $0
IRR = k = 14%
c)
Yes. NPV is positive and IRR > Cost of capital
10-10. a )
b)
10-11. a )
b)
Rifle Stock: NPV = -9,000 + 2,000 X .8850 + 5,000 X .7831 + 1,000 X .6931 + 4,000 X
.6133 = -168.20
Fork Lift: NPV = -12,000 +5,000 X .8850 + 4,000 X .7831 +6,000 X .6931 + 2,000 X .6133
= +942.60
Packaging Equip. NPV = -18,200 + 5,000 X .7831 + 10,000 X .6931 + 12,000 X .6133 =
+6.10
Fork Lift and Packaging; both have positive NPVs.
Cal's Project: NPV = -100,000 + 22,611 X (5.2064) = $17,721.23
Aron's Project:NPV = -300,000 + 63,655 X (5.2064) = $31,411.49
Cal's Project: 100,000/22,611 = PVIFAk,7 year; k = 13% = IRR
Aron's Project:300,000/63,655 = PVIFAk,7 year; k = 11% = IRR
71
c)
Aron’s Project; The NPV is positive and greater than the NPV for Cal’s Project..
d)
No.
10-12.
Time
Cash Flow
($10,000)
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
$9,432
$8,574
$7,795
$7,086
$6,442
$5,856
$5,324
$4,840
$4,400
$4,000
Terminal Value
$63,749
a.) IRR
38.5%
b.) MIRR
20.35%
Initial investment
T- 1
T- 2
T- 3
T- 4
T- 5
T- 6
T- 7
T- 8
T- 9
T- 10
10-13. a )
b)
9
8
7
6
5
4
3
2
1
0
Printer #1: Payback = 2 years
Printer #2: Payback = 1.77 years
Printer #1: NPV
Printer #2: NPV
c)
FV of Cash Flow at T10 if reinvested @ 10%
cost of capital (per Years
to go
Equation 8-1a)
= -2,000 +900 X .9259 + 1,100 X .8573 + 1,300 X .7938 = +808.28
= +808.39 financial calculator and Excel solution
= -2,500 + 1,500 X .9259 + 1,300 X .8573 + 800 X .7938 = +638.38
= +638.50 financial calculator and Excel solution
Printer #1: NPV = 0 = -2,000 + 900 X [1/(1+k)1] + 1,100 X [1/(1+k)2] + 1,300 X
[1/(1+k)3]
IRR = k = .2782 = 27.82%
= -2,500 + 1,500 X [1/(1+k)1] + 1,300 X [1/(1+k)2] + 800 X
[1/(1+k)3]
IRR = k = .2325 = 23.25%
Printer #2: NPV = 0
d)
Printer #1 with higher NPV and higher IRR
e)
Printer #1: NPV = -2,000 + 900 X .8621 + 1,100 X .7432 + 1,300 X .6407 = +426.32
Printer #2: NPV = -2,500 + 1,500 X .8621 + 1,300 X .7,432 + 800 X .6407 = +271.87
No. NPV of Printer #1 is still higher.
72
10-14. Expected Cash Flows
Year
0
1
2
3
4
5
6
7
8
9
10
Program
-20,000,000
1,000,000
2,000,000
5,000,000
6,000,000
6,000,000
6,000,000
6,000,000
6,000,000
6,000,000
6,000,000
I = 15%
NPV = $2,082,694.77
IRR = 17.14%
MIRR = 16.14%
TV = $89,336,820
10-15. a )
Project A:
Project B:
Project A.
NPV = -11,000 + 4,000 X (3.9975) = $4,990.00
NPV = -17,000 + 4,500 X (3.9975) = $988.75
Project A should be selected because it has the higher NPV
b)
Both. Both the NPVs are positive.
c)
Project A:
Project B:
d)
Mutually exclusive:
Independent:
e)
Project C:
Project C.
IRR : 11000/4000 = PVIFAk,6 year; k =28.16 %
IRR : 17000/4500 = PVIFAk,6 year; k = 15.07%
Project A has the higher IRR and would be selected.
Select both. (IRR > Cost of Capital for both the projects)
NPV = -17,000 + 37,500X(PVIF13%,6 year)
= -17,000 + 37,500 X .4803 = $1,011.25
NPV of Project C > NPV of Project B ∴ Project C would be chosen
of Project B if these projects were mutually exclusive.
f)
Project C:
IRR: 17,000/37,500 = .4533 = PVIFk,6 year; k = 14.09 %
IRR of Project C < IRR of Project B ∴ Project B would be chosen because it
has the higher IRR value.
g)
Selections based on NPV and IRR method contradict each other. Since NPV method is
generally preferred, select Project C.
73
10-16. a ) NPV = -5M + 1.85M(2.7982) -.25M(.4761) = $57,645
b ) Multiple IRRs are possible because of two sign changes in the cash flow series. In this case
there is only one IRR, however. Do an NPV profile if you don’t believe us. The IRR is 16.59%.
TI BAII PLUS Financial Calculator Solution
IRR
Keystrokes
Display
[CF]
CF0 = old contents
[2nd][CLR Work]
CF0 = 0.00
5000000[+/-][ENTER]
CF0 = -5,000,000.00
↓ 1850000[ENTER]
↓ 4 [ENTER]
C01 = 1,850,000.00
F01 = 4.00
↓ 250000[+/-][ENTER]
↓ [ENTER]
C02 = -250,000.00
F02 = 1.00
↓ [IRR]
IRR = 0.00
[CPT]
IRR = 16.59
c ) The IRR of 16.59% is greater than the required rate of return of 10%, so the project would get a
positive recommendation.
10-17. a) Hydroelectric Project
CF0 = ($100,000)
CF1 = $20,000
CF2 = $30,000
CF3 = $40,000
CF4 = $90,000
Geothermal Project
CF0 = ($100,000)
CF1 = $80,000
CF2 = $40,000
CF3 = $30,000
CF4 = $10,000
b) NPVhydro (k = 6%) = $50,441.02
NPVgeo (k = 6%) = $44,181.07
Accept the Hydroelectric Project since it has the higher NPV when using a 6% cost of capital. We
are assuming here that the two projects are mutually exclusive.
c) NPVhydro (k = 15%) = $17,834.06
NPVgeo (k = 15%) = $25,253.98
Accept the Geothermal Project since it has the higher NPV when using a 15% cost of capital. We
are assuming that the two projects are mutually exclusive.
d) Approximately 9.58%. This is where the NPV profiles cross.
e) Greater than 21.66%
f) Greater than 31.92%
74
10-18. The Chalk Line Machine, Gel Padded Glove, Insect Repellant, and Recycled Base Cover projects
collectively have initial cash outlays of $90,000 (under the budget limit) and have NPVs that sum to
$12,950. No other combination of projects gives a higher total NPV and stays under the budget
limit.
10-19.
Given Information:
Initial investment
$5,669.62
Year 1
Year 2
Year 3
Required rate of return
$2,200
$2,200
$2,200
12%
Year:
Annual cash flows
PV of cash flows
NPV
b. Comment on the acceptability of the investment:
0
($5,670)
($5,670)
($386)
Yearly net cash flows:
a. NPV of the investment:
1
$2,200
$1,964
2
$2,200
$1,754
5%
322
10%
(199)
Comment: The project is unacceptable because it has a negative NPV. You would not
accept it even if you had cash available.
c. NPV Profile:
Discount rate
NPV
0%
930
NPV
NPV PROFILE
930
$900
$700
$500
$300
$100
($100)
($300)
($500)
322
(199)
0%
5%
10%
DISCOUNT RATE
Comment:
Comment: According to the NPV profile, the discount rate would have to be less than about
8% in order for the project's NPV to be positive.
d. Comment:
Comment: The IRR is that discount rate which produces an NPV of zero. Therefore, the IRR
could be calculated to determine the "hurdle rate" below which the project's NPV would be
positive (8% in this case).
75
3
$2,200
$1,566
10-20. STD(IRR) = [(.05x(0%-6%)2 + .1x(1%-6%)2 + .2x(3%-6%)2 + .3x(6%-6%)2 + .2x(9%-6%)2 +
.1x(11%-6%)2 + .05x(12%-6%)2].5 = 3.49%
COEFF. OF VARIATION (CV) = 3.49%/6% = .5817
10-21. PORT. STD. WITH A = [(.22x.022)+(.82x.032)+(.82x.032)+(2x.2x.8x.5x.02x.03)].5
= .0262 = 2.62%
E(IRR) of portfolio with A = (.2x14%)+(.8x13%) = 13.2%
CV of portfolio with A = 2.62%/13.2% = .1985
PORT. STD. WITH B = [(.22x.062)+(.82x.032)+(2x.2x.8x.5x.02x.03)].5 = .0317 = 3.17%
E(IRR) of portfolio with B = (.2x16%)+(.8x13%) = 13.6%
CV of portfolio with B = .0317/.136 = .2331
PORT. STD. WITH C = [(.22x.052)+(.82x.032)+(2x.2x.8x.5x.05x.03)].5 = .0303 = 3.03%
E(IRR) of portfolio with C = (.2x11%)+(.8x13%) = 12.6%
CV of portfolio with C = .0303/.126 = .2405
PORT. STD. WITH D = [(.22x.042)+(.82x.032)+(2x.2x.8x.5x.04x.03)].5 = .0288 = 2.88%
E(IRR) of portfolio with D = (.2x14%)+(.8x13%) = 12.6%
CV of portfolio with B = .0288/.132 = .2182
Project A has the lowest risk and Project C the highest as measured by the CV.
10-22. a)
1. CVA = 2%/10% = .2
2. E(IRR) of new combined portfolio = (700,000/900,000 x 10%) + (200,000/900,000 x 11%
= 10.22%
3. STD. Of new combined portfolio = [(.7782x.022)+(.2222x.03)+(2x.222x.778x.9x.02x.03)].5
= .0218 = 2.18%
4. CV of new combined portfolio = .0218/.1022 = .2133
b)
.2133 - .20 = .0133 change in CV
c)
average risk
d)
1. Ave. Risk: NPV = $55,000/1.131 + 55,000/1.132 + 55,000/1.133 + 100,000/1.134 - 200,000
= ($8,805)
2. High Risk: NPV = $55,000/1.161 + 55,000/1.162 + 55,000/1.163 + 100,000/1.164 - 200,000
= ($21,247)
3. Low Risk: NPV = $55,000/1.101 + 55,000/1.102 + 55,000/1.103 + 100,000/1.104 - 200,000
= $5,078
76
10-23. a) (.125x2%)+(.20x5%)+(.35x9%)+(.20x13%)+(.125x16%) = 9.00%
b) .125(.02-.09)2 + .2(.05-.09)2 + .35(.09-.09)2 + .2(.13-.09)2 + .125(.16-.09)2 = .001865
= .1865%
square root of .001865 = .0432 = 4.32% standard deviation
c) CV of existing portfolio = .02/.08 = .25
d) E(IRR) of new combined portfolio = (.8x8%)+(.2x9%) = 8.20%
e) STD. DEV. of the combined portfolio = [(.22x.04322)+(.82x.022)+(2x.2x.8x1x.0432x.02)].5 = .0246
= 2.46%
f) CV of combined portfolio = .0246/.0820 = .3005
g) .3005 - .25 = .0505 increase in CV
10-24.
Proj. A
Proj. B
Proj.C
Proj. D
Standard deviation of existing portfolio:
Standard deviation of new project:
Standard deviation of combined portfolio
4.00%
9.00%
3.71%
4.00%
5.00%
3.63%
4.00%
3.00%
3.61%
4.00%
1.00%
3.60%
expected return E(R) of new project:
expected return E(R) of existing portfolio:
expected return E(R) of combined portfolio:
18.00%
12.00%
12.60%
15.00%
12.00%
12.30%
11.00%
12.00%
11.90%
8.00%
12.00%
11.60%
a. Coefficient of variation of existing portfolio:
33.33%
b.&c. Coefficient of variation of combined portfolio:
29.45%
29.55%
30.36%
31.05%
d.
A IS THE
LOWEST
RISK
PROJECT
D IS THE
HIGHEST
RISK
PROJECT
10-25. a. CV of existing portfolio = 5%/15% = 33.33%
b. WT of existing portfolio of PROJ1 is added = $820,000/($820,000+$194,000) = .809
= 8.09%
c. WT of PROJ1 if added to existing portfolio = 1 - .809 = .191 = 19.1%
d. STD. DEV. of combined portfolio = [(.8092x.052)+(.1912x.09)+(2x.809x.191x1x.05x.09)].5 =
.0577 = 5.77%
The combined portfolio standard deviation is higher than that of the existing portfolio (5.77% versus
5.00%).
e. CV of the combined portfolio = 5.77%/[(.809x15%)+(.191x18%)] = 5.77%/15.57%
= .3706
77
10-26.
1


 1 - (1.08 )10 
a) NPV = $298,500 x 
 - $2,000,000
.08




= $298,500 x 6.7100814 - $2,000,000
= $2,002,959.30 - $2,000,000
= $2,959.30
1 

1 - (1.10 )10 
 - $2,000,000
b) NPV = $298,500 x 
.10




= $298,500 x 6.14456711 - $2,000,000
= $1,834,153.28 - $2,000,000
= ($165,846.72)
c) The project should not be adopted.
d)
1 

1 - (1.10 )10 
 - $2,000,000
NPV = $0 = CF x 
.10




NPV = $0 = CF x 6.14456711 - $2,000,000
$2,000,000 = CF x 6.14456711
CF = $325,490.79
10-27 (Comprehensive Problem)
Given
Information:
Yearly net cash
flows:
Initial investment
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Project 1
Project 2
($200,000)
$0
$0
$20,000
$30,000
$40,000
$60,000
$90,000
($200,000)
$90,000
$70,000
$50,000
$30,000
$10,000
$10,000
$10,000
78
Year 8
$100,000
$10,000
Weighted average cost of capital
7.2%
a. NPVs of the
projects:
NPV
Project 1
Project 2
$19,398
$33,705
Project 1
Project 2
8.8%
14.4%
2%
99,769
65,526
4%
65,182
52,380
b. IRRs of the
projects:
IRR
c. NPV Profiles:
Discount rate
NPV Project 1
NPV Project 2
6%
35,340
40,396
8%
9,502
29,435
10%
(12,943)
19,376
12%
(32,504)
10,118
14%
(49,605)
1,573
16%
(64,600)
(6,337)
NPV PROFILES
$120,000
$100,000
$80,000
$60,000
NPV
$40,000
Project 1
$20,000
Project 2
$0
($20,000)
2%
4%
6%
8%
10%
12%
14%
16%
($40,000)
($60,000)
($80,000)
DISCOUNT RATE
Comment:
Both projects have the same NPV at a discount rate of approximately 5.5%. At that discount rate the NPV
of both projects is about $45,000.
d. Project selection at other
WACCs:
Select
i. WACC > 5.4% Project 2
ii. WACC > 8.81% Project 2
iii. WACC >
Neither project
14.39%
Reason
Project 2's NPV is higher
Project 1's NPV is negative
The NPV for both projects is negative
e) Look at the NPV profile. If the discount rate is 5%, this is to the left of the crossover point. Project 1
would have a higher NPV than Project 2. This would create a ranking conflict if the projects were mutually
exclusive. Project 2 has a higher IRR (14.3% for Project 2 versus 8.81 percent for Project 1).
At a discount rate below 5.4%, NPV and IRR give conflicting ranking signals. At a discount rate of
5.4% or more, the ranking of the two projects is the same.
f)
a. Both projects would be accepted at a 7.2% cost of capital.
79
Chapter 11 Solutions
Answers to Review Questions
1.
Why do we focus on cash flows instead of profits when evaluating proposed capital budgeting
projects?
We focus on cash flows instead of profits when evaluating proposed capital budgeting projects
because it is cash flow that changes the value of a firm. You can spend cash but you can not spend
profit.
2.
What is a sunk cost? Is it relevant when evaluating a proposed capital budgeting project? Explain.
A sunk cost is a cash flow that has already occurred, or that will occur, whether a project is accepted
or rejected. It is irrelevant when evaluating a proposed project.
3.
How do we estimate expected incremental cash flows for a proposed capital budgeting project?
We estimate expected incremental cash flows for a proposed project by estimating the changes in
sales and expenses that are incremental to the project, adding back the incremental depreciation
expense since depreciation expense is a non-cash expense.
4.
What role does depreciation play in estimating incremental cash flows?
Depreciation expense is a tax deductible expense and therefore affects cash flow through its effect on
taxes. Depreciation expense that is incremental to a proposed project therefore affects incremental
cash flows.
5.
How and why does working capital affect the incremental cash flow estimation for a proposed large
capital budgeting project? Explain.
Many large projects require additional working capital. This investment in additional working
capital becomes part of the initial investment. This investment is recovered at the end of the
project’s life. There may be some spontaneous increase in current liabilities associated with a
project, but the change in net working capital, if any, is likely to be a positive value requiring an
increase in the initial investment of that amount.
6.
How do opportunity costs affect the capital budgeting decision-making process?
Opportunity costs reflect the foregone benefits of the alternative not chosen when a capital budgeting
project is selected. Any decrease in the cash flows of the firm directly tied to the selection of a new
project could be part of the opportunity cost value and included in our capital budgeting analysis.
80
7.
How are financing costs generally incorporated into the capital budgeting analysis process?
Financing costs are usually captured in the discount or hurdle rate when doing NPV or IRR analysis.
The operating cash flows usually do not include financing costs because this would be double
counting.
Answers to End-of—Chapter Problems
11-1.
Price of Selected Model
Attachments
Paint Name
Garage and Maint. Facility
$6,000
5,000
300
12,000
$23,300
Cash Flow t0 = ($23,300)
11-2. (a) Resale Price: $60,000
Price of Equipment:
Resale Value:
Years Used:
MACRS Classification:
Income Tax:
Accumulated Depreciation:
Book Value:
Taxable Gain (Loss):
Tax (Refund):
Net Cash Flow:
$200,000
$60,000
3
5 years
40%
20% + 32% + 19.2% = 71.2% or,
0.712 X $200,000 = $142,400
$200,000 - $142,400 = $57,600
$60,000 - $57,600 = $2,400
$2,400 X 0.40 = $960
$60,000 - $960 = $59,040
(b) Resale Price: $80,000
Price of Equipment:
Resale Value:
Years Used:
MACRS Classification:
Income Tax:
Accumulated Depreciation:
Book Value:
Taxable Gain (Loss):
Tax (Refund):
Net Cash Flow:
$200,000
$80,000
3
5 years
40%
20% + 32% + 19.2% = 71.2% or,
0.712 X $200,000 = $142,400
$200,000 - $142,400 = $57,600
$80,000 - $57,600 = $22,400
$22,400 X 0.40 = $8,960
$80,000 - $8,960 = $71,040
81
11-3.
a) $10,000 - $3,000 - $2,000 = $5,000
b ) $5,000 X .35 = $1,750
c ) $5,000 - $1,750 = $3,250
d ) $3,250 + $2,000 depr. add back = $5,250
e ) Interest Expense. It is included in the cost of funds when calculating NPV and when setting the
IRR hurdle rate.
11-4.
Mower
Annual Revenues (increase)
Operating Costs (increase)
Depreciation (20%)
EBIT
Taxes (35%)
Depreciation
Net operating CF
$20,000
100,000
30,000
Year 1
$100,000
- 30,000
70,000
- 4,000
66,000
- 23,100
42,900
+ 4,000
$46,900
The net operating incremental cash flow for year 1 is $46,900
11-5.
$2,000 X (1 – 0.35) = $1,300
11-6.
Initial Cost of new Equipment $375,000
End of year:
1
2
3
4
5
6
Earnings Before Depreciation
and Taxes (EBDT) $120,000 $90,000 $70,000 $70,000 $70,000 $70,000
Discount rate
Tax rate
Year
MACRS depreciation
percentages for five-year class
life equipment
13%
40%
1
20.00%
2
3
4
5
32.00% 19.20% 11.50% 11.50%
6
5.80%
Calculations:
Incremental Cash Flows:
Year
1
2
3
4
5
6
EBDT $120,000 $90,000 $70,000 $70,000 $70,000 $70,000
New depreciation expense (75,000) (120,000) (72,000) (43,125) (43,125) (21,750)
82
Change in Operating Income
Income tax on new income
Change in earnings after tax
Add back depreciation
45,000 (30,000) (2,000) 26,875
(18,000)
12,000
800 (10,750)
27,000 (18,000) (1,200) 16,125
75,000 120,000 72,000 43,125
26,875
(10,750)
16,125
43,125
48,250
(19,300)
28,950
21,750
Net incremental
operating cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $50,700
Present value of cash flows
$90,265 $79,881 $49,068 $36,339 $32,159 $24,352
Total present value
of cash flows $312,064
Less initial cost ($375,000)
= NPV ($62,936)
The NPV is negative so the project should be rejected.
11-7.
