Solutions to Assigned Problems
Chapter One
2. Example One: An individual opens a savings account at a local commercial
bank with a $200 deposit. The bank loans out the $200 with other funds from other
savings accounts to a local business man who is expanding his business. The local
business man pays back the loan overtime with interest and the bank credits the savings
account with interest. The individual withdraws money from the savings account to buy a
new bike.
Example Two: An individual deposits his monthly paycheck in a checking
account. The bank accumulates the funds from many checking accounts and loans money
to an individual buying a house. The new homeowner makes monthly mortgage
payments to the bank. The bank uses the mortgage payments to cover the checks written
by the person with the checking account.
Example Three: An individual buys a municipal bond for an airport improvement
project. The individual usually buys a municipal from a bond dealer, an investment
banker marketing the bond, and the funds from the sale of the bond are delivered to the
city minus a fee from the investment banker. The city uses the funds to build new
facilities at the airport, for example a new parking lot. Once finished the fees received
from parking are used to payback the buyer of the bond with interest.
7. The goal of the financial manager is to maximize the current share price or
equity value of the firm. This goal encompasses many good business practices such as a
good working relationship with the surrounding community. If the firm pollutes local
streams, abuses local facilities such as roads, and in general does not participate in the
economic advancement of the local community its share price or equity value will suffer.
The local community may sue the company for its damages and the best local workforce
members may choose not to work for the company. Employees may not be loyal to the
company causing high turnover and increased personal costs for recruiting and training.
Finally, facilities such as roads and utilities may not be repaired or modernized by the
local community impacting the company’s ability to produce a profit. A good community
relationship is embedded in the goal of maximizing current share price or the equity value
of the company.
9. Principal-Agent pair: Shareholder – Chief Executive Officer
Conflict is the “perk” the CEO elects to take, a personal jet for flying to and from
business activities instead of flying commercial carriers. The cost of the jet outweighs the
expense of commercial carriers so it hurts the company profits. However the CEO feels
that the private jet allows for greater supervision of the operations and hence a more
efficient operation. This conflict could be reduced by the board of directors reviewing the
travel needs and frequency of the CEO and the inconvenience of using commercial
carriers. Once the pros and cons of the different travel options have been reviewed a
company policy can be issued so that shareholders understand the rationale if a private jet
is elected for the CEO.
Agent Pair: Supervisor – Employee.
The conflict is over the overtime assignment of the employee. The employee
wants sufficient lead time on overtime work while the supervisor assigns the work
whenever the situation arises. The employee is disgruntled when working overtime and
does not produce quality work. The cost of this is rework on some of the production
items. Solution: a policy on overtime and selection for overtime worked out between the
supervisor and all employees subject to selection for overtime.
Agent Pair: Teacher – Student
The conflict is on grading of individual student participation in group
assignments. The student feels that student not pulling their weight in the group
assignment should not receive full credit for the work. Credit should be based on the
contribution of the individual to the assignment. Teacher has difficulty determining each
student’s contribution on group assignment so minimizes errors in assigning incorrect
contribution levels by giving all individuals same grade. Solution: Have students grade
their contribution and all group member contributions. When the group is consistent in
evaluating all group member contributions then grades are assigned. When group is not
consistent, group must re-evaluate individual contributions to come to agreement. If
second evaluation is not consistent then teacher talks to group. This may only reduce
some agency problems and raise others. The group dynamics may be such that members
are “forced” to agree on all students contributed evenly when doing evaluations.
Agent Pair: Parent – Child
The conflict is on the appropriate driving of the family car by the child. The child
does not always adhere to speed limits and does not use a safety belt when driving. The
parents want the child to obey the speed limits and always wear a safety belt. Agency
cost is the increased potential for traffic tickets and increased potential for personal injury
to child. There are a number of potential solutions here, all the way from removing
driving privileges if the child does receive a ticket to installing a new device that
measures speed of the car and if seat belt is being worn by driver. Hopefully the agency
conflict can be reduced with the least amount of expense.
10. Answer: The first issue is why do employees take forty-five minutes for
lunch? The forty-five minutes may be the time natural time required to go through the
line, purchase a lunch and then eat the lunch at an appropriate pace. If this is the case
then it will be necessary to determine how to “speed” up the process to allow the
employees to meet the 30 minute lunch time frame.
The agency cost here is the lost 15 minutes of employee production time each
day. In order to eliminate this agency cost it may be necessary to significantly modify
the cafeteria or the serving procedure. If the management wants to maintain the thirty
minute lunch period it may have to look into the serving procedure in their cafeteria
to see how to shorten lines and speed up purchasing meals. Any cost to redesign the
cafeteria process is an agency cost. Any additional employees added to the cafeteria
staff to speed up the process is an agency cost.