Rhodes Manufacturing Corporation (with salvage value)
Given:
Initial Cost of new Equipment
End of year:
$375,000
1
2
Earnings Before Depreciation
and Taxes (EBDT)
$120,000
Discount rate
Tax rate
13%
40%
Year
MACRS depreciation
percentages for five-year class
life equipment
Resale value of equipment
1
20.00%
3
4
5
6
$90,000 $70,000 $70,000 $70,000 $70,000
2
32.00%
3
19.20%
4
11.50%
5
11.50%
6
5.80%
$50,000 at the end of the sixth year
Calculations:
Incremental Cash Flows:
Year
1
2
3
4
5
6
EBDT
New depreciation expense
Change in Operating Income
Income tax on new income
Change in earnings after tax
Add back depreciation
$120,000 $90,000 $70,000 $70,000 $70,000 $70,000
(75,000) (120,000) (72,000) (43,125) (43,125) (21,750)
45,000 (30,000) (2,000) 26,875 26,875 48,250
(18,000)
12,000
800 (10,750) (10,750) (19,300)
27,000 (18,000) (1,200) 16,125 16,125 28,950
75,000 120,000 72,000 43,125 43,125 21,750
Net incremental
operating cash flows
$102,000 $102,000 $70,800 $59,250 $59,250 $50,700
Resale value of equipment 50,000
Less income tax on sale (20,000)
Net cash flow from equipment sale 30,000
Total Net cash flows $102,000 $102,000 $70,800 $59,250 $59,250 $80,700
83
Present value of cash flows
$90,265 $79,881 $49,068 $36,339 $32,159 $38,762
Total present value
of cash flows $326,474
Less initial cost ($375,000)
= NPV ($48,526)
The NPV is negative so the project should be rejected.
11-8. a ) $85,000 + $20,000 = $105,000
b)
$125,000 X .10 =
Oper. Exp.
Depr. Exp.
$12,500
-20,000
-10,500
-18,000
7,200
-10,800
10,500
-300
Tax Saving@40%
Add back Depr.
Net Incremental Oper. Cash flow
c)
End of year 5 at the time of the sale
11-9.
GHOST SQUADRON HISTORICAL AIRCRAFT, INC.
ASSUMPTIONS:
MACRS Depreciation
Yr 1
14.3%
Tax rate
Cost of capital
35%
12%
Yr 2
24.5%
Yr 3
17.5%
Yr 4
12.5%
Yr 5
8.9%
Yr 6
8.9%
Yr 7
8.9%
ESTIMATED INCREMENTAL CASH FLOWS:
Initial Investment at t=0:
Crew transport & wreckage collection
Transport to restoration facility
Plane restoration
Total Initial Investment
($100,000)
($35,000)
($600,000)
($735,000)
Year:
1
2
3
4
5
6
7
New Revenues
Additional operating expenses
Depreciation on plane
Change in Operating Income
Tax on new income
Change in Earnings after tax
Add back depreciation
($40,000)
($105,105)
($145,105)
$50,787
($94,318)
$105,105
($40,000)
($180,075)
($220,075)
$77,026
($143,049)
$180,075
$70,000
($40,000)
($128,625)
($98,625)
$34,519
($64,106)
$128,625
$70,000
($40,000)
($91,875)
($61,875)
$21,656
($40,219)
$91,875
$70,000
($40,000)
($65,415)
($35,415)
$12,395
($23,020)
$65,415
$70,000
($40,000)
($65,415)
($35,415)
$12,395
($23,020)
$65,415
$70,000
($40,000)
($65,415)
($35,415)
$12,395
($23,020)
$65,415
Net Incremental Cash Flows
$10,787
$37,026
84
$64,519 $51,656 $42,395
$42,395 $42,395
Yr 8
4.5%
Additional Cash Flows at the end of year 7:
Proceeds from sale of plane $500,000
Book value of plane
$33,075
Taxable gain(loss) $466,925
Tax on gain $163,424
Net cash flow from sale of plane $336,576
(Salvage value less tax on gain)
SUMMARY OF NET CASH FLOWS:
Time:
0
1
($735,000)
$10,787
2
3
4
5
$37,026 $64,519 $51,656
6
$42,395 $42,395 $378,972
Net present Value: ($400,138)
Internal rate of Return:
11-10. a )
-2.7%
NWC = Current Assets - Current Liabilities
= ($8,000 + $10,000 + $12,000) - ($6,000 + $2,500) = $21,500
b)
Outflow
c)
Beginning of year 1
11-11.
Given:
Initial Cost of new Equipment
End of year:
New revenues
Discount rate
Tax rate
Year
MACRS depreciation percentages for
three-year class life equipment
Resale value of equipment
$90,000
1
$50,000
11%
30%
1
33.30%
$10,000
2
$30,000
3
$20,000
4
$20,000
2
3
4
44.50%
14.80%
7.40%
at the end of the fourth year
Calculations:
Incremental Cash Flows:
Year
Revenues
New depreciation expense
Change in Operating Income
Income tax on new income
Change in earnings after tax
Add back depreciation
Net incremental operating cash flows
Total Net cash flows
Present value of cash flows
Total present value of cash flows
85
1
$50,000
(29,970)
20,030
(6,009)
14,021
29,970
2
$30,000
(40,050)
(10,050)
3,015
(7,035)
40,050
7
3
$20,000
(13,320)
6,680
(2,004)
4,676
13,320
4
$20,000
(6,660)
13,340
(4,002)
9,338
6,660
$43,991
$33,015
$17,996
Resale value of equipment
Less income tax on sale
Net cash flow from equipment sale
$43,991
$33,015
$17,996
$39,632
$26,796
$13,159
$94,735
$15,998
10,000
(3,000)
7,000
$22,998
$15,149
Less initial cost
= NPV
($90,000)
$4,735
Comments: Yes, since the project has a positive NPV at the company's cost of capital, Flower
Belle should recommend that it be accepted.
11-12.
MACRS 3 YEARS
PRICE OF NEW EQUIPMENT:
YEARS USED
33.30% 44.50% 14.80% 7.40%
90,000
4
INCOME TAX RATE:
40.00%
COST OF CAPITAL 10.00%
SALVAGE VALUE OF NEW EQPT. 10,000
MACRS CLASSIFICATION:
3 YEARS
DEPRECIATION RATE
ACCUM. DEP. %)
1
2
3
4
33.30% 44.50% 14.80% 7.40%
100%
CASH FLOW FROM SALE OF NEW EQUIPMENT
6,000
CASH FLOW FROM SALE OF OLD EQUIPMENT
SALE PRICE
BOOK VALUE
TAXABLE GAIN (LOSS)
TAX (REFUND)
NET CASH FLOW
INCREMENTAL CASH FLOW
YEAR
1
10,000
20,000
(10,000)
(4,000)
14,000
1
2
3
4
REVENUE STREAM
DEPRECIATION EXPENSE
50,000 30,000 20,000 20,000
29,970 40,050 13,320 6,660
CHANGE IN OPERATING INCOME
TAX ON NEW INCOME
20,030 (10,050) 6,680 13,340
8,012 (4,020) 2,672 5,336
CHANGE IN EARNINGS
ADD BACK DEPRECIATION
12,018 (6,030) 4,008 8,004
29,970 40,050 13,320 6,660
NET INCREMENTAL OP. CASH FLOW 41,988 34,020 17,328 14,664
NET CASH FLOW
NEW EQUIPMENT
OLD EQUIPMENT
0
(90,000)
14,000
1
2
3
4
OPERATING CF
SALVAGE VALUE
41,988 34,020 17,328 14,664
NET CASH FLOW
(76,000) 41,988 34,020 17,328 14,664
DISCOUNT RATE
NPV
10.00%
$17,419.18
86
11-13.
Initial Cost of new equipment
End of year:
New revenues
Discount rate
Tax rate
$90,000
1
$50,000
10%
40%
Year
MACRS depreciation percentages for
three-year classlife equipment
1
33.30%
2
$30,000
2
44.50%
3
4
$20,000 $20,000
3
14.80%
4
7.40%
Book value of old equipment
Resale value of old equipment
Resale value of new equipment
Additional current assets required
Expected increase in current liabilities
Calculations:
Incremental Cash Flows:
Gain(loss) on sale of old equipment
(Tax)refund on transaction
Net cash received for old equipment
Cost of New Equipment
Net Cash Outflow at T-0 for equipment
Additional net working capital required
$20,000
$10,000
$10,000 at the end of the fourth year
$10,000
$5,000
($10,000)
$4,000
$14,000
($90,000)
($76,000)
($5,000)
Total Net Cash Outflow at T-0
($81,000)
Year
Revenues
New depreciation expense
Change in Operating Income
Income tax on new income
Change in earnings after tax
Add back depreciation
1
$50,000
(29,970)
20,030
(8,012)
12,018
29,970
2
$30,000
(40,050)
(10,050)
4,020
(6,030)
40,050
3
4
$20,000 $20,000
(13,320) (6,660)
6,680 13,340
(2,672) (5,336)
4,008
8,004
13,320
6,660
Net incremental operating cash flows
$41,988
$34,020
$17,328 $14,664
Resale value of equipment 10,000
Less income tax on sale (4,000)
Net cash flow from equipment sale
6,000
Recovery of net working capital investment
5,000
11-14. a )
Total Net cash flows
Present value of cash flows
Total present value of cash flows
Less initial cash outflow at T-0
$41,988
$38,171
$96,834
($81,000)
= NPV
$15,834
Book Value = $20,000 - $12,000 = $8,000
b)
Taxable Gain = $18,000 - $8,000 = $10,000
c)
Tax on Gain = $10,000 X 0.3 = $3,000
d)
Cash Flow = $18,000 - $3,000 = $15,000
This is an inflow.
87
$34,020
$28,116
$17,328 $25,664
$13,019 $17,529
e)
Incremental Cash Flow for to = $40,000 - $15,000 = $25,000 outflow
f)
b ) Taxable Income (Loss) = $6,000 - $8,000 = ($2,000)
c ) Tax Credit on Loss = $2,000 X 0.3 = $600
d ) Cash Flow = $6,000 + $600 = $6,600
This is an inflow.
e ) Incremental Cash Flow for to = $40,000 - $6,600 = $33,400 outflow
11-15.
MACRS 3 YEARS 33.30% 44.50% 14.80% 7.40%
PRICE OF NEW EQUIPMENT:
PRICE OF OLD EQUIPMENT:
RESALE VALUE OF OLD EQPT:
YEARS USED
$22,000
0
0
4
INCOME TAX RATE:
40.00%
COST OF CAPITAL 14.00%
SALVAGE VALUE OF NEW EQUIP.
$0
MACRS CLASSIFICATION:
3
YEARS
1
2
3
4
DEPRECIATION RATE 33.30% 44.50% 14.80% 7.40%
ACCUMULATED DEPR.(%)
100%
CASH FLOW FROM CHANGE IN NWC
CHANGE IN CURRENT ASSETS
CHANGES IN CURRENT LIABS.
CHANGE IN NWC
INCREMENTAL CASH FLOW
YEAR
CHANGE IN SALES:
INCREASE IN OPERATING EXPENSES
TOTAL INFLOW
DEPRECIATION EXPENSE
5000
3000
2000
1
2
3
4
20,000 20,000 10,000 10,000
(4,000) (4,000) (2,000) (2,000)
16,000 16,000 8,000 8,000
7,326 9,790 3,256 1,628
CHANGE IN OPERATING INCOME
TAX ON NEW INCOME
8,674
3,470
6,210
2,484
4,744 6,372
1,898 2,549
CHANGE IN EARNINGS
5,204
3,726
2,846 3,823
7,326 9,790
12,530 13,516
3,256 1,628
6,102 5,451
ADD BACK DEPRECIATION
NET INCREMENTAL OP. CASH FLOW
NET CASH FLOW
a.
NEW EQUIPMENT
b.
OPERATING CF
c.
NET CASH FLOW
0
(22,000)
(2,000)
NWC
DISCOUNT RATE
88
2
3
4
12,530 13,516
2,000
6,102 5,451
(24,000) 12,530 13,516
6,102 7,451
14.00%
$5,922.36
27.24%
NPV
IRR
1
Yes, Brenners should add this machine to their factory.
11-16.
Given:
Initial Cost of new Equipment
$150,000
Installation and calibration costs
$7,500
Decrease in operating expenses
$50,000
Discount rate
10%
Tax rate
35%
Year
1
annually
2
3
4
MACRS depreciation
percentages for three-year class
33.30%
44.50%
14.80%
7.40%
life equipment
Calculations:
Incremental Cash Flows at T-0:
Cost of New Equipment
($150,000)
Installation and calibration costs
($7,500)
Total Net Cash Outflow at T-0
($157,500)
Incremental cash flows in years 1 - 5:
Year
1
2
3
4
5
Reduction in operating costs
$50,000
$50,000
$50,000
$50,000
$50,000
New depreciation expense
(52,448)
(70,088)
(23,310)
(11,655)
0
Change in Operating Income
(2,448)
(20,088)
26,690
38,345
50,000
Income tax on new income
857
7,031
(9,342)
(13,421)
(17,500)
Change in earnings after tax
(1,591)
(13,057)
17,349
24,924
32,500
Add back depreciation
52,448
70,088
23,310
11,655
0
$50,857
$57,031
$40,659
$36,579
$32,500
Net incremental
operating cash flows
89
a. NPV of the investment:
Present value of cash flows
$46,233
Total present value of cash flows
$169,077
Less initial cash outflow at T-0
($157,500)
$47,133
$30,547
$24,984
$20,180
a.
NPV =
$11,577
b. Yes, since the NPV of the investment is positive at RHPS's cost of capital, Weiss and Majors
should go forward with the project.
90
11-17.
Chemical Company of Baytown
Given:
Original cost of old equipment
Resale value of old equipment
$40,000 on Dec 31, 2010
$4,000 on Dec 31, 2012
Discount rate
Tax rate
Year
MACRS depreciation
percentages for three-year class
life equipment
6%
40%
1
2
33.30%
44.50%
3
14.80%
4
7.40%
Calculations:
a. Cash flows from sale of old equipment:
Year 2011
Depreciation expense on old equipment
Total accumulated depreciation
Book value of old equipment
Resale value of old equipment
Gain(loss) on sale of old equipment
(Tax)refund on transaction
Net cash received for old equipment
Year 2012
$13,320
$17,800
$31,120
$8,880 on Dec 31, 2012
$4,000 on Dec 31, 2012
($4,880)
$1,952
$5,952
b. New net working capital requirements:
Additional current assets required:
Cash
Receivables
Inventory
Total
Expected increase in current liabilities:
Accounts payable
Accrued expenses
Total
$1,000
$5,000
$10,000
$16,000
$6,000
$3,000
$9,000
Incremental cash flow for net working capital
$7,000
c. Net cash outflow at the end of 2012 if new process line is installed:
Cost of New Equipment
Additional net working capital
Less proceeds from sale of old equipment
Net cash outflow at the end of 2012
$180,000
$7,000
($5,952)
$181,048
d. Incremental cash flows for 2010 - 2013:
End of year:
New revenues
Reduction in operating expenses
New depreciation expense
Change in Operating Income
Income tax on new income
Change in earnings after tax
Add back depreciation
2010
$60,000
6,000
(59,940)
6,060
(2,424)
3,636
59,940
91
2011
$60,000
6,000
(80,100)
(14,100)
5,640
(8,460)
80,100
2012
$60,000
6,000
(26,640)
39,360
(15,744)
23,616
26,640
2013
$60,000
6,000
(13,320)
52,680
(21,072)
31,608
13,320
Net incremental operating cash flows
$63,576
$71,640
$50,256 $44,928
e. NPV and IRR of the investment:
(Given) Resale value of new equipment
$20,000 at the end of the fourth year
Resale value of equipment 20,000
Less income tax on sale (8,000)
Net cash flow from equipment sale 12,000
Recovery of net working capital investment
Total Net cash flows
7,000
$63,576
$71,640
1
2
Present value of cash flows
$59,977
$63,759
$42,196 $50,637
Total present value
of cash flows
Less initial cash outflow at T-0
$216,570
($181,048)
= NPV
$35,522
Year
Net Cash Flow
0
($181,048)
1
$63,576
2
3
4
$71,640 $50,256 $63,928
IRR
14.4%
Year
$50,256 $63,928
3
4
Summary of all cash flows:
f. NPV Profile
Year
0
1
2
3
4
Net Cash Flow ($181,048) $63,576 $71,640 $50,256 $63,928
Assumed cost of capital
NPV of cash flows
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
$68,352 $62,338 $56,556 $50,994 $45,641 $40,487 $35,522 $30,736 $26,122 $21,672 $17,377
NPV Profile, Chemical Company of Baytown Project
$80,000
$70,000
$68,352
$62,338
$56,556
$50,994
$45,641
$40,487
$35,522
$30,736
$26,122
$21,672
$17,377
NPV
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
0%
1%
2%
3%
4%
5%
6%
Cost of Capital
92
7%
8%
9%
10%
11-18.
PROBLEM 11-18
Real Options Decision Tree NPV Analysis
J & T's Double Diamond Brewhouse
Time
t0
Time
1
25%
($300,000)
50%
25%
$200,000
$100,000
Time
2
100%
Time
3
$100,000
Time
4
Time
5
|-------- Part b. --------|
Joint
Path
Probability
NPV
|- Part c.
-|
JP x NPV
50%
$400,000
$400,000
$400,000
12.5%
$666,954
$83,369
30%
$200,000
$200,000
$200,000
7.5%
$309,669
$23,225
20%
$90,000
$90,000
$90,000
5.0%
$113,163
$5,658
100%
$100,000
100%
$100,000
$100,000
$100,000
50.0%
$43,308
$21,654
0%
($40,000)
100%
($40,000)
($40,000)
($40,000)
0.0%
($437,323)
$0
100%
$0
100%
$0
$0
$0
25.0%
($335,088)
($83,772)
Total NPV
of the
Deal:
$50,135
($40,000)
Cost of Capital:
14%
The Time 2 cash flow for the smash hit scenario
is $200,000 from operations minus $100,000
for the expansion.
93
Chapter 12 Solutions
Answers to Review Questions
1.
Describe the general pattern of cash flows from a bond with a positive coupon rate.
Cash flows from a bond with a positive coupon rate consist of periodic interest payments and the face
value payment at maturity. Coupon interest payments occur at regular intervals throughout the life of
the bond. The face value payment occurs on the maturity date.
2.
How does the market determine the fair value of a bond?
The fair value of a bond is the present value of the bond's coupon interest payments plus the present
value of the face value payment at maturity, discounted at the market’s required rate of return for the
bond in question. Equation 9-1 in the text is use to solve for the fair (present) value of a bond.
3.
What is the relationship between a bond's market price and its promised yield to maturity? Explain.
A bond's market price depends on its yield to maturity (YTM). When a bond has a YTM greater than
its coupon rate, it sells at a discount from its face value. When the YTM is equal to the coupon rate,
the market price equals the face value. When the YTM is less than the coupon rate, the bond sells at
a premium over face value.
4.
All other things held constant, how would the market price of a bond be affected if coupon interest
payments were made semiannually instead of annually?
Most bonds issued in the United States pay interest semiannually (twice per year). With semiannual
interest payments, we must adjust the bond valuation model (Equation 9-1 in the text) by multiplying
n, the number of years to maturity, by two, and dividing k, the annual interest rate, by two.
5.
What is the usual pattern of cash flows for a share of preferred stock? How does the market
determine the value of a share of preferred stock, given these promised cash flows?
Preferred stock has no maturity date, so it has no maturity value. Its future cash payments are
dividend payments that are paid to preferred stockholders at regular time intervals for as long as they
(or their heirs) own the stock. Cash payments from preferred stock dividends are scheduled to
continue forever. To value preferred stock, we adapt the discounted cash flow model to reflect that
preferred stock dividends are a perpetuity. See Equation 9-4 in the text.
6.
Name two patterns of cash flows for a share of common stock. How does the market determine the
value of the most common cash flow pattern for common stock?
94
Cash flows for a share of common stock consist of dividend payments and the price received for the
eventual sale of the share. Common stock valuation is complicated by the fact that common stock
dividends are difficult to predict compared to the interest and principal payments on a bond, or
dividends on preferred stock. Indeed, corporations may pay common stock dividends irregularly, or
not pay dividends at all.
As with bonds and preferred stock, the market values common stock by estimating the present value
of the expected future cash flows from the common stock. See Equation 9-6 in the text.
7.
Define the P/E valuation method. Under what circumstances should a stock be valued using this
method?
The P/E ratio indicates how much investors are willing to pay for each dollar of a stock's earnings. A
high P/E ratio indicates that investors believe the stock's earnings will increase, or that the risk of the
stock is low, or both.
Financial analysts often use a P/E model to estimate common stock value for businesses that are not
public. First, analysts compare the P/E ratios of similar companies within an industry to determine
an appropriate P/E ratio for companies in that industry. Second, analysts calculate an appropriate
stock price for firms in the industry by multiplying each firm's earnings per share (EPS) by the
industry average P/E ratio. See Equation 9-9 in the text.
8.
Compare and contrast the book value and liquidation value per share for common stock. Is one
method more reliable? Explain.