Another possibility is to extend the work day by fifteen minutes. The cost to
negotiate a new work day schedule is an agency cost. Any turnover caused by the
new workday is also an agency cost.
It may be more costly to enforce the thirty minute lunch time than to accept the
standard 45 minute break currently used by employees. Not all agency costs can be
eliminated or reduced. The norms of the employees and the ability of current facilities
to support a policy need to be considered when setting policies and in this case lunch
time in the first place.
Then again, if the facilities are sufficient to handle a 30 minute lunch it may be as
simple as reaffirming the lunch break time with the employees.
Chapter Two
5. Answers:
a. FV = $7,000 x (1.06)2 = $7,000 x 1.1236 = $7,865.20
b. FV = $7,000 x (1.06)5 = $7,000 x 1.3382 = $9,367.58
c. FV = $7,000 x (1.06)8 = $7,000 x 1.5938 = $11,156.94
d. FV = $7,000 x (1.06)15 = $7,000 x 2.3966 = $16,775.91
7.
Answers: a. PV = $2,500 x 1/(1.07)2 = $2,500 x 0.8734 = $2,183.60
b. PV = $2,500 x 1/(1.07)5= $2,500 x 0.7130 = $1,782.47
c. PV = $2,500 x 1/(1.07)9 = $2,500 x 0.5439 = $1,359.83
d. PV = $2,500 x 1/(1.07)14 = $2,500 x 0.3878 = $969.54
e. PV = $2,500 x 1/(1.07)18 = $2,500 x 0.2959 = $739.66
9. Answers:
a. r = ($786.86/$400)1/10 – 1 = 1.07 – 1 = 7.00%
b. r = ($10,927.45/$3,000)1/15 – 1 = 1.09 – 1 = 9.00%
c. r = ($100,000/$31,180.47)1/20 – 1 = 1.06 – 1 = 6.00%
d. r = ($1,000,000/$31,327.88)1/45 – 1 = 1.08 – 1 = 8.00%
11. Spreadsheet Solution
In Cells A1 through A16 put in the Present Value of the savings bond,
$100.00.
In Cells B1 through B16 put in the annual interest rate, 0.075, R.
In Cells C1 through C16 put in the waiting time in years, 5 through 20, N.
In Cell D1 put in the FV function using the row value in A1 for the PV,
row value in B1 for the interest rate, row value in C1 for n. Copy the
formula for cells D2 through D16. The displayed value will be the future
Value of the $100 savings bond at 7.5% annual interest.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
-100.00
B
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.075
C
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
D
FV (PV = A1, rate = B1, n = C1) = $143.56
FV (PV = A2, rate = B2, n = C2) = $154.33
FV (PV = A3, rate = B3, n = C3) = $165.90
FV (PV = A4, rate = B4, n = C4) = $178.35
FV (PV = A5, rate = B5, n = C5) = $191.72
FV (PV = A6, rate = B6, n = C6) = $206.10
FV (PV = A7, rate = B7, n = C7) = $221.56
FV (PV = A8, rate = B8, n = C8) = $238.18
FV (PV = A9, rate = B9, n = C9) = $256.04
FV (PV = A10, rate = B10, n = C10) = $275.24
FV (PV = A11, rate = B11, n = C11) = $295.89
FV (PV = A12, rate = B12, n = C12) = $318.08
FV (PV = A13, rate = B13, n = C13) = $341.94
FV (PV = A14, rate = B14, n = C14) = $367.58
FV (PV = A15, rate = B15, n = C15) = $395.15
FV (PV = A16, rate = B16, n = C16) = $424.79
Note the negative values in column A denote the cash outflow and produce a
positive cash inflow in column D.
19. The disease is spreading at a growth rate of nearly 57% per day.
r = (6/1)1/4 – 1 = 1.3161 - 1 = 56.51%
Using the same growth rate for the 16 day period, (two weeks and two days) the
number of patients infected will be:
FV = 1 x (1.5156)16 = 1,296 or 1,296 patients
Or you could realize that every four days the number of people infected
increases by six times and with four periods of four days you have
1 x 6 x 6 x 6 x 6 = 1 x (6)4 = 1,296
Chapter Three
10. Perpetuities. The Canadian Government has once again decided to issue a consul
(bond with a never ending interest payment and no maturity date). The bond will pay $50
each year interest (at the end of the year) but never return the principal. The current
discount rate for Canadian Government bonds is 6.5%. What should this bond sell for in
the market? What if the interest rate should fall to 4.5%? Rise to 8.5%? Why does the
price go up when interest rates fall? Why does the price go down when interest rates rise?
Answer: at 6.5%, $50 / 0.065 = $769.23
at 4.5%, $50 / 0.045 = $1,111.11
at 8.5%, $50 / 0.085 = $588.24
The price rises when interest rates fall because the present value of each future
interest payment is worth more in present value due to the lower discount rate. The price
falls when interest rates rise because the present value of each future interest payment is
worth less in present value due to the higher discount rate.
15. Future Value. Jack and Jill are saving for a rainy day and decide to put $50 away
every year for the next 25 years. The local bank UP-THE-HILL Bank will pay Jack and
Jill 7% on their account. If Jack and Jill put the money in the account faithfully at the end
of every year,
a. how much will they have in their account at the end of 25 years?
b. Unfortunately Jack fell down, breaking his crown, after only 10 years of
savings. The medical bill has come to $700. Is there enough in the rainy day fund to
cover this medical bill?
Answers
Part a. FV = $50 x (1.0725 -1)/0.07 = $50 x 63.2490 = $3,162.45
Part b. FV = $50 x (1.0710 -1)/0.07 = $50 x 13.8164 = $690.82 so the rainy day
fund is $9.18 short of being able to cover the medical bill.
17. Present Value. County Ranch Insurance Company wants to offer a guaranteed annuity
stream in units of $500 payable at the end of each year for twenty five years. The
company has a strong investment record and can consistently earn 7% on its investments
after tax. If the company wants to make 1% on this contract what price should the
company set on this contract? Use 6% as the discount rate, assume an ordinary annuity
and price is the same thing as present value.
Answer
Price = Present Value = $500.00 x (1 – 1/1.0625) / 0.06 = $500 x 12.7834 = $6,391.68
Payments = $30,000 / [(1 – 1/(1.085)10) / .085] = $30,000 / 6.5613 = $4,572.23
19. Payments. Cooley Landscaping Company needs to borrow $30,000 for a new frontend dirt loader. The bank is willing to loan the funds at 8.5% interest with annual
payments at the end of the year for the next ten years. What is the annual payment on this
loan for Cooley Landscaping?
Answer
Payments = $30,000 / [(1 – 1/(1.085)10) / .085] = $30,000 / 6.5613 = $4,572.23
21. Number of Payments. Bugsy Malone is offering two repayment plans for a long
overdue loan to Gambling Bob. Offer one is two broken legs and the debt completely
forgiven. Offer two is to pay back $3,900 per year at 20% interest rate until the loan
principal is paid off. Gambling Bob owes Mr. Malone $15,000. How long will it take for
Gambling Bob to payoff the loan if he takes offer two?
Answer
First remember to check if the payment is greater than the interest expense for the
period.
PMT > PV x R = $3,900 > $15,000 x 0.2 = $3,000 and now,
Number of Payments = ln [$3,900 / ($3,900 - $15,000 x 0.20)] / ln (1.20)
= ln [$3,900/$900] / ln (1.20)
= 1.4663 / 0.1823 = 8.0426
≈ 8 payments or 8 years…
Or on the calculator
INPUT
?
20.0
$15,000
Variables
N
I/Y
PV
OUTPUT
8.0426
-$3,900
$0
PMT
FV
24. Interest Rate with Annuity. A local government is about to run a lottery but does not
want to be involved in the payoff if a winner picks an annuity stream payoff. The
government contracts with a trust to pay the lump sum payout to the trust and have the
trust (probably a local bank) pay the annual payments. The first winner of the lottery
chose the annual stream and will receive $150,000 a year for the next twenty-five years.
The local government will give the trust $2,000,000 to pay for this annuity. What
investment rate must the trust earn to break even on this arrangement?
Answer
Using a calculator TVM keys with P/y=1 and C/y = 1 in end mode:
INPUT
25
?
$2,000,000
-$150,000
Variables
N
I/Y
PV
PMT
OUTPUT
$0
FV
5.5619%
25. Amortization. Loan Consolidated Incorporated is offering a special one-time package
to reduce Custom Autos outstanding bills to one easy to handle payment plan. LCI will
payoff the current outstanding bills of $242,000 for Custom Auto if they will pay an
annual payment to LCI at a 10% interest rate over the next 15 years. First, what is the
annual payment and what is the amortization schedule for this loan if Custom Autos
wants to pay off the loan before the loan maturity in 15 years? When will the balance be
half paid off? And what is the total interest expense on the loan over the 15 years?