The Book Value of a firm's common stock is found by subtracting the value of the firm's liabilities,
and preferred stock, if any, as recorded on the balance sheet, from the value of its assets. The result
is the book value or net worth of the company's common stock. To find the book value per share of
common stock, divide the company's book value by the number of outstanding common stock shares.
See Equation 9-10 in the text.
The liquidation value and book value valuation methods are similar, except that the liquidation
method uses the market values of the assets and liabilities, not book values. The market values of the
assets are the amounts the assets would earn on the open market if they were sold (or liquidated).
The market values of the liabilities are the amounts of money it would take to pay off the liabilities.
Since it is based on market values, the liquidation value method is more reliable than the book value
method. However, liquidation value is a worst-case valuation assessment. A company's common
stock should be worth at least the amount generated per share at liquidation.
95
9. Answer the following questions about the discounted free cash flow model illustrated in Figure 12-4:
a. What are “free cash flows?”
Free cash flows represent the total cash flows from business operations that are available to be
distributed to the suppliers of a firm’s capital each year either in the form of interest to the debt
holders, or dividends to the stockholders.
b. Explain the terminal value calculation at the end of the forecast period. Why is it necessary?
The firm whose business operation is being valued is not expected to suddenly cease operating at the
end of the discrete forecasting period, but to continue operating indefinitely into the future as a going
concern. The terminal value calculation estimates the values of the cash flows that occur in the year
following the discrete forecasting period and beyond.
c. Explain the term “present value of the firm’s operations” (also known as Enterprise Value). What
does this number represent?
The present value of the company’s free cash flows represents the market value of the firm’s core
income producing operations. In the world of finance and investing this is sometimes called the
firm’s Enterprise Value. It is not the total market value of the entire company, however, or the total
market value of the company’s assets, because the current, or non-operating assets of the company
have not yet been accounted for.
d. Explain the adjustments necessary to translate enterprise value to the total present value of common
equity.
To obtain the value of the company’s common stock, add the value of the firm’s current assets to the
enterprise value (this produces the value of the firm’s total assets). Next, subtract the values of
current liabilities, long-term debt, and preferred stock. The result is the present value of common
equity.
10. Explain the difference between the discounted free cash flow model as it is applied to the valuation of
common equity and as it is applied to the valuation of complete businesses.
The Free Cash Flow Model values the complete business as a part of the procedure to value common
equity. The value of a complete business is the sum of the values of the operating, or incomeproducing assets, plus the value of the non-operating, or current assets. All that is necessary to use
the Free Cash Flow Model to value a complete business, then, is to add the value of the company’s
operations to the value of the company’s current assets.
11. Why is the replacement value of assets method not generally used to value complete businesses?
The replacement value of assets method is not often applied to complete business valuations because
it is frequently very difficult to locate similar assets for sale on the open market, and because some
of a business’s assets are difficult to define and quantify.
96
Answers to End-of-Chapter Problems
12-1.
a)
b)
c)
$1,000 X .06 = $60
$60 X [(1-1/1.0810)/.08] + $1,000 X [1/1.0810] = $865.80
Yes.
12-2.
a)
b)
c)
$1,000 X .12 = $120
$120 X [(1-1/1.0815)/.08] + $1,000 X [1/1.0815] = $1,342.38
$60 X [(1-1/1.0430)/.04] + $1,000 X [1/1.0430] = $1,345.84
12-3.
3 X $2,000 = $6,000
12-4.
Semi-annual interest payment = .10 X $1,000 X 6/12 = $50
Price = $50 X [(1-1/1.0410)/.04] + $1,000 X [1/1.0410] = $1,081.11
12-5.
Since $1,100 > $1,000, YTM < Coupon Rate; YTM < 9%
$90 X [1-1/ (1 + k)10/k] + $1,000 X (1/1 + k10) = $1,100
k = 7.54%
12-6.
a)
b)
c)
12-7.
Since $872 < $1,000, k > 7%
$70 X [(1-1/(1+k)10/k] + $1,000 X [1/(1+k)10] = $872
If k=8%, VB = $932.90
If k=9%, VB = $871.65. So, k ≈ 9%.
12-8.
$10/0.12 = $83.33 per share
12-9.
kP = $1.75 /$ 20 = 0.0875 or 8.75%
Since, $1,125 > $1,000, YTM < Coupon Rate ∴ YTM < 12%
$120 X [(1-1/1.1010)/.10] + $1,000 X [1/1.1010] = $1,122.89; YTM ≈ 10%
YTM = 12%; YTM = Coupon Rate if Market Price = Par
12-10. a )
b)
VP = $8/0.13 = $61.54 per share
kP = $8/$50 = 16 %
12-11. a )
b)
$4/(.16-.01) = $26.67
$4/$26.67 = 15%
97
12-12. $2/$15 + .04 = 17.33%
12-13. a )
b)
P0 = $8/(.14 - .03) = $72.72
ks = $8/$65 + .03 = 15.31%
12-14. $90 X [1-1/ (1.12)5/0.12] + $1,000 X (1/1.125) = $891.86
12-15. $35 X [1-1/ (1.055)20/0.055] + $1,000 X (1/1.05520) = $761
12-16. $80/ (1 + 0.23)1 = $65.04
$150/ (1 + 0.23)2 = $99.15
$1,500/ (1 + 0.23)3 = $806.08
$65.04 + $99.15 + $806.08 = $970.27
12-17. $3.00/0.12 = $25.00
12-18. $2.20/(0.18 - 0.09) = $2.20/0.09 = $24.44
12-19. D6 = $1.22 (1+ 0.10) = $1.342
$1.342/ (0.12 – 0.10) = $67.10 = P5
$0.70 / (1+0.12)1 + $0.83 / (1+0.12)2 + $0.96 / (1+0.12)3 + $1.09 / (1+0.12)4 + $1.22 /
(1+0.12)5 + $67.10 / (1+.12)5
0.625 + 0.66167 + 0.6833 + 0.6927 + 0.6923 + $38.0743
=$41.43
12-20. D1 = 3.82(1 + 0.07) = 4.09
k = 4.09/82 + 0.07
k = .1199 = 11.99%
12-21. $85 X [1-1/ (1 + k)10/k] + $1,000 X (1/1 + k10) = $1,250
k = 5.23%
12-22. $2,100,000 / (0.18 – 0.09) = $23,333,333.33
12-23. Find the present values of cash flows for each year. Add them together to get the present value of the
firm.
Year 1 = $1,231,920,000 X [1/ (1 + 0.12)1] = $1,099,928,571
Year 2 = $1,453,665,600 X [1/ (1 + 0.12)2] = $1,158,853,316
98
Year 3 = $1,686,252,096 X [1/ (1 + 0.12)3] = $1,200,240,935
Year 4 = $1,922,327,389 X [1/ (1 + 0.12)4] = $1,221,673,808
Year 5 = $2,153,006,676 X [1/ (1 + 0.12)5] = $1,221,673,809
Year 6 CF = Year 5 CF X (1 + .10) = $2,153,006,676 X 1.10 = 2,368,307,344
Year 6 - ∞ = (((2,368,307,344 / (0.12 - 0.10)) X (1/1.12)5 ) = $67,192,060,000
Enterprise value of the firm today = $1,099,928,571 + $1,158,853,316 + $1,200,240,935 +
$1,221,673,808 + $1,221,673,809 + $67,192,060,000 = $73,094,430,440
12-24. a )
b)
$675,000 - $120,000 = $555,000
$555,000/100,000 = $5.55 per share
12-25. a )
b)
c)
d)
e)
Net Worth = $38,400 - ($13,400 + $6,000) = $19,000 (in '000 dollars)
Book Value = $19,000,000/500,000 = $38 per share
EPS = $5,610,000/500,000 = $11.22
Stock Price = EPS X P/E ratio = $11.22 X 6 = $67.32
Since $67.32 (the stock price) > $38.00 (the book value), the firm seems to have goingconcern value.
($50,000,000 - $20,000,000)/500,000 = $60 per share.
f)
12-26. a)
Corporate Bond
Let YTM = k
$130 X [(1-1/(1+k)16)/k] + $1,000 X [1/(1+k)16] = 1,147.58
Solving, kd = 11%
b)
Preferred Stock
k = $14/$140
kp = 10%
c)
Common Stock
Let ks be the required rate of return for a similar common stock
ks = D1/Po + g = $39/$300 + .03 = .16 = 16%
Remember that these are three different companies. The cost of preferred stock for Supernova could be
lower than the cost of debt for Star, as suggested by the above numbers. Lucky should choose the alternative
that, in his opinion, gives the best return/risk tradeoff. There is no clear answer here as to which investment
is the best.
99
12-27.
The Nonconstant, or Supernormal Dividend Growth Model
Flash in the Pan Corporation
Given:
Year
1
Dividend growth rates
Dividend expected in 1 year
Assumed required rate of return
Year
2
20%
Year
3
30%
Year
4
20%
Year Year
5
6 and on
10% 5%
$3.00
15%
Calculations:
a. Present value of Dividends during the supernormal growth period:
Expected future dividends during
the supernormal growth period
$3.00
$3.60
$4.68
$5.62
$6.18
Present values of dividends during
the supernormal growth period
$2.61
$2.72
$3.08
$3.21
$3.07
Total
$14.69
b. Present value of dividends during the normal growth period (year 6 and on)
Terminal value at end of year 5
per Equation 12-7
Present value of terminal value
c. Total present value per share
of Flash in the Pan Corp. stock
$64.86
$32.25
$46.94
100
12-28. The Discounted Free Cash Flow Model for Total Common Equity
Hardi-Pets Corporation
Forecasting Variables:
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
10% 15% 20% 25% 30% 25% 20% 15% 10%
5%
50% 50% 50% 50% 50% 50% 50% 50% 50% 50%
20% 20% 20% 20% 20% 20% 20% 20% 20% 20%
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
10% 10% 10% 10% -10% -10% -10% -10% -10% -10%
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
Revenue growth factor
Expected gross profit margin
S, G, & A expense % of revenue
Depr. & Amort. % of revenue
Capital expenditure growth factor
Net working capital to sales ratio
Income tax rate
Assumed long-term sustainable growth rate
Discount rate
40%
5% per year after 2022
20%
FORECAST:
Total revenue
Actual
2012
Years Ending December 31
|--------------------------------------------------------- Forecast ----------------------------------------------------------------------------------|
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
$1,000,000
$1,100,000 $1,265,000 $1,518,000 $1,897,500 $2,466,750 $3,083,438 $3,700,125 $4,255,144 $4,680,658 $4,914,691
Cost of Goods Sold
Gross profit
500,000
500,000
550,000
550,000
632,500
632,500
759,000
759,000
948,750
948,750
1,233,375
1,233,375
1,541,719
1,541,719
1,850,063
1,850,062
2,127,572
2,127,572
2,340,329
2,340,329
2,457,346
2,457,345
Selling, general and administrative expenses
Earnings before interest, taxes, depr. & amort.
(EBITDA)
200,000
300,000
220,000
330,000
253,000
379,500
303,600
455,400
379,500
569,250
493,350
740,025
616,688
925,031
740,025
1,110,037
851,029
1,276,543
936,132
1,404,197
982,938
1,474,407
Depreciation and amortization
Earnings before Interest and taxes (EBIT)
100,000
200,000
110,000
220,000
126,500
253,000
151,800
303,600
189,750
379,500
246,675
493,350
308,344
616,687
370,013
740,024
425,514
851,029
468,066
936,131
491,469
982,938
Federal and State Income Taxes
Net Operating Profit After-Tax (NOPAT)
80,000
120,000
88,000
132,000
101,200
151,800
121,440
182,160
151,800
227,700
197,340
296,010
246,675
370,012
296,010
444,014
340,412
510,617
374,452
561,679
393,175
589,763
Add back depreciation and amortization
Subtract Capital Expenditures
Subtract New Net Working Capital
Free Cash Flow
100,000
(15,000)
110,000
(16,500)
(10,000)
$215,500
126,500
(18,150)
(16,500)
$243,650
151,800
(19,965)
(25,300)
$288,695
189,750
(21,962)
(37,950)
$357,538
246,675
(19,766)
(56,925)
$465,994
308,344
(17,789)
(61,669)
$598,898
370,013
(16,010)
(61,669)
$736,348
425,514
(14,409)
(55,502)
$866,220
$205,000
468,066
491,469
(12,968)
(11,671)
(42,551)
(23,403)
$974,226 $1,046,158
Terminal value, 2022
Present Value of Free Cash Flows @ 20%
$7,323,106
179,583
169,201
101
167,069
172,424
187,273
200,570
205,501
201,455
188,812
1,351,683
Total Present Value of Company Operations
Plus Current Assets
Less Current Liabilities
Less Long-Term Debt
Less Preferred Stock
$3,023,571
100,000
(80,000)
(500,000)
0
Net Market Value of Common Equity
$2,543,571
from Hardi-Pets December 31, 2012 Balance Sheet
from Hardi-Pets December 31, 2012 Balance Sheet
from Hardi-Pets December 31, 2012 Balance Sheet
from Hardi-Pets December 31, 2012 Balance Sheet
12-29. The Discounted Free Cash Flow Model for a Complete Business
Great Expectations Company
Forecasting Variables:
2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Revenue growth factor
Expected gross profit margin
S, G, & A expense % of revenue
Depr. & Amort. % of revenue
Capital expenditure growth factor
Net working capital to sales ratio
Income tax rate
Assumed long-term sustainable growth rate
Discount rate
20%
50%
50%
10%
40%
19%
30%
51%
40%
10%
35%
18%
40%
52%
30%
10%
30%
17%
50%
53%
29%
10%
25%
16%
60%
54%
28%
10%
20%
15%
50%
55%
27%
10%
-10%
14%
40%
56%
26%
10%
-15%
13%
30%
57%
25%
10%
-20%
12%
20%
58%
24%
10%
-25%
11%
10%
59%
23%
10%
-30%
10%
40%
5% per year after 2022
20%
FORECAST:
Actual
Years Ending December 31
|---------------------------------------------------------------------- Forecast -----------------------------------------------------------------------------|
2012
2013
2014
2015
$2,000,000
$2,400,000
$3,120,000
$4,368,000
Cost of Goods Sold
Gross profit
1,200,000
800,000
1,200,000
1,200,000
1,528,800
1,591,200
2,096,640
2,271,360
3,079,440
3,472,560
4,822,272
5,660,928
7,076,160
9,686,477 12,306,228 14,424,045 15,488,676
8,648,640 12,328,243 16,312,908 19,918,918 22,288,584
Selling, general and administrative expenses
Earnings before interest, taxes, depr. & amort.
(EBITDA)
1,200,000
(400,000)
1,200,000
0
1,248,000
343,200
1,310,400
960,960
1,900,080
1,572,480
2,935,296
2,725,632
4,245,696
4,402,944
5,723,827
6,604,416
7,154,784
8,242,311
8,688,770
9,158,124 11,676,607 13,599,814
Depreciation and amortization
Earnings before Interest and taxes (EBIT)
Available tax-loss carryforwards
Net taxable earnings
200,000
(600,000)
0
0
240,000
(240,000)
(600,000)
0
312,000
31,200
(840,000)
0
436,800
524,160
(808,800)
0
655,200
917,280
(284,640)
632,640
1,048,320
1,677,312
0
1,677,312
1,572,480
2,830,464
0
2,830,464
2,201,472
4,402,944
0
4,402,944
2,861,914
6,296,210
0
6,296,210
3,434,296
8,242,311
0
8,242,311
3,777,726
9,822,088
0
9,822,088
Federal and State Income Taxes
Net Operating Profit After-Tax (NOPAT)
0
(600,000)
0
(240,000)
0
31,200
0
524,160
253,056
664,224
670,925
1,006,387
1,132,186
1,698,278
1,761,178
2,641,766
2,518,484
3,777,726
3,296,924
4,945,387
3,928,835
5,893,253
Total revenue
102
2016
2017
2018
2019
2020
2021
2022
$6,552,000 $10,483,200 $15,724,800 $22,014,720 $28,619,136 $34,342,963 $37,777,260
Add back depreciation and amortization
Subtract Capital Expenditures
Subtract New Net Working Capital
Free Cash Flow
200,000
(1,000,000)
240,000
312,000
436,800
655,200
1,048,320
1,572,480
2,201,472
2,861,914
3,434,296
3,777,726
(1,400,000) (1,890,000) (2,457,000) (3,071,250) (3,685,500) (3,316,950) (2,819,408) (2,255,526) (1,691,645) (1,184,151)
76,000
129,600
212,160
349,440
589,680
733,824
817,690
792,530
629,621
343,430
($1,400,000) ($1,324,000) ($1,417,200) ($1,283,880) ($1,402,386) ($1,041,113)
$687,632 $2,841,521 $5,176,644 $7,317,659 $8,830,257
Terminal value, 2022
$61,811,799
Present Value of Free Cash Flows @ 20%
(1,103,333)
(984,167)
(742,986)
(676,305)
(418,400)
Total Present Value of Company Operations
$11,129,331
Plus Current Assets
500,000 from Great Expectations' December 31, 2009 Balance Sheet
Total Market Value of Great Expectations' Assets
$11,629,331
103
230,287
793,016
1,203,922
1,418,211 11,409,086
Chapter 13 Solutions
Answers to Review Questions
1.
What is the operating leverage effect and what causes it? What are the potential benefits and
negative consequences of high operating leverage?
The operating leverage effect is the phenomenon whereby a small change in sales triggers a relatively
large change in operating income. It is caused by the presence of fixed operating costs. The
potential benefits are that if sales are rising operating income will rise more quickly. The negative
consequences are that falling sales will cause operating income to fall more quickly, including
negative values.
2.
Does high operating leverage always mean high business risk? Explain.
High operating leverage does not always mean high business risk. If the companies sales are quite
stable then the variation in operating income would be small even if the degree of operating leverage
were large.
3.
What is the financial leverage effect and what causes it? What are the potential benefits and negative
consequences of high financial leverage?
Financial leverage is the additional volatility of net income caused by the presence of fixed-cost
funds. The potential benefits are that if operating income is rising net income will rise more quickly.
The negative side is that if operating income is falling net income will fall more quickly, including
possibly negative values.
4.
Give two examples of types of companies likely to have high operating leverage. Find examples
other than those cited in the chapter.
Long distance telephone companies and electricity generating companies are likely to have operating
leverage. These two types of companies have very high fixed costs, because they are capital
intensive, and have relatively low variable costs.
5.
Give two examples of types of companies that would be best able to handle high debt levels.
Companies that handle local telephone service and those that handle natural gas delivery to
consumers would be expected to comfortably be able to handle high debt levels. This is because the
sales of these two types of companies tend not to react very much to the business cycle. Their sales
tend to grow with the population. They are often regulated and protected from competition, although
this is not so much true as it was a few years ago.
104
6.
What is an LBO? What are the risks for the equity investors and what are the potential rewards?
A leveraged buyout is a purchase of a publicly owned corporation by a small group of investors using
a large amount of borrowed money. The risks for the equity investors are those that exist whenever a
high degree of financial leverage exists. So too are the rewards, where small returns become large
returns because of leverage.
7.
If an optimal capital structure exists, what are the reasons why too little debt is as undesirable as is
too much debt?
Too little debt may be as undesirable as too much debt because if a firm has a very conservative
capital structure it may be losing the opportunity to reap the positive benefits of financial leverage.
A company with a bright future is probably not maximizing shareholder wealth if it has a very small
amount of debt in its capital structure. A more aggressive capital structure may create more value for
the owners.
Answers to End-of-Chapter Problems
13-1.
a) Breakeven sales per month = $2,300/($50 – 5.75) = 51.98 units
b) New Breakeven sales per month = $2,300 x .7 / ($45 – 5.75) = 41.02 units
13-2.
a) 30 x $125 + 30 x $90 + 30 x 55 = $8,100
b) $10,000 + 90 x $15 = $11,350
c) 10 x $125 + 15 x $90 + 35 x $55 = $4,525
d) $10,000 + 60 x $15 = $10,900
13-3.
DOL = (17,900,000 – 9,220,000) / 9,220,000 ÷ (25,000,000 – 15,000,000) / 15,000,000 = 1.41
or DOL = (15,000,000 – 1,980,000) / (15,000,000 – 1,980,000 – 3,800,000) = 1.41
13-4.