Answer
Payment = $242,000 / [(1 – 1/1.1015) / 0.10] = $242,000 / 7.6060 = $31,816.65
Amortization Schedule with Interest per period based on beginning balance x 0.15
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Total
Beg.
Balance
$242,000.00
$234,383.35
$226,005.03
$216,788.86
$206,651.11
$195,499.57
$183,232.87
$169,739.50
$154,896.80
$138,569.82
$120,610.15
$100,854.51
$79,123.31
$55,218.99
$28,924.23
Payment
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
$31,816.65
Interest
$24,200.00
$23,438.33
$22,600.50
$21,678.89
$20,665.11
$19,549.96
$18,323.29
$16,973.95
$15,489.68
$13,856.98
$12,061.01
$10,085.45
$7,912.33
$5,521.90
$2,892.42
$235,249.81
Principal
Reduction
$7,616.65
$8,378.32
$9,216.15
$10,137.77
$11,151.54
$12,266.70
$13,493,37
$14,842.70
$16,326.97
$17,959.67
$19,755.64
$21,731.20
$23,904.32
$26,294.76
$28,924.23
Ending
Balance
$234,383.35
$226,005.03
$216,788.86
$206,651.11
$195,499.57
$183,232.87
$169,739.50
$154,896.80
$138,569.82
$120,610.15
$100,854.51
$79,123.31
$55,218.99
$28,924.23
$0.00
The loan balance will be half-way paid off at the end of the tenth year or 2/3rds
the way through the contract. The total interest expense over the contract is $235,249.81.
This can be determined by adding up the interest expenses or multiplying the payment
($31,816.65) times the number of payments (15) and subtracting the original principal
($242,000). This shows that the payments go toward principal and interest only!
Interest Expense = $31,816.65 x 15 - $242,000 = $235,249.75
The six cents difference is due to rounding.
Chapter Four
3. EAR. What is the effective annual rate of a mortgage rate that is advertised at
7.75% over the next twenty years with monthly payments?
ANSWER
Periodic Rate = 0.0775 / 12 = 0.0064583333
EAR = (1 + Periodic Rate)C/Y - 1 = 1.0064583312 – 1 = 1.0803 – 1 = 0.0803 = 8.03%
5. Present Value with Periodic Rates. Let’s revisit Sam Hind’s the dentist from chapter
three and his remodeling project (Problem 3-18). The cost of the equipment is
$18,000 and the purchase will be financed with a 7.5% loan over six years. Originally
the loan called for annual payments. Redo the payments based on quarterly payments
(four per year) and monthly payments (twelve per year). Compare the annual cash
outflow of the two payments. Why does the monthly payment plan have less total
cash outflow each year?
ANSWER
Quarterly Payment = $18,000 / (1 – 1/[1 + (0.075/4)]6 x 4 ) / (0.075/4)
Quarterly Payment = $18,000 / 19.1845 = $938.26
Monthly Payment = $18,000 / (1 – 1/[1 + (0.075/12)]6 x 12 ) / (0.075/12)
Monthly Payment = $18,000 / 57.8365 = $311.22
Annual Cash Outflow Quarterly Payment = $938.26 x 4 = $3,753.04
Annual Cash Outflow Monthly Payment = $3,734.64
Difference of $18.04
It is lower for the monthly payment because each payment reduces some
of the principal and so over the three months between the quarterly payments the average
borrowed amount is lower so that the accumulated interest expense is lower.
7.Future Value with Periodic Rates. Matt Johnson, a paper delivery boy, is putting
away $15.00 every month from his paper route collections. Matt is eight years old and
will use the money when he goes to college in ten years. What will the value be in
Matt’s account in ten years with his monthly payments if he is earning 6% (APR), 8%
(APR) or 12% (APR)?
ANSWER
FV at 6% APR = $15.00 x [(1 + 0.06/12)10 x 12 – 1] / (0.06/12)
FV at 6% APR = $15.00 x 163.8793 = $2,458.19
FV at 8% APR = $15.00 x [(1 + 0.08/12)10 x 12 – 1] / (0.08/12)
FV at 8% APR = $15.00 x 182.9460 = $2,744.19
FV at 12% APR = $15.00 x [(1 + 0.12/12)10 x 12 – 1] / (0.12/12)
FV at 12% APR = $15.00 x 230.0387 = $3,450.58
9. Payments with Periodic Rates. What payment does Denise need to make at the
end of each month over the coming 44 years at 6% to reach her retirement goal of
$1,000,000?