DOL = (11,333,000 – 5,257,000) / 5,257,000 ÷ (17,900,000 – 9,220,000) / 9,220,000 = 1.23
or DOL = 9,220,000 / (9,220,000 – 1,710,000) = 1.23
13-5.
a)
Contribution Margin = $28 - $16 = $12
b)
Unit Sales b.e. = $20,000/($28 - $16) = 1,666.67 units; 1,667 units rounded up
DOLLARS b.e = $28 x 1,667 units = $46,676
c)
(i) Operating profit (loss) = 1,500 units X $12/unit - $20,000 = ($2,000)
(ii) Operating profit (loss) = 3,000 units X $12/unit - $20,000 = $16,000
105
d)
$180,000
$160,000
$140,000
$120,000
$100,000
$80,000
$60,000
$40,000
$20,000
FIXED COST
13-6. a)
VAR. COST
TOT. COST
6,
00
0
50
0
5,
5,
00
0
50
0
4,
00
0
4,
50
0
3,
00
0
3,
50
0
2,
00
0
2,
50
0
1,
00
0
0
50
1,
0
$0
REVENUE
Contribution Margin = $28 - $20 = $8
b)
Unit Sales b.e. = $10,000/($28 - $20) = 1,250 units
DOLLARS b.e = $28 x 1,250 units = $35,000
c)
(i) Operating profit (loss) = 1,500 units X $8/unit - $10,000 = $2,000
(ii) Operating profit (loss) = 3,000 units X $8/unit - 10,000 = $14,000
d)
$180,000
$160,000
$140,000
$120,000
$100,000
$80,000
$60,000
$40,000
$20,000
$0
0
500
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000
FIXED COST
VAR. COST
106
TOT. COST
REVENUE
e)
Howard Beal Co., having higher fixed costs, and a lower variable cost per unit, has a higher profit
potential once they break-even. However, they have a greater loss potential, and need to achieve a higher
sales level to break even, because of the high fixed costs.
13-7.
YEAR
2012
2013
SALES IN UNITS
3000
3300
SALES IN DOLLARS
$84,000
$92,400
VAR.COST, $16/unit
$48,000
$52,800
FIXED COST
$20,000
$20,000
OP. INCOME (EBIT)
$16,000
$19,600
$2,000
$2,000
$14,000
$17,600
INTEREST EXP.
EBT
TAX @30%
$4,200
$5,280
NET INCOME
$9,800
$12,320
%CHANGE IN SALES
10.00%
%CHANGE IN EBIT
22.50%
%CHANGE IN NI
25.71%
a)
Percentage change in operating income = ($19,600 - $16,000)/$16,000 = 22.5%
Percentage change in sales = ($92,400 - $84,000)/$84,000 = 10%
b)
Due to presence of fixed costs a given percentage change in sales gives a higher percentage change in
operating income (EBIT) (10% and 22.5% respectively). This is the operating leverage effect.
c)
(i)
DOL = %∆ EBIT/%∆ SALES = [($19,600 - $16,000)/$16,000]/[($92,400 $84,000)/$84,000] = 22.5%/10% = 2.25
(ii)
DOL = (SALES-VC)/(SALES-VC-FC) = ($84,000 - $48,000)/($84,000 - $48,000$20,000) = $36,000/$16,000 = 2.25
d)
(i) shows the effect of operating leverage -- EBIT varies at a larger percentage than sales.
(ii) pinpoints the source of operating leverage -- fixed operating costs.
13-8.
a)
Percentage change in NI = ($12,320 - $9,800)/$9,800= 25.71%
Percentage change in operating income = ($19,600 - $16,000)/$16,000 = 22.5%
b)
Due to presence of fixed interest expense a given percentage change in EBIT gives a higher
percentage change in net income (22.5% and 25.71% respectively). This is the financial leverage
effect.
c)
(i)
DFL = %∆ NI/%∆ EBIT = [($12,300 - $9,800)/$9,800]/[($19,600 - $16,000)/$16,000] =
25.71%/22.5% = 1.14
(ii)
DFL = EBIT/(EBIT - I) = $16,000/($16,000 - $2,000) = 1.14
d)
(i) shows the effect of financial leverage -- NI varies by a larger percentage than operating income
(EBIT).
107
(ii) pinpoints the source of financial leverage -- fixed interest expense.
13-9.
a)
$9,000/($15 - $1.50) = 666.67 sq. yards
b)
Break-even point in sales units
c)
666.67 X $15 = $10,000
d)
$9,000/($18 - $1.50) = 545.5 sq. yards, break-even units
545.5 X $18 = $9,819, break-even dollar sales
e)
SALES IN UNITS
14,000 sq.yards
SALES IN DOLLARS, units x $18 each
$252,000
VAR.COST, units x $1.50 each
$21,000
FIXED COST
$9,000
OP. INCOME (EBIT)
$222,000
INTEREST EXP.
$3,000
EBT
$219,000
TAX @40%
$87,600
NET INCOME
$131,400
13-10. a ) Contribution Margin = $800 - $250 = $550 per unit
Sale of 600 suits: Op. Income = 600 X $550 - $200,000 = $130,000
Sale of 3,000 suits: Op. Income = 3,000 X $550 - $200,000 = $1,450,000
b ) Sale of 600 suits: DOL
Sale of 3,000 suits: DOL
= [600 X ($800 - $250)]/[600 X ($800 - $250) - $200,000] = 2.5
= [3,000 X ($800 - $250)]/[3,000 X ($800 - $250) - 200,000] = 1.1
c)
Unit Sales b.e. = $200,000/$550 = 363.64 units; rounded up to 364
DOLLARS b.e = 364 suits X $800 price per suit = $291,200
d)
Unit Sales b.e. = $200,000/($800 - $350) = 444.44 units; rounded up to 445
DOLLARS b.e = 445 suits X $800 price per suit = $356,000
e)
Let P be the selling price per unit.
3,000 units X (P - $350) - $200,000 fixed costs = $1,450,000 op. income
P - $350 = ($1,450,000 + $200,000)/$3,000 = $550
P = $550 + $350 = $900
Tom should increase price per unit by $100 ($900 - $800)
13-11.
COMPANY A
COMPANY B
COMPANY C
12,000
12,000
12,000
$120,000
$120,000
$120,000
$60,000
$48,000
$12,000
$0
$10,000
$40,000
$60,000
$62,000
$68,000
SALES IN UNITS
SALES IN DOLLARS, units x $10 each
VARIABLE COST, $5, $4, and $1 per unit
respectively
FIXED COST
OPERATING INCOME (EBIT)
108
b)
C, B, A.
13-12. a )
Year 1: $30 X 50,000 = $1,500,000
Year 1: $30 X 60,000 = $1,800,000
b)
($1,800 - $1,500)/$1,500 = 0.2 or 20%
METHOD 1
c)
YEAR 1
UNITS
SALES, units x $29 each
METHOD 2
YEAR 2
YEAR 1
YEAR 2
50,000
60,000
50,000
60,000
1,500,000
1,800,000
1,500,000
1,800,000
FC
700,000
700,000
100,000
100,000
VC, units x $6 each for
Method 1 and x $16.50
each for Method 2
300,000
360,000
825,000
990,000
$500,000
$740,000
$575,000
$710,000
EBIT
d)
METHOD 1: %∆ EBIT = ($740,000 - $500,000)/$500,000 = 0.48 OR 48%
METHOD 2: %∆ EBIT = ($710,000 - $575,000)/$575,000 = 0.235 OR 23.5%
e)
METHOD 1: DOL = 0.48/0.20 = 2.4
METHOD 2: DOL = 0.235/0.20 = 1.175
f)
METHOD 1: DOL = ($1,500,000 - $300,000)/($1,500,000 - $300,000 - $700,000) = 2.4
METHOD 2: DOL = ($1,500,000 - $825,000)/($1,500,000 - $825,000 - $100,000) = 1.175
g)
METHOD 1
h)
The high fixed operating costs
METHOD 1
i)
YEAR 1
UNITS
SALES, units x $30 each
METHOD 2
YEAR 2
YEAR 1
YEAR 2
50,000
53,000
50,000
53,000
1,500,000
1,590,000
1,500,000
1,590,000
FC
700,000
700,000
100,000
100,000
VC, units x $6 each for
Method 1 and x $16.50
each for Method 2
300,000
318,000
825,000
874,500
$500,000
$572,000
$575,000
$615,500
EBIT
%∆ SALES = ($53,000 - $50,000)/$50,000 = .06 or 6%
METHOD 1: %∆ EBIT = ($572,000 - $500,000)/$500,000 = 0.144 or 14.4%
METHOD 2: %∆ EBIT = ($615,500 - $575,000)/$575,000 = 0.0704 or 7.04%
METHOD 1: DOL = 0.144/0.06 = 2.4
METHOD 2: DOL = 0.0704/0.06 = 1.17
109
13-13. a )
b)
C, B, A.
COMPANY A:DFL = $100,000/($100,000 - $0) = 1.0
COMPANY B: DFL = $100,000/($100,000 - $2,000) = 1.02
COMPANY C: DFL = $100,000/($100,000 - $40,000) = 1.67
Answer to part a) was correct.
c)
CAPITAL STRUCTURE
COMPANY A
COMPANY B
COMPANY C
ALL EQUITY
90% EQUITY
10% EQUITY
$100,000
$100,000
$100,000
EBIT
INTEREST EXP.
$0
$2,000
$40,000
$100,000
$98,000
$60,000
TAXES @40%
$40,000
$39,200
$24,000
NET INCOME
$60,000
$58,800
$36,000
MICHAEL DORSEY
DOROTHY MICHAELS
EBT
13-14.
a.
EBIT
INTEREST EXPENSE
EBT
TAXES @40%
NET INCOME
YEAR 1 YEAR 2
YEAR 1
$50,000
$9,100
$40,900
$16,360
$24,540
$50,000
$900
$49,100
$19,640
$29,460
$60,000
$9,100
$50,900
$20,360
$30,540
b. %CHANGE in NI
24.45%
20.37%
c. %CHANGE in EBIT
20.00%
20.00%
d. DFL
1.22
1.02
e. DFL
1.22
1.02
YEAR 2
$60,000
$900
$59,100
$23,640
$35,460
f. MICHAEL DORSEY'S COMPANY
g. HIGHER DFL DUE TO GREATER AMOUNT OF INTEREST EXPENSE
h.
MICHAEL DORSEY DOROTHY MICHAELS
YEAR 1 YEAR 2
YEAR 1
EBIT
INTEREST EXPENSE
EBT
TAXES @40%
NET INCOME
$50,000
$9,100
$40,900
$16,360
$24,540
$50,000
$900
$49,100
$19,640
$29,460
DFL
1.22
110
$53,000
$9,100
$43,900
$17,560
$26,340
1.02
YEAR 2
$53,000
$900
$52,100
$20,840
$31,260
13-15. DCL = (200,000 – 75,000) / 75,000 ÷ (400,000 – 230,000) / 230,000 = 2.25
13.16.
FUNNY GIRLS COMICS
YEAR 1
YEAR 2
SALES
$200,000
$225,000
EBIT
$95,000
NET INCOME
$30,000
DOL
1.35
DFL
1.09
a. %CHANGE in SALES =
12.50%
%CHANGE in EBIT = DOL X %CHANGE in SALES
b. EBIT IN YEAR 2 = 1.1688X95,000 =
c. %CHANGE in NI = DFL X %CHANGE in EBIT
d. NI in YEAR 2 = 1.1839 X 30,000 =
e. DCL = DOL X DFL =
16.8750%
$111,031.25
18.3938%
$35,518.13
1.4715
f. %CHANGE in SALES =
20.00%
%CHANGE in NI = DCL X %CHANGE in SALES
NI in YEAR 2 = 1.2943 X 30,000 =
29.43%
$38,829.00
13-17. Interest Expense = $2,000,000 X 0.10 = $200,000
DCL = DOL X DFL =1.4 X [$600,000/($600,000 - $200,000)= 1.4 X 1.5= 2.1
13-18. a) DOL = ($5,000,000 - $700,000)/($5,000,000 - $700,000 - $300,000) = 1.075
b)
Also,
c)
Interest Expense = $16,666,666.67 X 0.09 = $1,500,000
EBIT = $2,500,000 + $1,500,000 = $4,000,000
DFL = $4,000,000/($4,000,000 - $1,500,000) = 1.600
DFL = DCL/DOL = 1.720/1.075 = 1.600
%∆NI = $∆Sales x DCL
%∆NI = 20% x 1.72
= 34.4%
111
13.19.
Soccer International, Inc.
Given:
2012
2013
Sales
Variable Costs
Fixed Costs
$560,000
$240,000
$160,000
$616,000
$264,000
$160,000
Interest Expense
$40,000
$40,000
Price of each soccer ball
$16
a. Completed income statements:
2012
2013
$560,000
$240,000
$160,000
$160,000
$40,000
$120,000
$36,000
$84,000
$616,000
$264,000
$160,000
$192,000
$40,000
$152,000
$45,600
$106,400
2012
2013
Number of balls sold
Variable cost per ball
Contribution margin
35,000
$6.86
$9.14
38,500
$6.86
$9.14
Breakeven point in units
17,500
17,500
2009
2010
$280,000
$280,000
Sales
Variable Costs
Fixed Costs
EBIT
Interest Expense
EBT
Income Taxes (30%)
Net Income
b. Breakeven point in units:
c. Breakeven point in dollars:
Breakeven point in dollars
d. Unit sales required to produce $200,000 in operating income in 2012:
Fixed costs
Operating profit requirement
Total dollars needed
Contribution margin, each ball
Number of balls needed to be sold
$160,000
$200,000
$360,000
$9
39,375
e. Effect on operating profit of greater or lesser sales in 2012:
Assumed number of balls sold
18,000
24,000
$164,571
$160,000
$4,571
$219,429
$160,000
$59,429
2012
2013
2.0
1.83
Total contribution margin
Fixed costs
Operating profit
f. Degree of Operating Leverage (DOL):
DOL
112
h. Degree of financial leverage (DFL):
DFL
2012
2013
1.33
1.26
2008
2009
2.67
2.32
2012
2013
j. Degree of combined leverage (DCL):
DCL
k. Effect of a price increase that produces higher sales:
Sales
$560,000
% increase in net income
$650,000 given 16.1%
42.86%
Net income in dollars
$84,000
13-20. %∆NI = %∆ΕΒΙΤ x DFL
%∆NI = ($50,000 - $35,000)/$35,000 x 1.71
%∆NI = $15,000/$35,000 x 1.71
%∆NI = .429 x 1.71
%∆NI = .733, or 73.3%
113
$120,000
Chapter 14 Solutions
Answers to Review Questions
1.
How does a mortgage bond compare to a debenture?
A mortgage bond is a secured bond while a debenture is an unsecured bond.
2.
How does a sinking fund function in the retirement of an outstanding bond issue?
A sinking fund is where a company puts payments that are then used to buy back outstanding bonds.
3.
What are some examples of restrictive covenants that might be specified in a bond’s indenture?
An indenture might include limitations on future borrowings, restrictions on dividend payments,
and/or requirements that working capital be maintained at least at some minimum level.
4.
Define the following terms that relate to a convertible bond: conversion ratio, conversion value, and
straight bond value.
The conversion ratio is the number of shares of common stock that would be obtained if a convertible
bond were converted. The conversion value is the total value of the common stock that would be
obtained. The straight bond is the value a convertible bond would have without the conversion
feature.
5.
If a convertible bond has a conversion ratio of 20, a face value of $1,000, a coupon rate of 8 percent,
and the market price for the company’s stock is $15 per share, what is the convertible bond’s
conversion value?
The conversion value would equal the conversion ratio of 20 times the $15 market price of the stock
or $300.
6.
What is a callable bond? What is a putable bond? How do each of these features affect their
respective market interest rates?
A callable bond can be retired early at the discretion of the issuer. A putable can be retired early at
the discretion of the investor. A call provision increases the market interest rate and a put provision
decreases it.
114
Answers to End-of-Chapter Problems
14-1.
VB = $80 X [(1 - 1/1.1210)/.12] + $1,000 X 1/1.1210 = $773.99
14-2.
VB = $40 X [(1 - 1/1.0620)/.06] + $1,000 X 1/1.0620 = $770.60
14-3.
Conversion Value = $60 X 20 = $1,200
14-4.
$32 X 26.5 = $848
$848 X 6 = $5,088.00
14-5.
22.5 [ 1-(1/(1.0375)60)/0.0375] + 1,000/(1.0375)60
22.5 X 23.7379 + 109.828 = $643.93
14-6.
$85 X 30 = $2,550
14-7.
33.75 [1 – (1/1.0430)/0.04] + 1,000/1.0430 = $891.92
14-8.
Funds required to buy 1,000 bonds from the open market = $800 X 1,000 = $800,000. Therefore
savings from buying the bonds back instead of depositing $1 million in the sinking fund =
$1,000,000 - $800,000 = $200,000.
14-9.
(7.0% - 5.0%) X 30,000 X 1,000 = $600,000
14-10. Yearly savings = (10% - 8%) X 20,000 X $1,000 = $400,000
14-11. Face Value + Call Premium = $1,000 + 0.5 X $1,000 = $1,050
Annual interest paid over last ten years = 0.10 X $1,000 = $100
$950 = $100 X (PVIFAk,10) + $1,050 X (PVIFk,10)
Realized return for Brooks = k = 11.15%
0
1
2
3
4
5
6
YEARS
7 8 9
10 11 12 13 14 15 16 17 18 19 20
-950 100 100 100 100 100 100 100 100 100 100
1050
-950 100 100 100 100 100 100 100 100 100 1150
11.15% IRR
115
14-12. a)
b)
Annual interest to be paid over next ten years = 0.08 X $1000
= $80
$950 = $80 X (PVIFAk,10) + $1,000 X (PVIFk,10)
Return for Brooks for the newly issued bond = k
= 8.77%
Overall return if the is bond held to maturity = 10.52% (See table below)
Return on the bond in Problem #4 if they had not been called = 10.61% (See table below).
Brooks didn't welcome the recall (10.61% > 10.52%).
YEARS
0
1
PROB 14-12a
-950
-950
8.77%
-950
2
3
4
5
6
7
8
9
80 80 80 80 80 80 80 80 80
10 11 12 13 14 15 16 17 18 19
80
1000
80 80 80 80 80 80 80 80 80 1080
IRR
100 100 100 100 100 100 100 100 100 100 80 80 80 80 80 80 80 80 80
1050
-950
-950
10.52%
20
80
1000
100 100 100 100 100 100 100 100 100 200 80 80 80 80 80 80 80 80 80 1080
IRR
PROB 14-12b
-950
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
-950
10.61%
1000
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 1100
IRR
14-13. Conversion Value = $70 X 20 = $1,400
14-14. VB = $90 X [(1 - 1/1.0714)/.07] + $1,000 X 1/1.0714 = $1,174.90
He would consider converting, but since the market value of the convertible bond would be greater
than the larger of the conversion value or straight bond value he would sell the bond instead if he
wanted to cash out.
14-15. Conversion Value = $30 X 30 = $900
VB = 110 X [(1 - 1/1.135)/.13] + 1,000 X 1/1.135 = $929.66
No, he should not convert. The straight bond value is greater than the conversion value.
14-16. VB = $90 X [(1 - 1/1.1314)/.13] + $1,000 X 1/1.1314 = $747.90
Since the putable bond can be redeemed at a higher price, i.e., $900, Ms. Carter should redeem the
bond.
116
$1,000 = $90 X (PVIFAk,6) + $900 X (PVIFk,6)
Realized return for Ms. Carter = k = 7.62%
14-17. VB = $90 X [(1 - 1/1.145)/.14] + $1,000 X 1/1.145 = $828.34
Since the bond can be redeemed at a higher price, i.e., $900, Diana should redeem the bond.
$1,000 = $90 X (PVIFAk,5) + $900 X (PVIFk,5)
Realized return for Diana from original bond = k = 7.27%
$900 = $130 X (PVIFAk,5) + $1,000 X (PVIFk,5)
Realized return for Diana from new bond = k = 16.06%
YEARS
0
1
2
3
4
5
-1000
90
90
90
90
90
6
7
8
9
130
130
130
130
10
900
-900
130
1000
CF
-1000
90
90
90
90
90
130
130
130
0.1051 = 10.51%IRR
Realized overall return for Diana = k = 10.51%
14-18. VB = $80 X [(1 - 1/1.2510)/.25] + 1,000 X 1/1.2510 = $393.01
14-19.
1st Mortgage bonds
2nd Mortgage bonds
Senior Debentures
Subordinated Debentures
Common Stock
Total
Claim
$5 million
5 million
10 million
4 million
10 million
34 million
Received
5 million
5 million
10 million
0
0
20 million
14-20.
a) Call Premium paid
New Bond Underwriting Costs
Total incremental Cash Outflow
$60,000,000 X .04 =
$60,000,000 X .03 =
$2,400,000
$1,800,000
$4,200,000
b) Savings = (8% - 6%) = 2% annually
Total Savings in interest payments = 2% X $60,000,000 = $1,200,000
c) Interest on old bonds:
$60,000,000 X .08 = $4,800,000
117
130
1130
Interest on new bonds:
$60,000,000 X .06 = $3,600,000
$1,200,000 difference each year for 10 years
Less taxes on the additional income at 40%:
$1,200,000 X (1 - .40) = $720,000
Net Savings = $720,000 per year
d) Present value of the net savings for 10 years at 3.6%
$720,000 X ((1-(1/(1.036)10))/.036) = $720,000 X 8.274844044 = $5,957,887.71
e) Note: Call premiums are tax deductible and amortized over the life of the bond
$60,000,000 X .04 X .40 = $960,000
Amortized over 10 years =
$960,000/10 = $96,000 per year
f) Present Value of the annual tax savings for 10 years:
$96,000 X ((1-(1/(1.036)10))/.036) = $96,000 X 8.274844044 = $794,385.03
g) Unamortized amount =
$60,000,000 X .02 X (10/20) = $600,000 current deduction
PV of unamortized amount if bond is not called:
($600,000/10) X ((1-(1/(1.036)10))/.036 =
$60,000 X 8.274844044 = $496,490.64
Net Tax Savings = $600,000 - $496,490.64 = $103,509.36
h) ($60,000,000 X .03)/10 = $180,000 annual write off
Tax Savings = $180,000 X .40 = $72,000
i) PV of tax Savings =
$72,000 X ((1-(1/(1.036)10))/.036 = $72,000 X 8.274844044 = $595,788.77
j) PV Total Inflows = $5,957,887.71 + $794,385.03 + $103,509.36 + $595,788.77 =
$7,451,570.87
k) NPV of the bond proposal = PV of total cash inflows – Total outflows
NPV = $7,451,570.87 - $4,200,000 = $3,251,570.87
118
14-21.
Aurora Glass Fibers Lease-Buy Analysis
Part a, the buy option:
Assumptions:
Cost of new computers
Expected Life
Salvage value
Amount to be borrowed
Interest rate on loan
$800,000
4 years
$100,000
$800,000
10%
MACRS Depreciation:
(3-year asset class)
Yr 1
33.3%
Cost of capital
Tax rate
Yr 2
44.5%
Yr 3
14.8%
Yr 4
7.4%
6% (after-tax cost of debt)
40%
Estimated Incremental Cash Flows to Equity:
Year:
Cost of new computers
Amount to be borrowed
Depreciation on new computers
Tax savings on depreciation
Interest payments on loan
Tax savings on interest
Repayment of principal on loan
Salvage value of new computers
Tax on gain
Net Incremental Cash Flows
PV of Cash Flows
0
($800,000)
800,000
1
2
3
4
($266,400)
106,560
(80,000)
32,000
($356,000)
142,400
(80,000)
32,000
($118,400)
47,360
(80,000)
32,000
$58,560
$55,245
$94,400
$84,016
($640)
($537)
($59,200)
23,680
(80,000)
32,000
(800,000)
100,000
(40,000)
($764,320)
($605,413)
Total PV of Cash Flows Associated With the Buy Option =
($466,689)
$0
$0
Part b, the lease option:
Assumptions:
Annual lease payment
Lease term
Value at termination of lease
($200,000) paid at the end of each year
4 years
$0
Estimated Incremental Cash Flows to Equity:
Year:
Lease payment
Tax savings on lease payment
Net Incremental Cash Flows
PV of Cash Flows
0
3
($200,000)
$80,000
($120,000)
($100,754)
4
($200,000)
$80,000
($120,000)
($95,051)
Total PV of Cash Flows Associated With the Lease Option =
($415,813)
$0
$0
119
1
($200,000)
$80,000
($120,000)
($113,208)
2
($200,000)
$80,000
($120,000)
($106,800)
Part c, comparison of alternatives and decision:
Total PV of Cash Flows Associated With the Buy Option =
Total PV of Cash Flows Associated With the Lease Option =
($466,689)
($415,813)
Net Advantage to Leasing (NAL) =
$50,877
Decision:
120
Lease
Chapter 15 Solutions
Answers to Review Questions
1.
What are some of the government requirements imposed on a public corporation that are not imposed
on a private, closely held corporation?
Public corporations must submit audited financial statements to the government for release to the
public. Private corporations can keep their financial information confidential.
2.
How are the members of the board of directors of a corporation chosen and to whom do these board
members owe their primary allegiance?
Members of a corporation’s board of directors are elected by the common stockholders and owe their
allegiance to these stockholders
3.
What are the advantages and the disadvantages of a new stock issue?
A new stock issue raises funds and decreases the riskiness of the firm. It also tends to send a
negative signal to the market since many investors believe a company would only sell new stock if
future financial prospects were dim.
4.
What does an investment banker do when underwriting a new security issue for a corporation?
When underwriting a new security issue an investment banker buys it and then resells it to investors.
5.
How does a preemptive right protect the interests of existing stockholders?
A preemptive right protects the interests of existing stockholders by giving them the opportunity to
preempt other investors in the purchase of new shares. If these rights are exercised, existing
shareholders would maintain their same percentage of ownership after the new stock issue as before.
6.
Explain why warrants are rarely exercised unless the time to maturity is small?
Warrants are rarely exercised until the time to expiration is small because the market price of the
warrant is greater than the exercise value. The holder of the warrant would therefore sell it in the
secondary market instead of exercising it if he or she wanted to cash in.
7.
Under what circumstances is a warrant’s value high? Explain.
121
A warrant’s value would be high when the stock price, time to expiration, and/or expected stock
price volatility are high.
Answers to End-of-Chapter Problems
15-1.
Original Ownership = 20,000/1,000,000 = 2%
Diluted Ownership = 20,000 /1,500,000 = 1.33%
15-2.
1. Book Value Approach: (200mil. - 150mil.)/5mil. = $10 per share
2. Liquidation Value Approach: (250 - 150)/5 = $20 per share
3. Replacement Value Approach: (400 - 150)/5 = $50 per share
4. Dividend Growth Model: $2/(0.13 - 0.08) = $40 per share
Ms. Phinlay should buy the stock as the share is selling at a price ($20) which is lower than what she is
prepared to pay ($40) to get her required rate of return.
15-3.
a) .45(2,500,000) = 1,125,000
[(1,125,000 - 1) X (5 + 1)] / 2,500,000 = 2.669
2 directors
b) .55(2,500,000) = 1,375,000
[(1,375,000 – 1) X (5 + 1)] / 2,500,000 = 3.299
3 directors
15-4.
a) [(1 X 2,500,000) / (5 + 1)] + 1 = 416,667
b) [(3 X 2,500,000) / (5 + 1)] + 1 = 1,250,001
c) [(5 X 2,500,000) / (5 + 1)] + 1 = 2,083,334
15-5.
a) .35 (2,500,000) = 875,000
[(875,000 – 1) (5 + 1)] / 2,500,000 = 2.1
2 directors
b) [(2 X 2,500,000)/ (5 + 1)] + 1 = 833,334
15-6.
Length of term = (9/3) X 3 = 9 years for each board members
15-7.
NUM DIR = [(0.35 X 1,000,000 - 1) X (4 + 1)]/1,000,000 = 1.75 rounded down to 1
The minority group can elect 1 of their people to the board out of the 4 to be elected.
122
15-8.
NUM VOTING SHARES NEEDED = [(1 X 200,000)/(7 + 1)] + 1 = 25,001. Since Ms. O'Niel holds
more shares than required, she can elect herself to the board.
15-9.
a) How many directors can the young stockholders elect under
(i) cumulative voting procedure
NUM DIR = (600,000 X 0.30-1) X (13 + 1)/600,000 = 4.2 rounded down to 4
(ii) majority rule: NONE
b) What percentage of voting shares and/or proxies the dissident group must have to be able to elect
7 out of the 13 board members?
NUM VOTING SHARES NEEDED=[(7 X 600,000)/(13 + 1)] + 1=300,001
Percentage of voting shares and/or proxies = 300,001/600,000 ≈ 50% (slightly greater than 50%)
15-10. Number of rights required to buy a share = 500,000/50,000 = 10
15-11. N = 2,000,000/500,000 = 4
Approx. Market Value of a Right = R = (65 - 55)/(4 + 1) = $2
15-12. Market Price of stocks selling ex-rights = 65 - 2 = $63
Approx. Market Value of a Right = R = (63 - 55)/(4) = $2
15-13. N = 7
Approx. Market Value of a Right = R = (77 - 65)/(7 + 1) = $1.50
Market Price of stocks selling ex-rights = 77 - 1.5 = $75.50
15-14. a) Approx. Market Value of a Right = R = (72 - 60)/(4 + 1) = $2.40
b) Maximum number of new shares that Johnny can buy = 700/4 = 175
c) Amount Johnny would spend = 175 X 60 = $10,500
d) Selling price of all of Johnny's rights = 700 X 2.40= $1,680
15-17. a) Approx. Market Value of a Right = R = (62 - 50)/(4 + 1) = $2.40
b) Ex-rights price = $62 - $2.40 = $59.60 per share
Diluted price after issue of new stock = $59.6 X 4/5 = $47.68
123
Option I: Sell rights and hold stocks at diluted value:
Amount obtained by selling rights
Value of stocks held at diluted price
Unused Cash
= $2.40 X 60 = $144.00
= 60 X $47.68 = $2,860.80
= $750.00
Net worth from Option I = $3,784.80
Option II: Buy new shares:
Number of shares Selena can buy = 60/4 = 15
Amount to be spent to buy 15 shares = $50 X 15 = $750. So, Selena can buy all the 15 new shares
with her available cash.
Diluted price of stocks = $47.68
Net worth from Option II = $47.68 X (60 + 15) = $3,576.00
So, Selena should go for Option I, that is, Sell rights and hold her stocks at diluted value.
15-18. XV = (100 - 85) X 5 = $75
What happens to the exercise value of the warrant if the stock price changes to
a) $110 : XV = (110 - 85) X 5 = $125
b) $80 : XV = $0
15-19.
Issue of new common stock by Wilkerson Corporation:
Current Market Price per share of Common Stock
Number of Common Shares outstanding
Amount of additional funds needed
Net Income for the year
Number of shares owned by Guy Hamilton
$40
600,000
$2,000,000
$1,000,000
10,000
Possible Subscription Prices
$36
a.
Number of shares to be issued
Number of Rights required to buy one share
b.
EPS before the rights issue
EPS after the rights issue
c.
Max number of new shares Guy can buy
Guy's claim to earning before the rights issue
Guy's claim to earning after the rights issue
124
$33
$29
$26
55,556 60,606 68,966 76,923
10.8
9.9
8.7
7.8
$1.67
$1.53
$1.67
$1.51
$1.67
$1.49
$1.67
$1.48
926 1,010 1,149 1,282
$16,667 $16,667 $16,667 $16,667
$16,667 $16,667 $16,667 $16,667
Chapter 16 Solutions
Answers to Review Questions
1.
Explain the role of cash and of earnings when a corporation is deciding how much, if any, cash
dividends to pay to common stockholders.
In the long-run earnings are necessary to maintain dividend payments, but at the time an actual
dividend payment is made, adequate cash is necessary.
2.
Are there any legal factors that could restrict a corporation in its attempt to pay cash dividends to
common stockholders? Explain.
A firm may be legally restricted as to the dividends it can pay by existing bond indentures or loan
agreements. It may also be restricted as to the payment of common stock dividends is scheduled
preferred stock dividends have not been paid.
3.
What are some of the factors that common stockholders consider when deciding how much, if any,
cash dividends they desire from the corporation in which they have invested?
Common stockholders would consider the company’s investment opportunity, their need for income,
and their tax bracket when deciding on their desire for dividends.
4.
What is the Modigliani and Miller theory of dividends? Explain.
The Modigliani-Miller theory of dividends says that dividend theory is irrelevant. They claim that it
is the income produced by assets that is important, not how funds are distributed.
5.
Do you believe an increased common stock cash dividend can send a signal to the common
stockholders? If so, what signal might it send?
An increase in cash dividends is often seen as a positive signal. A company would be unlikely to
increase its dividend if it did not believe its future prospects were good enough to sustain the higher
level of dividends. This is because the market usually frowns upon a cut in dividends.
6.
Explain the bird in the hand theory of cash dividends.
The bird in the hand dividends theory says that dividends received now are better than a promise of
future dividends. Uncertainty is resolved when a dividend is paid.
125
7.
What is the effect of stock (not cash) dividends and stock splits on the market price of common
stock? Why do corporations declare stock splits and stock dividends?
Stock splits and stock dividends decrease the price per share of the common stock but should not
increase the total market value of all common stock outstanding unless other positive things are
perceived to occur. Many companies believe that a stock split or stock dividend makes their stock
more affordable and therefore more attractive to a wider range of potential investors.
Answers to End-of-Chapter Problems
16-1.
Retention Ratio = $600/$1,000 = 0.6 or 60%
∴ Payout Ratio = 1-.6 = .4 = 40%
16-2.
Dividend Paid = 0.4 X $50 million = $20 million
Addition to Retained Earnings = $50 mil. - $20 mil. = $30 million
16-3.
Retained Earnings Maintain
Retained Earnings end of 2011
Additional needed for maintenance
$1,000,000
750,000
$250,000
Earnings Avail. to Common Stockholders
Needed for maintenance
Dividend Payout
$800,000
250,000
$550,000
$550,000 / $800,000 = .6875 = 68.75%
16-4.
Net income
Dividend Payout (35%)
Addition to retained earnings
$4,000,000
1,400,000
$2,600,000
Retained earnings end of 2011
Addition to retained earnings
Retained earnings end of 2012
$1,200,000
2,600,000
$3,800,000
16-5.
(Figures in $ millions) Year 1 Year 2 Year 3
Net Income
30
20
25
Dividend Payout ratio 0.3
0.3
0.3
Dividend Paid
9
6
7.5
Addition to RE
21
14
17.5
Total Addition to RE = 21 + 14 + 17.5 = 52.5
126
16-6.
(Figures in $ millions) Year 1 Year 2
Net Income
30
20
Dividend Paid
10
10
Dividend Payout ratio 0.33
0.5
Addition to RE
20
10
Total Addition to RE = 20 + 10 + 15 = 45
16-7.
Year 3
25
10
0.4
15
Equity Investment = $14mil. X 0.6 = $8.4 million
Dividend to be Paid = $10mil. - $8.4 mil. = $1.6 million
16-8.a) Equity Investment = $14mil. X 0.6 = $8.4 million
Dividend to be Paid = $16 mil. - $8.4 mil. = $7.6 million
b)
16-9.
Equity Investment = $14 mil. X 0.6 = $8.4 million
Dividend to be Paid = $0
Equity funds needed
$12,000,000 X .80 = $9,600,000
Amount avail. to stockholders $24,000,000 – 9,600,000 = $14,400,000
Dividend per share
$14,400,000 / 20,000,000 = $0.72
16-10. 20% Stock Dividend ($000s)
Increase in number of shares = 0.2 X $2 million
Increase in common stock account = 400 X $1
Increase in capital in excess of par account
Total increase = $12,000 + $400 = $12,400
= 400 thousand
= $400
= 400 X $30 = $12,000
This increase is greater than the Retained Earnings of $10,000. Hence it is not possible to pay a 20%
stock dividend.
10% Stock Dividend($000s)
Increase in number of shares = 0.1 X $2 million = 200 thousand
Increase in common stock account = 200 X $1 = $200
Increase in capital in excess of par account = 200 X $30 = $6,000
Total increase = $6,000 + $200 = $6,200
This increase can be covered by a matching decrease in the retained earning account keeping the total
equity capital unchanged. The new retained earning will be 10,000 - 6,200 = $3,800. Hence it is
possible to pay a 10% stock dividend.
127
16-11.
($000s)
2,000
8,000
10,000
20,000
Common Stock ( 2 million shares, $1 par)
Capital in excess of par
Retained Earnings
Total Common Equity
After Payment of Dividend:
($000s)
2,200
14,000
3,800
20,000
Common Stock ( 2.2 million shares, $1 par)
Capital in excess of par = 8,000 + 6000 =
Retained Earnings = 10,000 - 6,000 - 200 =
Total Common Equity
New Market Price of the Stock = $31 X 2,000/2,200 = $28.18 per share.
16-12. a) 800,000 X (1 + 0.30) = 1,040,000 new total shares
1,040,000 – 800,000 = 240,000 new shares
b) CIEP = Capital in Excess of Par
CIEPbefore = $13,600,000
CIEPafter = $13,600,000 + (240,000 new shares X ($40 - $3))
CIEPafter = $22,480,000
c) CS = Common Stock
CSbefore = 800,000 X $3 = $2,400,000
CSafter = 1,040,000 X $3 = $3,120,000
RE = Retained Earnings
REbefore = $60,000,000
REafter = $60,000,000 – ($3,120,000 - $2,400,000) – ($22,480,000 - 13,600,000)
REafter = $50,400,000
16-13. 800,000 X $40 = $32,000,000
x = new stock price
1,040,000 x = $32,000,000
New stock price = $30.77
16-14. Before the stock split
Common Stock ( 3 million shares, $1.00 par)
Capital in excess of par
Retained Earnings
Total Common Equity
128
3,000
7,000
10,000
20,000
After the stock split
Common Stock ( 9 million shares, $0.33 1/3 par)
Capital in excess of par
Retained Earnings
Total Common Equity
3,000
7,000
10,000
20,000
New Market Price of the stock = 33 X 1/3 = $11.00 per share.
16-15. EPS (Before the stock split) = $800,000/3,000,000 = $0.27
EPS (After the stock split) = $800,000/9,000,000 = $0.09
The P/E ratio will remain the same (123.75) before and after the split unless other factors influence
the market’s perception of this stock’s value.
16-16. a) Dividend per share last year = $1.33 X 5/1 = $6.65
b) Dividend per share last year = $1.33/1.1 X 5/1 = $6.05
16-17. Dividend per share = EPS X Payout Ratio = ($10/1) X 0.4 = $4
Price of stock (ex-dividend) = $30 - $4 = $26 per share.
16-18.
Spring Field Manufacturing Company's Dividend Payments:
NUMBER OF SHARES OF COMMON STOCK OUTSTANDING =
NUMBER OF SHARES OF COMMON STOCK OWNED BY YOU =
YEAR
NET
INCOME
2013
2014
2015
2016
2017
$1,000,000
$1,100,000
$1,200,000
$1,300,000
$1,400,000
CAPITAL
INVESTMENTS
EQUITY DIVIDEND DIVIDEND DIVIDEND
FINANCING PAYMENT PER SHARE RECEIVED
$800,000
$480,000
$1,000,000
$600,000
$2,000,000 $1,200,000
$800,000
$480,000
$1,000,000
$600,000
129
500,000
500
$520,000
$500,000
$0
$820,000
$800,000
$1.04
$1.00
$0.00
$1.64
$1.60
$520
$500
$0
$820
$800
16-19.
Spring Field
Payments:
Manufacturing
Company's
Dividend
NUMBER OF SHARES OF COMMON STOCK OWNED BY YOU =
YEAR
NET
INCOME
2013 $1,000,000
2014 $1,100,000
2015 $1,200,000
2016 $1,300,000
2017 $1,400,000
CAPITAL
INVESTMENTS
$800,000
$1,000,000
$2,000,000
$800,000
$1,000,000
EQUITY
FINANCING
$480,000
$600,000
$1,200,000
$480,000
$600,000
AMOUNT
FROM
NEW
SHARES
500
NO. OF
SHARES
DIVIDEND DIVIDEND DIVIDEND
OUTSTANDING PAYMENT
PER
RECEIVED
SHARE
500,000
500,000
600,000
600,000
600,000
$600,000
$520,000
$500,000
$600,000
$820,000
$800,000
$1.04
$1.00
$1.00
$1.37
$1.33
$520
$500
$500
$683
$667
16-20. Comprehensive Problem:
a)
Expected Dividend per share = $3,000,000 X 0.5/500,000 = $3
Repurchase Price = $47 + $3 = $50 per share
b)
Number of shares that could be repurchased
c)
Before Repurchase of Stock
= $3,000,000/$50 = 60,000
Common Stock (500,000 shares, $3 par)
Capital in excess of par ($7/share)
Retained Earnings
Total Common Equity
($ 000s)
1,500
3,500
5,000
10,000
After Repurchase of Stock
Common Stock (440,000 shares, $3 par)
Capital in excess of par = 7 X 440 =
Retained Earnings = 5,000 + (1,500 - 1,320)
+ (3,500 - 3,080) =
Total Common Equity
($ 000s)
1,320
3,080
5,600
10,000
d) If net income next year is expected to be $4 million, what would be the EPS next year with and
without the repurchase?
EPS (without repurchase) = $4,000,000/500,000 = $8
EPS (with repurchase) = $4,000,000/440,000 = $9.09
e) If you own 50 shares of common stock of the company, would you like the company's decision of
buying back the stocks instead of paying a dividend?
Without Repurchase:
Dividend Earning Last Year = $3/Share X 50 shares = $ 150
Value of stock = $47/share X 50 shares
= $2,350
Total
= $2,500
130
With Repurchase:
Price of stock = $50/share X 500/440 = $56.82 per share
Value of stock = $56.82 X 50 = $2,841.00
The decision to buy back instead of paying a dividend would be preferred if the stock price were to
increase to $56.82 per share with the repurchase. The taxes that may be owed on the $150 in dividends
under the no repurchase scenario would decrease further the attractiveness of this alternative.
16-21. Before the split
# of shares
Common Stock
Par Value
Capital in Excess of Par
Retained Earnings
Total Common Stock Equity
300,000
$1,200,000
$4
$1,500,000
$10,000,000
$12,700,000
After the split
# of shares
Common Stock
Par Value
Capital in Excess of Par
Retained Earnings
Total Common Stock Equity
1,200,000
$1,200,000
$1
$1,500,000
$10,000,000
$12,700,000
131
Chapter 17 Solutions
Answers to Review Questions
1.
What is working capital?
Working capital consists of the current assets of the firm.
2.
What is the primary advantage to a corporation of investing some of its funds in working capital?
By investing in working capital a firm gets the liquidity it needs helping it to pay its bills. The risk of
the firm is therefore reduced.
3.
Can a corporation have too much working capital? Explain.
A firm can have too much working capital if it is losing the opportunity to invest in high returning
fixed assets and if it goes beyond the amount of working capital needed for reasonable liquidity
needs.
4.
Explain how a firm determines the optimal level of current assets.
The optimal level of working capital is determined by finding the amount that balances the need for
liquidity and for profitability.
5.
What are the risks associated with using a large amount of short-term financing for working capital?
Using a large amount of short-term financing generally allows funds to be raised at a lower cost but
increases the firm’s risk.
6.
What is the matching principle of working capital financing? What are the benefits of following this
principle?
The matching principle is when short-term financing is used for temporary current assets while longterm financing is used for permanent current assets and fixed assets. The main benefit of this
approach is that as temporary current assets are sold off the proceeds can be used to pay off the shortterm debt.
7.
What are the advantages and disadvantages of the aggressive working capital financing approach?
An aggressive working capital financing approach usually results in a lower cost of funds for a firm
but a higher level of risk.
132
8.
What is the most conservative type of working capital financing plan a company could implement?
Explain.
An all equity capital structure would be the most conservative type of working capital financing plan
approach. The more long-term financing used the more conservative the financing plan, and equity
is permanent financing.
Answers to End-of-Chapter Problems
17-1.
a) ($150,000 + $120,000 + $80,000) = $350,000
b) $350,000 – ($100,000 + $90,000) = $160,000
c) ($150,000 + $120,000 + $80,000) X 0.25 = $87,500
d) ($150,000 + $120,000 + $80,000) X 0.75 = $262,500
17-2.
Firm 1:
$10,000 + $3,000 + $2,500 = $15,500 (working capital)
$15,500 - $7,500 - $4,000 = $4,000 (net working capital)
Current ratio = $15,500 / ($7,500 + $4,000) = 1.35
Quick ratio = ($15,500 - $3,000) / $11,500 = 1.09
Firm 2:
$8,000 + $6,000 + $3,500 = $17,500 (working capital)
$17,500 - $3,500 - $11,000 = $3,000 (net working capital)
Current ratio = $17,500 / ($3,500 + $11,000) = 1.21
Quick ratio = ($17,500 - $6,000) / $14,500 = 0.79
Firm 1 is more liquid due to its higher liquidity ratios.
17-3.
Company A: NWC = ($1,000 + $400) - $900 = $500
Company B: NWC = ($80 + $880) - $600 = $360
Company A has the higher net working capital and would therefore generally be considered the more
liquid company. Although Company A has a slightly smaller current ratio value (1.56 for A and 1.6
for B) Company A has a much higher percentage of cash in its current assets, so would likely be
considered by most analysts the more liquid firm.
17-4.
a)
CA = $30,000 + $15,000 + $130,000 = $175,000
b)
CL = $100,000 + $60,000 = $160,000
c)
NWC = $175,000 - $160,000 = $15,000
d)
160/(175 X .5) or 183.86% of TCA is financed by CL. This is an aggressive approach since
all TCA and most of PCA are being financed with riskier short-term funds.
133
17-5.
17-6.
a)
CA = $30,000 + $15,000 + $130,000 = $175,000
b)
CL = $30,000 + $20,000 = $50,000
c)
NWC = $175,000 - $50,000 = $125,000
d)
50/(175 X .5) or 57.14% of TCA is financed by CL. This is a relatively conservative
approach. Long-term financing of $625,000 exceeds the total of fixed assets and permanent
current assets, $587,500, by $37,500. Only $50,000 of the $87,500 in temporary current
assets is being financed with short-term funds.
a)
CA = $50 + $0 + $40 + $70 = $160
b)
CL = $80 + $90 = $170
NWC = $160 - $170 = ($10)
c)
All of LuLu Belle’s current assets, and some of the fixed assets, are financed with short-term
funds (current liabilities). This is an aggressive approach.
d)
Reduce short-term debt, increase long-term debt and equity and invest in marketable
securities. This will increase net working capital and the current ratio.
17-7.
Cash
$100,000
Inventory
$200,000
Accounts Receivable
$150,000
Net Fixed Assets
$550,000
Total Assets
$1,000,000
Accounts Payable
$35,000
Notes Payable
$60,000
Long-term Debt
$505,000
Common Equity
$ 400,000
Total Liabilities and Equity $1,000,000
Permanent assets, net fixed assets and a small portion of temporary assets are financed with long-term debt
and equity. This is using a very conservative approach. Your exact numbers are likely to be different, but
the point is that long-term debt and equity financing are emphasized.
17-8.
PCA = $225,000 X 0.60 = $135,000
PCA + FA = $135,000 + $475,000 = $610,000
LTD + CSEQ = $410,000 + $200,000 = $610,000
a)
Cash
Accounts Receivable
Inventory
Fixed Assets
$50,000
25,000
150,000
475,000
$700,000
Accounts Payable__$40,000_
Notes Payable ___50,000_
Long-term Debt __410,000_
Common Equity __ 200,000_
134
b)
Cash
Accounts Receivable
Inventory
Fixed Assets
17-9.
$50,000
25,000
150,000
475,000
$700,000
Accounts Payable__$30,000_
Notes Payable ___60,000_
Long-term Debt __185,000_
Common Equity __425,000_
a) Accounts payable = $180,000
Notes payable = $320,000
Long-term debt = $0
Common Equity = $200,000
Your exact numbers are likely to be different, but the point is that short-term debt is emphasized.
17-10.
CA = $30,000 + $15,000 + $130,000 = $175,000
Perm. CA = $15,000 + $5,000 + $80,000 = $100,000
Temp. CA = $175,000 - $100,000 = $75,000
CL = Short-Term Debt + $20,000 = $75,000 = Temp.CA (By Matching Principle)
Short-Term Debt = $75,000 - $20,000 = $55,000
Long-Term Debt = $675,000 - $450,000 - $55,000 - $20,000 = $150,000
17-11.
NWC = CA - CL
$25,000 = ($30,000 + $15,000 + $130,000) - ($20,000 + Short-Term Debt)
Short-Term Debt = $175,000 - $25,000 - $20,000 = $130,000
Long-Term Debt = $675,000 - $450,000 - $130,000 - $20,000 = $75,000
17-12.
AGG.(A)(HIGH
RISK)
MOD.(M)(MOD.
RISK)
CON.(C)(LOW
RISK)
Temporary CA
75
75
75
Permanent CA
100
100
100
Fixed Assets
500
500
500
Total Assets
675
675
675
Current Liabilities
160
75
50
Long Term Debt
90
150
150
Stockholders' Equity
425
450
475
COMMENTS
Net Income
70
70
70
NWC
15
100
125
LOWEST FOR A, HIGHEST
FOR C
Current Ratio
1.09
2.33
3.50
LOWEST FOR A, HIGHEST
FOR C
Debt to Asset
0.37
0.33
0.30
HIGHEST FOR A, LOWEST
FOR C
ROE
16.47%
15.56%
14.74%
HIGHEST FOR A, LOWEST
FOR C
135
17-13. Assumption (i)
(a) Interest Expense: 0.13 X 5 X $500,000 = $325,000
(b) Interest Expense: .11 X 5 X $500,000 = $275,000
Alternative (b) will save $50,000
Assumption (ii)
(a) Interest Expense: 0.13 X 5 X $500,000 = $325,000
(b) Interest Expense: (0.11 X 2 X $500,000) + (.14 X 2 X $500,000) + (.16 X $500,000)
= $330,000
Alternative (a) will save $5,000
17-14.
Data for graph:
Total assets Fixed assets
Date
(given)
(given)
31-Jan
28-Feb
31-Mar
30-Apr
31-May
30-Jun
31-Jul
31-Aug
30-Sep
31-Oct
30-Nov
31-Dec
$45
$46
$34
$48
$40
$30
$28
$39
$45
$39
$52
$50
Permanent Temporary Current Liabilities
Current
Current if Matching Principle
Assets
Assets is Followed
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$14
$17
$18
$6
$20
$12
$2
$0
$11
$17
$11
$24
$22
$17
$18
$6
$20
$12
$2
$0
$11
$17
$11
$24
$22
Working Capital Trends
$60
$50
$40
$30
Temporary Current Assets
Temporary Current Assets
Permenant Current Assets
$20
$10
Fixed Assets
$0
31Jan
28- 31Feb Mar
30Apr
31May
30Jun
31Jul
136
31- 30Aug Sep
31Oct
30- 31Nov Dec
17-15.
Working Capital Trends
$60
Temporary Current Assets
$55
$50
$45
Permanent Current Assets
$40
Fixed Assets
$35
$30
Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct
MONTH/ YEAR
b) Sep. of year 4:
TA= $52.04
TCA= $4.00
PCA= $9.04
FA= $39.00
Aug. of year 5:
TA= $54.80
TCA= $5.00
PCA= $10.80
FA= $39.00
c) Sep. of year 4:
(i) aggressive approach
CL = over $4.00
LT Financing = the remainder of $52.04
(ii) moderate approach
CL = $4.00
LT Financing = $48.04
(iii) conservative approach
CL = less than $4.00
LT Financing = the remainder of $52.04
Aug. of year 5:
(i) aggressive approach
CL = over $5.00
LT Financing = the remainder of $54.80
(ii) moderate approach
CL = $5.00
LT Financing = $49.80
(iii) conservative approach
CL = less than $5.00
LT Financing = the remainder of $54.80
137
17-16.
Working Capital Trends
$120
$110
$100
$90
$80
$70
$60
$50
$40
Temporary Current Assets
Permenant Current Assets
Fixed Assets
Jan
May
Sep
Jan
May
Sep
Jan
May
Sep
Jan
May
Sep
Jan
May
Sep
MONTH/ YEAR
17-16.
b) Sep. of year 2:
TA = $89.00
TCA = $18.00
PCA = $16.00
FA = $55.00
Oct. of year 4:
TA = $101.00
TCA = $22.50
PCA = $23.50
FA = $55.00
Year 5 minimum total assets occur in January in the amount of $79.40.
Year 5 maximum total assets occur in December in the amount of $115.70.
c) Sep. of year 2:
(i) aggressive approach
CL = over $18.00
LT Financing = the remainder of $89.00
(ii) moderate approach
CL = $18.00
LT Financing = $71.00
(iii) conservative approach
CL = less than $18.00
LT Financing = the remainder of $89.00
Oct. of year 4:
(i) aggressive approach
CL = over $22.50
LT Financing = the remainder of $101.00
(ii) moderate approach
CL = $22.50
LT Financing = $78.50
(iii) conservative approach
CL = less than $22.50
LT Financing = the remainder of $101.00
138
Chapter 18 Solutions
Answers to Review Questions
1.
What are the primary reasons that companies hold cash?
Companies hold cash to make necessary payments, to take advantage of opportunities as they arise,
and to cover unforeseen emergencies.
2.
Explain the factors affecting the choice of a minimum cash balance amount.
The minimum cash balance amount is determined by how easy it is to raise funds when needed, how
predictable the cash flows are, and how risk averse managers are.
3.
What are the negative consequences of a company holding too much cash?
A company holding too much cash would be giving up the opportunity to invest more in income
producing assets
4.
Explain the factors affecting the choice of a maximum cash balance amount.
The maximum cash balance amount is determined by available investment opportunities, the
expected return on investments, and the transaction cost of making investments.
5.
What is the difference between pro forma financial statements and a cash budget? Explain why pro
forma financial statements are not used to forecast cash needs.
Pro forma income statements deal with revenues and expenses that are not always cash flows while
cash budgets deal only with projected cash inflows and outflows.
6.
What are the benefits of “collecting early” and how do companies attempt to do this?
Money has time value. The sooner cash is collected, the better. Companies use regional collection
centers and lock boxes to facilitate this.
7.
What are the benefits of “paying late” (but not too late) and how do companies attempt to do this?
Because money has time value, the later cash is paid, but not too late, the better. Companies use
remote disbursement banks to facilitate holding onto funds longer.
139
8.
Refer to the Bulldog battery company’s cash budget in Table 18-7. Explain why the company would
probably not issue $1 million worth of new common stock in January to avoid all short-term
borrowing during the year.
Common stock financing is long-term financing so it would probably not be used to meet this shortterm financing need.
Answers to End-of-Chapter Problems
18-1. Miller-Orr Model:
H = 3Z - 2L
Target Cash Balance = Z = (H + 2L)/3 = ($9,000 + 2 X $3,000)/ 3 = $5,000
18-2. Miller-Orr Model:
a)
Z=3
3 X TC X V
+L
4r
OR
Z=3
3 X $40 X $39,000
+ $2,200
4 X .03/365
Target Cash Balance = Z = $2,424 + $2,200 = $4,624
b)
Upper Limit of cash balance = H = 3Z -2L = 3 X $4,624 - 2 X $2,200 = $9,472
18-3. Miller-Orr Model:
a)
Z=3
3 X TC X V
+L
4r
OR
Z=3
3 X $40 X $52,000
+ $3,900
4 X .03/365
Target Cash Balance = Z = $2,667 + $3,900 = $6,567
b)
Upper Limit of cash balance = H = 3Z -2L = 3 X $6,567 - 2 X $3,900 = $11,901
3
18-4.
Z = √ [(3 X $25 X $65,580) / (4 X (.05/365))] + $15,000
140
3
Z = √ (4,918,500 / .000547945) + $15,000
3
Z = √ 8,976,265,866 + $15,000
Z = $2,078.25 + $15,000
Z = $17,078.25
18-5.
H = (3 X $17,078.25) – (2 X $15,000)
H = $51,234.75 – $30,000
H = $21,234.75
141
18-6.
Lifelong Appliances Cash Collections
Given:
20% of customers pay off their accounts in month of sale
70% of customers pay off their accounts in first month following sale
10% of customers pay off their accounts in second month following sale
2012 --->
Nov
Sales ($000s)
2013 --->
Jan
Dec
$131
$129
Aug Sep Oct Nov Dec
20011 --->
Jan
Feb
$133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143
$136 $139
Feb
$126
Mar
Apr May Jun
Jul
Monthly Cash Collections Worksheet:
(in $000s)
2012 --->
Nov
Dec
2013 --->
Jan
Cash collections:
in month of sale
first month after sale
second month after sale
Total monthly cash collections
Feb
$25
90
13
$129
Mar
Apr May Jun
Jul
Aug Sep Oct Nov Dec
2011 --->
Jan
Feb
$27
$28 $29 $38 $45 $48 $45 $37 $35 $33 $29
88
93
97 100 134 158 169 157 129 121 116
13
13
13 14 14 19 23 24 22 18 17
$128 $134 $139 $152 $193 $226 $237 $218 $186 $173 $162
18-7.
Lifelong Appliances Cash Collections with Stricter Credit Terms
Given:
40% of customers pay off their accounts in month of sale
55% of customers pay off their accounts in first month following sale
5% of customers pay off their accounts in second month following sale
2012 --->
Nov
Sales ($000s)
$131
Dec
$129
2013 --->
Jan
$126
Feb
$133
Aug Sep Oct Nov Dec
2011 --->
Jan
Feb
$139 $143 $191 $226 $242 $224 $184 $173 $166 $143
$136 $139
Mar
Apr May Jun
Jul
Monthly Cash Collections Worksheet:
(in $000s)
2012 --->
Nov
Cash collections:
in month of sale
first month after sale
second month after sale
Total monthly cash collections
2013 --->
Dec
Jan
$50
71
7
$128
Feb
$53
69
6
$129
Mar
Apr May Jun
Jul
Aug Sep Oct Nov Dec
$56 $57 $76 $90 $97 $90 $74 $69 $66 $57
73
76 79 105 124 133 123 101 95 91
6
7
7
7 10 11 12 11
9
9
$135 $140 $162 $203 $231 $234 $209 $182 $171 $157
142
2011 --->
Jan
Feb
18-8.
a) ($18,366 X .45) + ($16,523 X .40) + ($17,956 X .15) =
$8,264.70 + $6,609.20 + $2693.40 =
$17,567.30
b) ($22,980 X .45) + ($22,890 X .40) + ($19,500 X .15) =
$10,341 + $9,156 + 2,925 =
$22,422
c) ($21,650 X .45) + ($23,000 X .40) + ($23,157 X .15) =
$9,742.50 + $9,200 + $3,473.55 =
$22,416.05
18-9.
a) $2,000 + ($17,956 X .05) + $62.50 = $2,960.30
b) $2,000 + ($22,890 X .05) + $62.50 +$1,125 = $4,332.00
c) $2,000 + ($19,250 X .05) + $62.50 = $3,025.00
18-10.
Lifelong Appliances Cash Expenditures
Given:
2012 --->
Nov
Sales ($000s)
2013 --->
Dec
$131
Jan
$129
Dec
Materials purchasing Schedule: Order materials
Feb
$126
Mar Apr May Jun
Jul
2011 --->
Aug Sep Oct Nov Dec Jan Feb
$133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139
Jan
Feb
Mar
Manufacture Appliances Sell appliances Repeat each month
Cost of materials =
30% of sales
Payment for materials one month after purchase
Production costs other than purchases =
Selling and marketing Expenses =
General and Administrative Expenses =
Interest Payments =
Tax payments =
Dividend payments =
80%
19%
$11
$31
$100
$50
of purchases
of sales
thousand each month
thousand, paid in December
thousand, paid in 4 installments in April, June, September, and December
thousand each, paid in June and December
143
Monthly Cash Expenditures Worksheet:
(in $000s)
2012 --->
Nov
2013 --->
Dec
Materials Purchases
(reference only; not a cash flow)
Payments for materials purchases:
Other cash payments:
Production costs other than purchases
Selling and marketing Expenses
General and Administrative Expenses
Interest Payments
Tax payments
Dividend payments
Total Cash Outflows
Jan
$40
Feb
Mar Apr May Jun
Jul
2011 --->
Aug Sep Oct Nov Dec Jan Feb
$42
$43 $57 $68 $73 $67 $55 $52 $50 $43 $41 $42
$40
$42 $43 $57 $68 $73 $67 $55 $52 $50 $43 $41
$33
$24
$11
$34 $46 $54 $58 $54 $44 $42 $40 $34 $33 $33
$25 $26 $27 $36 $43 $46 $43 $35 $33 $32 $27
$11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11
$31
$25
$25
$25
$25
$50
$50
$112 $126 $175 $173 $255 $168 $150 $163 $128 $118 $218
$108
18-11.
Lifelong Appliances Cash Expenditures, Revised
Given:
2012 --->
Nov
Sales ($000s)
2013 --->
Dec
$131
Jan
$129
Dec
Materials purchasing Schedule: Order materials
Cost of materials =
Feb
$126
Mar Apr May Jun
Jul
2011 --->
Aug Sep Oct Nov Dec Jan Feb
$133 $139 $143 $191 $226 $242 $224 $184 $173 $166 $143 $136 $139
Jan
Feb
Mar
Manufacture Appliances Sell appliances Repeat each month
30% of sales
Payment schedule for materials:
30% paid in cash in month of purchase
70% paid in cash in month following month of purchase
Production costs other than purchases =
Selling and marketing Expenses =
General and Administrative Expenses =
Interest Payments =
Tax payments =
Dividend payments =
80%
19%
$11
$31
$100
$50
of purchases
of sales
thousand each month
thousand, paid in December
thousand, paid in 4 installments in April, June, September, and December
thousand each, paid in June and December
144
Monthly Cash Expenditures Worksheet:
(in $000s)
2012 --->
Nov
2013 --->
Dec
Materials Purchases
(reference only; not a cash flow)
Payments for materials purchases:
in month of purchase
in month following month of purchase
Other cash payments:
Production costs other than purchases
Selling and marketing Expenses
General and Administrative Expenses
Interest Payments
Tax payments
Dividend payments
Total Cash Outflows
Jan
$40
Feb
Mar Apr May Jun
Jul
2011 --->
Aug Sep Oct Nov Dec Jan Feb
$42
$43 $57 $68 $73 $67 $55 $52 $50 $43 $41 $42
$13
$28
$13 $17 $20 $22 $20 $17 $16 $15 $13 $12 $13
$29 $30 $40 $47 $51 $47 $39 $36 $35 $30 $29
$33
$24
$11
$34 $46 $54 $58 $54 $44 $42 $40 $34 $33 $33
$25 $26 $27 $36 $43 $46 $43 $35 $33 $32 $27
$11 $11 $11 $11 $11 $11 $11 $11 $11 $11 $11
$31
$25
$25
$25
$25
$50
$50
$113 $130 $178 $175 $254 $165 $149 $162 $126 $117 $219
$109
18-12.
Fit-and-Forget Fittings Cash Budget
Given:
Sales:
2012 --->
Nov
Sales ($000s)
$2,266
Dec
$2,230
2013 --->
Jan
Feb
$2,116
$2,300
Mar
$2,402
Apr
30% of customers pay off their accounts in month of sale
65% of customers pay off their accounts in first month following sale
5% of customers pay off their accounts in second month following sale
Purchases & Expenses:
Jan
Manufacture
Products
Feb
Sell
Products
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
2011 --->
Feb
$2,420 $3,390 $3,909 $4,164 $3,933 $3,163 $2,912 $2,886 $2,424 $2,353 $2,442
Collections:
Dec
Materials purchasing Order
Schedule: materials
May
Mar
Repeat each
month
Cost of materials
20% of sales
=
Payment schedule for materials:
20% paid in cash in month of purchase
80% paid in cash in month following month of purchase
145
Production costs other than purchases =
Selling and marketing Expenses =
General and Administrative Expenses =
Interest Payments =
Tax payments =
Dividend payments =
Cash Inflows:
14%
16%
$180
$500
$1,600
$855
(in $000s)
2012 ---> 2013 --->
Nov Dec
Jan
Feb
Mar
Cash collections:
in month of sale
first month after sale
second month after sale
Total monthly cash collections
Cash Outflows:
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
2011 --->
Jan Feb
$635 $690 $721 $726 $1,017 $1,173 $1,249 $1,180
$949
$874
$866
$727
1,450 1,375 1,495 1,561 1,573 2,204 2,541 2,707 2,556 2,056 1,893 1,876
113
112
106
115
120
121
170
195
208
197
158
146
$2,198 $2,177 $2,321 $2,402 $2,710 $3,497 $3,960 $4,082 $3,714 $3,126 $2,917 $2,749
(in $000s)
2012 ---> 2013 --->
Nov Dec
Jan
Feb
Mar
Materials Purchases
(reference only; not a cash flow)
Payments for materials purchases:
in month of purchase
in month following month of purchase
Other cash payments:
Production costs other than purchases
Selling and marketing Expenses
General and Administrative Expenses
Interest Payments
Tax payments
Dividend payments
Total Cash Outflows
$460
Net Cash Gain(Loss)
Cash Flow Summary:
of purchases
of sales
thousand each month
thousand, paid in December
thousand, paid in 4 installments in April, June, September, and December
thousand each, paid in June and December
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
$480
$484
$678
$782
$833
$787
$633
$582
$577
$485
$471
$488
$96
$368
$97
$384
$136
$387
$156
$542
$167
$625
$157
$666
$127
$629
$116
$506
$115
$466
$97
$462
$94
$388
$98
$376
$67
$339
$180
$68
$368
$180
$95
$384
$180
$109
$387
$180
$117
$542
$180
$110
$625
$180
$89
$666
$180
$82
$629
$180
$81
$506
$180
$68
$466
$180
$66
$462
$180
$68
$388
$180
$500
$400
$400
$400
$400
$855
$855
$1,050 $1,097 $1,182 $1,775 $1,631 $2,994 $1,691 $1,513 $1,748 $1,273 $1,190 $2,865
$1,148 $1,080 $1,139
$627 $1,079
$503 $2,269 $2,569 $1,965 $1,854 $1,727
($117)
Apr
Jun
Dec
(in $000s)
Jan
1. Cash Balance at start of month
2. Net Cash Gain(Loss) during month
3. Cash balance at end of month before financing
(line 1 plus line 2)
4. Minimum Cash Balance Desired
5. Surplus cash(deficit) (Line 3 minus line 4)
Feb
Mar
May
Jul
Aug
Sep
Oct
Nov
$1,133 $2,281 $3,361 $4,500 $5,127 $6,206 $6,709 $8,978 $11,547 $13,512 $15,366 $17,093
1,148 1,080 1,139
627 1,079
503 2,269 2,569 1,965 1,854 1,727
(117)
2,281 3,361 4,500 5,127 6,206 6,709 8,978 11,547 13,512 15,366 17,093 16,976
1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110 1,110
$1,171 $2,251 $3,390 $4,017 $5,096 $5,599 $7,868 $10,437 $12,402 $14,256 $15,983 $15,866
146
2011 --->
Jan Feb
External Financing Summary:
(in $000s)
6. External financing balance at start of month
7. New financing required
(negative amount from line 5)
8. Financing repayments
(positive amount from line 5)
9. External financing balance at end of month
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
$0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10. Cash balance at end of month after financing $2,281 $3,361 $4,500 $5,127 $6,206 $6,709 $8,978 $11,547 $13,512 $15,366 $17,093 $16,976
147
Chapter 19 Solutions
Answers to Review Questions
1.
Accounts receivable are sometimes not collected. Why do companies extend trade credit when they
could insist on cash for all sales?
Extending trade credit almost always leads to more sales. If the incremental cashflows, including the
investment in accounts receivable give a positive NPV, the decision to extend trade credit would
increase the value of the firm.
2.
Inventory is sometimes thought of as a necessary evil. Explain.
Inventory ties up funds and these funds are not earning an explicit return. Some inventory is often
necessary, however, as companies try to hold the lowest acceptable amount.
3.
What are the primary variables being balanced in the EOQ inventory model? Explain
The primary variables being balanced in the EOQ model are carrying costs and ordering costs. The
more frequent orders are placed the lower the firm’s carrying costs and the higher its ordering costs.
4.
What are the benefits of the JIT inventory control system?
The just-in-time (JIT) inventory control system lowers inventory carrying costs and tends to increase
quality.
5.
What are the primary requirements for a successful JIT inventory control system?
For a JIT system to be successful the supplier must be willing and able to deliver materials
immediately and the quality of delivered materials must be high.
6.
Can a company have a default rate on its accounts receivable that is too low? Explain.
A company could have a default rate on AR that would be considered too low if by liberalizing credit
terms a significant increase in sales revenue and cash inflows were to result. If the increase in the
default rate is more than offset by the increase in sales revenue, after all incremental cash flows are
considered a positive NPV could result.
7.
How does accounts receivable factoring work? What are the benefits to the two parties involved?
What are the risks?
148
Factoring is when one firm sells accounts receivable (AR) to another. The purchasing firm is called
a factor. The factor makes a profit by purchasing the AR at a discount. Its risk is that some of the
AR may default. The selling firm gets the cash it needs.
Answers to End-of-Chapter Problems
19-1. Accounts Receivable, ACP:
Accounts Receivable = ACP X Sales/365 = 22 X $8,030,000/365 = $484,000
19-2. Accounts Receivable, ACP:
Accounts Receivable = ACP X Sales/365 = 26 X $7,600,000/365 = $541,369.86
The company appears to have relaxed its credit policy since accounts receivable increased as did the
average collection period.
19-3. Accounts Receivable, ACP, Credit Policy:
(a) ACP = 0.4 X 15 + 0.57 X 60 + 0.03 X 100 = 43.2 days
(b) AR = 43.2 X $730,000/365 = $86,400
19-4. Accounts Receivable, ACP, Credit Policy:
ACP = 0.4 X 10 + 0.58 X 30 + 0.02 X 100 = 23.4 days
AR = 23.4 X $657,000/365 = $42,120
19-5.
(0.25 X 10) + (0.60 X 20) + (0.15 X 30) =
2.5 + 12 + 4.5 = 19 days
19-6.
(0.32 X 10) + (0.67 X 30) + (0.01 X 45) =
3.2 + 20.1 + 0.45 = 23.75 days
No, the new policy should not be implemented because the ACP would increase.
149
19-7 Effect of Change of Credit Policy:
Given:
All sales on credit
Old credit terms
New credit terms
2/15, n40
2/15, n60
Sales expected under old credit policy:
Sales change expected with new credit policy:
$350,000
20%
increase
Under old credit policy:
40% of customers take discount, pay in 15 days
58% of customers pay at the end of
40 days
2% of customers pay in
100 days
Under new credit policy:
40% of customers take discount, pay in 15 days
57% of customers pay at the end of
60 days
3% of customers pay in
100 days
Bad debt expenses under old credit policy:
Bad debt expenses under new credit policy:
Short-term interest rate
Long term interest rate
Income tax rate
Cost of capital
Cost of goods sold
Other operating expenses
2%
3%
of sales
of sales
7%
10%
40%
11%
80% of sales
$10,000 under old credit policy
Question a:
Average collection period under old policy
Average collection period under new policy
Accounts Receivable under old policy
Accounts Receivable under new policy
31.2 days (weighted average of customers paying)
43.2 days (weighted average of customers paying)
$29,918 AR = ACP X Credit sales per day
$49,710 AR = ACP X Credit sales per day
Question b:
East-West Trading Company Financial Statements
INCOME STATEMENT
With old
With new
credit
credit
terms:
terms:
2/15, n40 2/15, n60
(given) (pro forma)
Sales (all on credit)
Cost of Goods Sold
Gross Profit
Bad debt expenses
Other operating expenses
Operating Income
Interest Expense
Before-Tax Income
Income Taxes
Net Income
$350,000
280,000
70,000
7,000
10,000
53,000
5,450
47,550
19,020
$28,530
$420,000
$336,000
84,000
12,600
$12,000
59,400
5,940
53,460
21,384
$32,076
20% increase
increase in proportion with sales
from assumptions
increase in proportion with sales
(ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of Debt)
150
BALANCE SHEET, as of Dec 31
Assets
Current Assets:
Cash & Securities
Accounts Receivable
Inventory
Total Current Assets
Property, Plant & Equipment, Net
Total Assets
Liabilities & Equity
Current Liabilities:
Accounts Payable
Notes Payable
Total Current Liabilities
Long-Term Debt
Total Liabilities
Common Stock
Capital in Excess of Par
Retained Earnings
Total Stockholders' Equity
Total Liabilities & Equity
$15,000
29,918
50,000
94,918
120,000
$214,918
$18,000
49,710
60,000
127,710
120,000
$247,710
increase in proportion with sales
from Tab a
increase in proportion with sales
$14,918
35,000
49,918
30,000
79,918
25,000
60,000
50,000
135,000
$214,918
$17,902
$42,000
59,902
30,000
89,902
25,000
60,000
50,000
135,000
$224,902
increase in proportion with sales
increase in proportion with sales
AFN to balance:
same
same
same
same
same
$22,808 obtain from ST sources
Question c:
Incremental cash flows associated with the credit policy change
Initial investment at T-0
($22,808) AFN from Tab B
Future incremental cash flows, T-1 onward:
Inflows:
Increase in Sales
Outflows:
Increase in Cost of Goods Sold
Increase in Bad Debt Expense
Increase in Other Operating Exps
Increase in Interest Expense
Increase in Taxes
Total Outflows
$70,000
$56,000
$5,600
$2,000
$490
$2,364
$66,454
Net future incremental cash flows
$3,546 each year from T-1 onward
Question d, Investment Decision:
NPV of the Credit Policy Change:
Initial Investment
($22,808)
NPV =
Future Cash Flows
$3,546
per year
$9,428 at a cost of capital of
151
11%
19-8.
Given:
All sales on credit
Old credit terms
New credit terms
2/15, n40
2/15, n60
Sales expected under old credit policy:
Sales change expected with new credit policy:
$350,000
20%
increase
Under old credit policy:
40% of customers take discount, pay in 15 days
58% of customers pay at the end of
40 days
2% of customers pay in
100 days
Under new credit policy:
30% of customers take discount, pay in 15 days
60% of customers pay at the end of
60 days
10% of customers pay in
100 days
Bad debt expenses under old credit policy:
Bad debt expenses under new credit policy:
Short-term interest rate
Long term interest rate
Income tax rate
Cost of capital
Cost of goods sold
Other operating expenses
2%
4%
of sales
of sales
7%
10%
40%
11%
80% of sales
$10,000 under old credit policy
Question a:
Average collection period under old policy
Average collection period under new policy
Accounts Receivable under old policy
Accounts Receivable under new policy
31.2 days (weighted average of customers paying)
50.5 days (weighted average of customers paying)
$29,918 AR = ACP X Credit sales per day
$58,110 AR = ACP X Credit sales per day
Question b:
East-West Company Financial Statements
INCOME STATEMENT
With old
With new
credit
credit
terms:
terms:
2/15, n40 2/15, n60
(given) (pro forma)
Sales (all on credit)
Cost of Goods Sold
Gross Profit
Bad debt expenses
Other operating expenses
Operating Income
Interest Expense
Before-Tax Income
Income Taxes
$350,000
280,000
70,000
7,000
10,000
53,000
5,450
$420,000
$336,000
84,000
16,800
$12,000
55,200
5,940
47,550
19,020
49,260
19,704
152
20% increase
increase in proportion with sales
from assumptions
increase in proportion with sales
(ST Debt X ST Cost of Debt) +
(LT Debt X LT Cost of Debt)
Net Income
$28,530
$29,556
BALANCE SHEET, as of Dec 31
Assets
Current Assets:
Cash & Securities
Accounts Receivable
Inventory
Total Current Assets
Property, Plant & Equipment, Net
Total Assets
Liabilities & Equity
Current Liabilities:
Accounts Payable
Notes Payable
Total Current Liabilities
Long-Term Debt
Total Liabilities
Common Stock
Capital in Excess of Par
Retained Earnings
Total Stockholders' Equity
Total Liabilities & Equity
$15,000
29,918
50,000
94,918
120,000
$214,918
$18,000 increase in proportion with sales
58,110
60,000 increase in proportion with sales
136,110
120,000 same
$256,110
$14,918
35,000
49,918
30,000
79,918
25,000
60,000
50,000
135,000
$214,918
$17,902
$42,000
59,902
30,000
89,902
25,000
60,000
50,000
135,000
$224,902
AFN to balance:
increase in proportion with sales
increase in proportion with sales
same
same
same
same
$31,208 obtain from ST sources
Question c:
Incremental cash flows associated with the credit policy change
Initial investment at T-0
($31,208) AFN
Future incremental cash flows, T-1 onward:
Inflows:
Increase in Sales
Outflows:
Increase in Cost of Goods Sold
Increase in Bad Debt Expense
Increase in Other Operating Exps
Increase in Interest Expense
Increase in Taxes
Total Outflows
$70,000
$56,000
$9,800
$2,000
$490
$684
$68,974
Net future incremental cash flows
$1,026 each year from T-1 onward
Question d, Investment Decision:
NPV of the Credit Policy Change:
Initial Investment Future Cash Flows
($31,208)
NPV =
$1,026
per year
($21,881) at a cost of capital of 11%
153
19-9. Effect of Change of Credit Policy:
Given:
All sales on credit
Old credit terms
New credit terms
3/10, n40
3/15, n30
Sales expected under old credit policy:
Sales change expected with new credit policy:
$2,000,000
-10%
decrease
Under old credit policy:
30% of customers take discount, pay in
60% of customers pay at the end of
10% of customers pay in
10 days
40 days
100 days
Under new credit policy:
42% of customers take discount, pay in
57% of customers pay at the end of
1% of customers pay in
15 days
30 days
100 days
Bad debt expenses under old credit policy:
Bad debt expenses under new credit policy:
Short-term interest rate
Long term interest rate
Income tax rate
Cost of capital
Cost of goods sold
Other operating expenses
3%
1%
of sales
of sales
8%
11%
40%
13%
80% of sales
$60,000 under old credit policy
Question a:
Average collection period under old policy
Average collection period under new policy
Accounts Receivable under old policy
Accounts Receivable under new policy
37 days (weighted average of customers paying)
24.4 days (weighted average of customers paying)
$202,740 AR = ACP X Credit sales per day
$120,329 AR = ACP X Credit sales per day
Question b:
A-Z Trading Company Financial Statements
INCOME STATEMENT
With old
With new
credit
credit
terms:
terms:
3/10, n40 3/15, n30
(given) (pro forma)
Sales (all on credit)
Cost of Goods Sold
Gross Profit
Bad debt expenses
Other operating expenses
Operating Income
Interest Expense
Before-Tax Income
Income Taxes
Net Income
$2,000,000 $1,800,000 10% decrease
1,600,000 $1,440,000 decrease in proportion with sales
400,000
360,000
60,000
18,000 from assumptions
60,000
$54,000 decrease in proportion with sales
280,000
288,000
34,810
33,210 (ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of Debt)
245,190
254,790
98,076
101,916
$147,114 $152,874
154
BALANCE SHEET, as of Dec 31
Assets
Current Assets:
Cash & Securities
$86,000
$77,400
Accounts Receivable
202,740
120,329
Inventory
285,000
256,500
Total Current Assets
573,740
454,229
Property, Plant & Equipment, Net
652,000
652,000
Total Assets
$1,225,740 $1,106,229
Liabilities & Equity
Current Liabilities:
Accounts Payable
$85,000
$76,500
Notes Payable
200,000 $180,000
Total Current Liabilities
285,000
256,500
Long-Term Debt
171,000
171,000
Total Liabilities
456,000
427,500
Common Stock
143,000
143,000
Capital in Excess of Par
342,000
342,000
Retained Earnings
285,000
285,000
Total Stockholders' Equity
770,000
770,000
Total Liabilities & Equity
$1,225,740 $1,197,500
AFN to balance:
decrease in proportion with sales
decrease in proportion with sales
same
decrease in proportion with sales
decrease in proportion with sales
same
same
same
same
($91,271) excess financing
Question c:
Incremental cash flows associated with the credit policy change
Initial investment at T-0
$91,271
Future incremental cash flows, T-1 onward:
Inflows:
Increase in Sales
Outflows:
Increase in Cost of Goods Sold
Increase in Bad Debt Expense
Increase in Other Operating Exps
Increase in Interest Expense
Increase in Taxes
Total Outflows
($200,000)
($160,000)
($42,000)
($6,000)
($1,600)
$3,840
($205,760)
Net future incremental cash flows
$5,760 each year from T-1 onward
Question d, Investment Decision:
NPV of the Credit Policy Change:
Initial Investment Future Cash Flows
$91,271
NPV =
$5,760 per year
$135,579 at a cost of capital of 13%
155
19-10. Economic Order Quantity
EOQ = √[2 X 500 X $250/$300] = 28.87 units ≈ 29 units
Number of orders per year = 500/29 = 17.24 orders ≈ 17 orders
Ordering Cost = 17 X $250 = $4,250
19-11. Economic Order Quantity:
EOQ = √[2 X 500 X $250/$330] = 27.52 units ≈ 28 units
Number of orders per year = 500/28 = 17.86orders ≈ 18 orders
Ordering cost = 18 X $250 = $4,500
19-12. a) √ (2 X 1,200 X $250) / $100
√ 6,000
=
= 77.46 units per order
b) 1200 / 78 = 15.38 orders per year
19-13. Sales (2010) = 200 X (1 + 0.25) = 250 units
Carrying Costs = $150 X (1 + 0.10) = $165
Ordering Costs = $50 X (1 + 0.10) = $55
√ (2 X 250 X $55) / $165 = √ 166.66
= 12.91 units
19-14. Credit Scoring
Total Score = 3 + 4 + 3 + 4 + 3 + 2 = 19 > 12. Yes, Danny should approve the credit.
19-15.
Criteria
Length of
payment:
Points
Score
time since last delinquent
Greater 2.5 years
2-2.5 years
1.5-2 years
1-1.5 years
Less than 1 year
Length of Time in Business
Greater 5 years
4-5 years
3-4 years
2-3 years
Less than 2 years
156
4
3
2
1
0
___4____
_______
_______
_______
_______
4
3
2
1
0
___4____
_______
_______
_______
_______
Net Income
Greater $100,000
$75,000-$100,000
$50,000-$75,000
$25,000-$50,000
Less than $25,000
4
3
2
1
0
_______
_______
___2____
_______
_______
Total Score: 10
$1,200,000 X 0.30 = $360,000
Yes, they will be approved. TWI will be approved for $360,000.
19-16.
Sunrise Corporation Inventory Policy
Given:
Present inventory level
Proposed inventory level
60
100
Sales expected under old inventory policy:
Sales expected with new inventory policy:
Ordering cost
Carrying cost
Unit sales price
Unit purchase price
350
450
units per year
units per year
$200 per order
$600 per unit per year
$10,000
$8,000
Short-term interest rate
7%
Long term interest rate
10%
Income tax rate
40%
Cost of capital
11%
Cost of goods sold
80% of sales
Other operating expenses $100,000 under current inventory policy
Question a:
Under old inventory policy Under new inventory policy
60 units
100 units
E.O.Q
Number of orders per year
Ordering cost
Carrying cost
Total inventory cost
15
23
$4,583
$36,000
$40,583
157
17
26
$5,196
$60,000
$65,196
Question b:
Sunrise Company Financial Statements
INCOME STATEMENT
Under old inventory
policy
60 units
(given)
Sales (all on credit)
Cost of Goods Sold
Gross Profit
Inventory costs
Other operating expenses
Operating Income
Interest Expense
Before-Tax Income
Income Taxes
Net Income
Under new inventory policy
100 units
(pro
forma)
$3,500,000 $4,500,000 unit sales x price, from assumptions
2,800,000 3,600,000 unit sales x purchase price, from assumptions
700,000
900,000
40,583
65,196 from Tab a
100,000
128,571 increase in proportion with sales
559,417
706,232
13,150
15,050 (ST Debt X ST Cost of Debt) + (LT Debt X LT Cost of
Debt)
546,267
691,182
218,507
276,473
$327,760 $414,709
BALANCE SHEET, as of Dec 31
Assets
Current Assets:
Cash & Securities
Accounts Receivable
Inventory
Total Current Assets
Property, Plant & Equipment,
Net
Total Assets
Liabilities & Equity
Current Liabilities:
Accounts Payable
Notes Payable
Total Current Liabilities
Long-Term Debt
Total Liabilities
Common Stock
Capital in Excess of Par
Retained Earnings
Total Stockholders' Equity
Total Liabilities & Equity
$55,000
105,000
480,000
640,000
100,000
70,714 increase in proportion with sales
135,000 increase in proportion with sales
800,000 assumed inventory level x unit purchase price, from
assumptions
1,005,714
100,000 same
$740,000 $1,105,714
$100,000
95,000
195,000
65,000
260,000
60,000
220,000
200,000
480,000
$740,000
AFN to balance:
128,571
122,143
250,714
65,000
315,714
60,000
220,000
200,000
480,000
$795,714
increase in proportion with sales
increase in proportion with sales
same
same
same
same
$310,000
Question c:
Incremental cash flows associated with the credit policy change
Initial investment at T-0
($310,000) AFN
Future incremental cash flows, T-1 onward:
Inflows:
158
Increase in Sales
Outflows:
Increase in Cost of Goods Sold
Increase in Inventory Expense
Increase in Other Operating Exps
Increase in Interest Expense
Increase in Taxes
Total Outflows
$1,000,000
$800,000
$24,614
$28,571
$1,900
$57,966
$913,051
Net future incremental cash flows
$86,949 each year from T-1 onward
Question d, Investment Decision:
NPV of the Credit Policy Change:
Initial Investment
Future Cash Flows
($310,000)
NPV =
$86,949
per year
$480,445 at a cost of capital of
11%
19-17.
Given:
Present inventory level
Proposed inventory level
60
90
Sales expected under old inventory policy:
Sales expected with new inventory policy:
Ordering cost
Carrying cost
Unit sales price
Unit purchase price
Short-term interest rate
Long term interest rate
Income tax rate
Cost of capital
Cost of goods sold
Other operating expenses
350
390
units per year
units per year
$200 per order
$600 per unit per year
$10,000
$8,000
7%
10%
40%
11%
80% of sales
$100,000 under current inventory policy
Question a:
Under old inventory policy Under new inventory policy
60 units
90 units
E.O.Q
Number of orders per year
Ordering cost
Carrying cost
Total inventory cost
15
23
$4,583
$36,000
$40,583
159
16
24
$4,837
$54,000
$58,837
Question b:
Sunrise Company Financial Statements
INCOME STATEMENT
Under old inventory policy
60 units
(given)
Sales (all on credit)
Cost of Goods Sold
Gross Profit
Inventory costs
Other operating expenses
Operating Income
Interest Expense
Before-Tax Income
Income Taxes
Net Income
Under new inventory policy
90 units
(pro forma)
$3,500,000
2,800,000
700,000
40,583
100,000
559,417
13,150
$3,900,000
3,120,000
780,000
58,837
111,429
609,734
13,910
546,267
218,507
$327,760
595,824
238,330
$357,494
unit sales x price, from assumptions
unit sales x purchase price, from assumptions
increase in proportion with sales
(ST Debt X ST Cost of Debt) +
(LT Debt X LT Cost of Debt)
BALANCE SHEET, as of Dec 31
Assets
Current Assets:
Cash & Securities
Accounts Receivable
Inventory
$55,000 61,286 increase in proportion with sales
105,000 117,000 increase in proportion with sales
480,000 720,000 assumed inventory level x unit
purchase price, from assumptions
Total Current Assets
640,000 898,286
Property, Plant & Equipment, Net 100,000 100,000 same
Total Assets
$740,000 $998,286
Liabilities & Equity
Current Liabilities:
Accounts Payable
$100,000 111,429 increase in proportion with sales
Notes Payable
95,000 105,857 increase in proportion with sales
Total Current Liabilities
195,000 217,286
Long-Term Debt
65,000 65,000 same
Total Liabilities
260,000 282,286
Common Stock
60,000 60,000 same
Capital in Excess of Par
220,000 220,000 same
Retained Earnings
200,000 200,000 same
Total Stockholders' Equity
480,000 480,000
Total Liabilities & Equity
$740,000 $762,286
AFN to balance:
$236,000
Question c:
Incremental cash flows associated with the credit policy change
Initial investment at T-0
($236,000) AFN
Future incremental cash flows, T-1 onward:
Inflows:
Increase in Sales
Outflows:
Increase in Cost of Goods Sold
$400,000
$320,000
160
Increase in Inventory Expense
Increase in Other Operating Exps
Increase in Interest Expense
Increase in Taxes
Total Outflows
$18,255
$11,429
$760
$19,823
$370,266
Net future incremental cash flows
$29,734 each year from T-1 onward
Question d, Investment Decision:
NPV of the Credit Policy Change:
Initial Investment Future Cash Flows
($236,000)
NPV =
$29,734 per year
$34,309 at a cost of capital of 11%
19-18.
Given:
Inventory Level in Units
Present inventory level
Proposed inventory level (1)
Proposed inventory level (2)
Proposed inventory level (3)
70
80
90
100
Expected Sales
340
375
390
400
Ordering cost
Carrying cost
units per year
units per year
units per year
units per year
$160 per order
$400 per unit per year
Unit sales price
Unit purchase price
$16,000
$12,800
Short-term interest rate
Long term interest rate
Income tax rate
Cost of capital
Cost of goods sold
Other operating expenses
7%
11%
40%
13%
80% of sales
$130,000 under current inventory policy
Question a:
Under old inventory
policy
70 units
E.O.Q
Number of orders per
year
Ordering cost
Carrying cost
Total inventory cost
Under new inventory
policy (1)
80 units
Under new inventory
policy (2)
90 units
Under new inventory
policy (3)
100 units
16
21
17
22
18
22
18
22
$3,298
$28,000
$31,298
$3,464
$32,000
$35,464
$3,533
$36,000
$39,533
$3,578
$40,000
$43,578
161
Question b:
Windermere Corporation
INCOME STATEMENT
Under old inventory
policy
70 units
(given)
Sales (all on credit)
Cost of Goods Sold
Gross Profit
Inventory costs
Other operating
expenses
Operating Income
Interest Expense
Before-Tax Income
Income Taxes
Net Income
Under new inventory
policy (1)
80 units
(pro forma)
Under new inventory
policy (2)
90 units
(pro forma)
Under new inventory
policy (3)
100 units
(pro forma)
$5,440,000
4,352,000
1,088,000
31,298
130,000
$6,000,000
4,800,000
1,200,000
35,464
143,382
$6,240,000
4,992,000
1,248,000
39,533
149,118
$6,400,000
5,120,000
1,280,000
43,578
152,941
926,702
13,800
912,902
365,161
$547,741
1,021,154
14,485
1,006,669
402,668
$604,001
1,059,350
14,778
1,044,572
417,829
$626,743
1,083,481
14,974
1,068,508
427,403
$641,105
BALANCE SHEET, as of Dec 31
Assets
Current Assets:
Cash & Securities
$65,000
71,691
74,559
Accounts Receivable
114,000
125,735
130,765
Inventory
896,000 1,024,000 1,152,000
Total Current Assets
1,075,000 1,221,426 1,357,324
Property, Plant & Equipment, Net
113,000
113,000
113,000
Total Assets
$1,188,000 $1,334,426 $1,470,324
Liabilities & Equity
Current Liabilities:
Accounts Payable
$110,000
121,324
126,176
Notes Payable
95,000
104,779
108,971
Total Current Liabilities
205,000
226,103
235,147
Long-Term Debt
65,000
65,000
65,000
Total Liabilities
270,000
291,103
300,147
Common Stock
80,000
80,000
80,000
Capital in Excess of Par
320,000
320,000
320,000
Retained Earnings
518,000
518,000
518,000
Total Stockholders' Equity
918,000
918,000
918,000
Total Liabilities & Equity
$1,188,000 $1,209,103 $1,218,147
AFN to balance:
$125,324
$252,176
76,471
134,118
1,280,000
1,490,588
113,000
$1,603,588
129,412
111,765
241,176
65,000
306,176
80,000
320,000
518,000
918,000
$1,224,176
$379,412
Question c:
Incremental cash flows associated with the credit policy changes
Under new inventory policy Under new inventory policy
Under new inventory policy (3)
(1)
(2)
80 units
90 units
100 units
Initial investment at T-0
($125,324)
($252,176) ($379,412) Excess financing
(AFN)
162
Future incremental cash flows, T-1 onward:
Inflows:
Increase in Sales
Outflows:
Increase in Cost of Goods
Sold
Increase in Inventory Expense
Increase in Other Operating
Exps
Increase in Interest Expense
Increase in Taxes
Total Outflows
Net future incremental cash
flows
$560,000
$800,000 $960,000
$448,000
$640,000 $768,000
$4,166
$13,382
$8,234
$19,118
$685
$37,507
$503,740
$12,279
$22,941
$978
$1,174
$52,668
$62,242
$720,998 $866,636
$56,260
$79,002
$93,364 each year from T-1
onward
Question d, Investment Decision:
NPV of the Credit Policy Change:
Initial Investment Future Cash Flows per Year
Under new inventory policy (1)
Under new inventory policy (2)
Under new inventory policy (3)
($125,324)
($252,176)
($379,412)
$56,260
$79,002
$93,364
NPV
at a cost of capital of
13%
$307,449
$355,532
$338,770
Comments: All three proposed inventory policy changes have positive NPVs, and would therefore
be acceptable at the firm's cost of capital of 13%. Policy #2, inventory level of 90 units, has the
highest NPV, so it should be the alternative selected.
163
Chapter 20 Solutions
Answers to Review Questions
1.
Companies with rapidly growing levels of sales do not need to worry about raising funds from
outside the firm. Do you agree or disagree with this statement? Explain.
Disagree. Rapidly growing firms need more assets to accommodate the increasing sales. Such firms
are more likely, not less, to seek outside financing. Internal funds are often insufficient.
2.
Banks like to make short-term, self-liquidating loans to businesses. Why?
Banks like to be able to see where the funds are likely to come from such that the borrower is able to
use to make the required loan payments. Short term, self-liquidating loans do this since the borrowed
funds are used to purchase assets that generate the needed funds.
3.
What are compensating balances and why do banks require them from some customers? Under what
circumstances would banks be most likely to impose compensating balances?
Compensating balances are funds that a bank requires a customer to maintain in a non-interest
bearing account until the loan is retired. Banks sometimes impose compensating balance
requirements so as to increase the bank’s return on a loan. Compensating balances are most likely to
be used when the stated interest rate on a loan is below the bank’s required rate of return.
4.
What happens when a bank charges discount interest on a loan?
When a bank charges discount interest on a loan the required interest payment is subtracted from the
loan proceeds at the time the loan is made. This makes the effective interest rate greater than the
stated rate.
5.
What is trustworthy collateral from the lenders’ perspective? Explain whether accounts receivable
and inventory are trustworthy collateral.
Assets that are readily marketable, of stable value, and not likely to “disappear” make for trustworthy
collateral. Accounts receivable and inventory could meet this test depending upon their particular
characteristics.
6.
Trade credit is free credit. Do you agree or disagree with this statement? Explain.
Trade credit is not free. It has a cost. Who bears that cost depends on the terms of the transaction
between the grantor and the recipient of the trade credit.
164
7.
What are the pros and cons of commercial paper relative to bank loans for a company seeking shortterm financing?
Commercial paper is usually a cheaper source of short-term financing for a firm, compared to bank
loans. Also, a larger amount of funds can often be raised by issuing commercial paper. Bank loans
are usually a more flexible source of short-term financing and establishing an on-going business
relationship with a bank may prove beneficial when money is tight.
Answers to End-of-Chapter Problems
20-1.
a) at the end of the year $1,600/$20,000 = 8%
b) at the beginning of the year (discount loan) $1,600/($20,000 - $1,600) = 8.696%
20-2.
Effective annual interest
= $2,400/($40,000 - $2,400 - $40,000 X 0.10)
= $2,400/$33,600 = 7.143%
20-3.
a) Effective annual interest = 1,800/20,000 =
b) Interest = $20,000 X 0.08 =
Effective annual interest = 1,600/(20,000-1,600) = 1,600/18,400 =
c) Interest = $20,000 X 0.075 =
Compensating balance = $20,000 X 0.10 =
Effective annual interest = $1,500/($20,000 - $2,000) = 1,500/18,000 =
9%
$1,600
8.70%
$1500
$2,000
8.33%
(i) Which alternative is best for Ralph from minimum effective interest rate point of view?
Alternative c
(ii)
Let B be the amount Ralph should borrow
So, X - 0.1 X B = $20,000
Solving, B = $22,222.22
So, Ralph should borrow $22,222.22 and
Interest payment = 22,222.22 X .075 = $1,666.67
20-4.
Interest = 14,000 X (0.16/4) = $560
Compensating Balance = 14,000 X 0.10 = $1400
Effective annual interest = {1 + [560/(14,000 - 1,400 - 560)]}4 - 1 = 19.94%
20-5.
Duration of loan = 2 weeks = 1/26 year
Interest = 10,000 X (0.07/26) = $26.92
Compensating Balance = 10,000 X 0.10 = $1,000
Effective annual interest = [1 + 26.92/(10,000 - 1,000 - 26.92)]26 - 1 = 8.10%
165
20-6.
a) Discount = 0.06 X $1,000,000 X 60/360 = $10,000
b) Price = $1,000,000 - $10,000 = $990,000
c) Effective annual interest rate = [$1,000,000/$990,000]365/60 - 1 = 6.305%
20-7.
Discount = 0.04 X $2,000,000 X 60/360 = $13,333.33
Price = $2,000,000 - $13,333.33 = $1,986,666.67
Effective annual interest rate = [$2,000,000/$1,986,666.67]365/60 - 1 = 4.15%
20-8.
[1 + 2/98]365/(45 - 15) - 1 = 27.86%
20-9.
a) 3/10, n 60
[1 + 3/97]365/(60 - 10) - 1 = 24.90%
b) 2/15, n 30
[1 + 2/98]365/(30 - 15) - 1 = 63.49%
Re-calculate the costs assuming payments were made on the 40th day in each of the above cases. Compare
your results.
a) 3/10, n 60
[1 + 3/97]365/(40 - 10) - 1 = 44.86% (Higher)
b) 2/15, n 30
[1 + 2/98]365/(40 - 15) - 1 = 34.31% (Lower)
20-10. k = [1 + (3 / (100 – 3)) (365 / (45 –15))] – 1
k = .4486 = 44.86%
20.11. a) (.038 X $2,000,000 X 90) / 360 = $19,000
b) $2,000,000 - $19,000 = $1,981,000
c) ($2,000,000 / $1,981,000)(365/90) – 1 = .03947 = 3.95%
20-12. $20,000 X 0.065 = $1,300 (interest)
$1,300 / ($20,000 - $1,300) = .0695 = 6.95%
20-13. $30,000 X 0.10 = $3,000
$30,000 X 0.13 = $3,900
$3,000 / ($30,000 - $3,900) = .1149 = 11.5%
20-14. a)
b)
c)
d)
1.00512 – 1 = 0.0617 = 6.17%
1.00612 – 1 = 0.0744 = 7.44%
1.0075 12 – 1 = 0.0938 = 9.38%
1.008 12 – 1 = 0.1003 = 10.03%
166
20-15. a) [1 + 1/99]365/(45 - 10) - 1 =11.05% (Lower)
b) Interest = $100,000 X 0.10 = $10,000
Effective annual interest = $10,000/($100,000 - $10,000) = 11.11%
a is the better source since 11.11% is higher than 11.05%.
20-16. a) [1 + 1/99]365/(60 - 15) - 1 = 8.49%
b) Interest = $100,000 X 0.10 = $12,000
Compensating Balance = $100,000 X 0.12 = $12,000
Effective annual interest = $10,000/($100,000 - $10,000 - $12,000) = 12.82%
a is still the better source.
20-17. $1,500,000 / (1 - 0.09 – 0.12) = $1,898,734.18
167
Chapter 21 Solutions
Answers to Review Questions
1.
What does it mean when the U.S. dollar weakens in the foreign exchange market?
When the U.S. dollar weakens in the foreign exchange market one U.S. dollar buys fewer units of
another country’s currency. It costs more U.S. dollars to buy a given quantity of another country’s
currency.
2.
What kinds of U.S. companies would benefit most from a stronger dollar in the foreign exchange
market? Explain.
U.S. companies that import goods from other countries would benefit from a stronger dollar. More
units of a foreign currency could be purchased for a given number of dollars. Other things equal, this
would lower the cost of foreign goods for the U.S. importer.
3.
Under what circumstance would the U.S. dollar and the Canadian dollar be said to have achieved
purchasing power parity?
The U.S. dollar and the Canadian dollar would be considered to have achieved purchasing power
parity when the exchange rate reflects the relative prices of a market basket of traded goods and
services at the current exchange rate. There would be no incentive to convert U.S. dollars to
Canadian dollars nor to convert Canadian dollars to U.S. dollars and purchase goods or services in
the other country.
4.
What are some of the primary advantages when a corporation has operations in countries other than
its home country? What are some of the risks?
Foreign operations may reduce a company’s labor or material costs, and may increase its sales.
Risks include possible seizure of company assets by a foreign government, possible cultural blunders
that lead to lost sales, and exchange rate risks.
5.
What is GATT, and what is its goal?
GATT is the General Agreement on Tariffs and Trade. It is a treaty that seeks to reduce trade
barriers among participant nations.
168
Answers to End-of-Chapter Problems
21-1.
a) British pound
b) Indian rupee
c) Japanese yen
d) Australian dollar
e) Mexican peso
f) Israeli shekel
1,000,000/1.5616
1/.017778
1/.012475
1/1.0054
1/.0721
1/.2570
=
=
=
=
=
=
£640,369
Rs56.249 million
¥80.160 million
A$994.629 thousand
Peso 13.869 million
Shekel 3.891 million
21-2.
a) Chilean pesos
1/.001992
b) HK dollars
1/.1289
c) Singaporean dollars
1/.7833
d) euros
1,000,000/1.2558
e) Indian rupees
1/.017778
f) Mexican pesos
1/.0721
g)Thai baht
1/.0315
=
=
=
=
=
=
=
Pesos 502.008 million
HK$7.758 million
S$1.277 million
796,305
Rs56.249 million
Peso 13.870 million
Baht 31.746 million
21-3.
a) 2 million Australian dollars
b) 1.6 million Singaporean dollars
c) 5 million euros
d) 2.6 million Mexican pesos
e) 2 million Japanese yen
f) 25 million Thai baht
2 X 1.0054
1.6 X 0.7833
5 X 1.2558
2.6 X 0.0721
2 X 0.012475
25 X 0.0135
=
=
=
=
=
=
$2,010,800
$1,253,280
$6,279,000
$187,460
$24,950
$337,500
21-4.
a) 1.2558
b) (1) $100,000 X 80.16032064 = 8,016,032
(2) $100,000 X 0.640368852 = 64,037
(3) $100,000 X 1.025956705 = 102,596
(4) $100,000 X 13.86962552 = 1,386,963
21-5.
a) 93.38812103 X 0.0721 = 5.7796 ¥ / peso
b) 13.86962552 X 1.5616 = 21.6588 pesos / ₤
c) .796305144 X 0.9747 = 0.7762 € / Canadian Dollar
d) 93.38812103 X 0.9747 = 78.1323 ¥ / Canadian Dollar
21-6.
0.8910 X 1/0.2567 = 3.4710
21-7.
1 euro = 58 rupees = 9.67 HK dollars
1 HK dollar = 58/9.67 = 6.00 rupees
21-8.
1 British pound = 16.9 Mexican pesos = 2.8 Singapore dollars
10 million Mexican pesos = 10 X 2.8/16.9 = 1.657 million Singapore dollars
169
21-9.
If one British pound is equivalent to 1.5 euros, and one euro can purchase 60 baht, how many baht
can one purchase with 1 million British pounds?
1 British pound = 1.5 euros = 60 X 1.5 = 90 baht
1 million British pounds = 90 million baht
21-10. British pound = 1.5 euros; .8 X 1.5 euros = 1.2 dinars; 1.2 dinars X 160 yen
= 192 yen;
1 million British pounds = 192 million yen
21-11. a) 16.5 X 1/.90 = $18.33 per share
$18.33 X 100 = $1,833
b) 16.5 X 1/.70 = $23.57 per share
$23.57 X 100 = $2,357
c) 16.5 X 1/1.2 = $13.75 per share
$13.75 X 100 = $1,375
21-12. 55,150 X 1.020408163 = $56,275.51
21-13. 230,000 ¥ / $2,000 = 115 ¥ / $
21-14. Initial Investment
=
Current Value
=
Return on Investment =
$100,000
$100,000 X 119/100 = $119,000
($119,000 - $100,000)/$100,000 = 19%
21-15. Initial Investment
=
Current Value
=
Return on Investment =
1,000 shares X $37/shareXRs42/$ = Rs1,554,000
1,000 shares X $37/shareXRs44/$ = Rs1,628,000
(Rs1,628,000 - Rs1,554,000)/Rs1,554,000 = 4.76%
170