ANSWER
Payment = $1,000,000 / [(1 + 0.06/12)44 x 12 -1 ] / (0.06/12)
Payment = $1,000,000 / 2,584.2652 = $386.96
10. Amortization Schedule with Periodic Payments. Moulton Motors is advertising
the following deal on a new Honda Civic: Monthly Payments of $400.40 for the
next 60 months and this beauty can be yours. The sticker price of the car is
$18,000. First what is the interest rate you are paying in both APR and EAR
terms? Second, what is the amortization schedule of these 60 payments?
ANSWER
The periodic or monthly interest rate, r, is the solution to the equation
PV = Payment x (1 – 1/(1+r)n) / r
$18,000 = $400.40 x (1 – 1/(1+r)60) / r
PVIFA = (1 – 1/(1+r)n) / r = PV / Payment = $18,000 / 400.40 = 44.9550
(Look up in Appendix A-3 the PVIFA tables, with N = 60, and see 44.9550 for
1% column. The periodic or monthly interest rate is 1%.
The annual percentage rate is 12%, periodic rate times 12, 1% x 12 = 12% and the
EAR is
EAR = 1.0112 – 1 = 12.68%.
Amortization Schedule (Can be done effectively on a spread sheet)
Cell A1 is Beginning Balance for month 1
Cell B1 is the Monthly Payment
Cell C1 is the Monthly Interest Expense and is the periodic or monthly interest rate
times the beginning balance: A1 * 0.01 (formula for the cell)
Cell D1 is the amount of the monthly payment that is applied to the principal and is
the payment minus the interest expense: B1 – C1 (formula for the cell)
Cell E1 is the ending balance after the applying of the monthly payment to interest
and principal. It is the beginning balance minus the principal reduction: A1 – D1
(formula for the cell).
Cell A2 is the ending balance from the previous month or the value in Cell E1.
Then for cells B2 through E2 copy the formulas down from the row above.
Repeat this for the sixty months…
1
2
3
…
57
58
59
60
A
$18,000.00
$17,779.60
$17,557.00
$1,562.35
$1,177.57
$788.94
$396.44
B
$400.40
$400.40
$400.40
…
$400.40
$400.40
$400.40
$400.40
C
$180.00
$177.80
$175.57
D
$220.40
$222.60
$224.83
E
$17,779.60
$17,557.00
$17,332.17
$15.62
$11.78
$7.90
$3.96
$384.78
$388.62
$392.50
$396.44
$1,177.57
$788.94
$396.44
$0.00
Chapter Five
5. Holding Period and Annual (Investment) Returns. Gary Baker Trading Cards
Incorporated originally purchased the rookie card of Hammerin’ Hank Aaron for
$35.00. After holding the card for five years, Baker Trading Cards auctioned off the
card for $180.00. What are the holding period return and the annual return on this
investment?
ANSWER
Holding Period Return = ($180 - $35) / $35 = 4.1429 or 414.29%
Annual Return = (1 + 4.1429)1/5 – 1 = 1.3875 – 1 = 0.3875 or 38.75%
8. Comparison of Returns. Wei Guan Investors are looking at three different investment
opportunities. Investment One is a five year investment with a cost of $125 and a
promised payout of $250 at maturity. Investment Two is a seven year investment with
a cost of $125 and a promised payout of $350. Investment Three is a ten year
investment with a cost of $125 and a promised payout of $550. Wei Guan Investors
can only take one of the three investments. Calculate the annual return for each
investment and select the best investment choice if all three investment opportunities
have the same level of risk.
ANSWER
Holding Period Return for Investment One = ($250 - $125) / $125 = 1.00 or 100.00%
Annual Return Investment One = (1 + 1.00)1/5 – 1 = 1.1487 – 1 = 0.1487 or 14.87%
Holding Period Return for Investment Two = ($350 - $125) / $125 = 1.80 or 180.00%
Annual Return Investment Two = (1 + 1.80)1/7 – 1 = 1.1585 – 1 = 0.1585 or 15.85%
Holding Period Return for Investment Three = ($550 - $125) / $125 = 3.40 or
340.00%
Annual Return Investment Three = (1 + 3.40)1/10 – 1 = 1.1596 – 1 = 0.1596 or 15.96%
Investment Two has the highest annual return rate of the three choices. If all choices
have the same level of risk, choose Investment Two.
9. Historical Returns (from Table do some averaging). Calculate the average return of
the U.S. Treasury Bills, Long-Term Government Bonds, and Large Company Stocks
for the 90s from Table 5.1. Which had the highest and which had the lowest return?
Answer from data is:
Average Return U.S. Treasury Bill for 90s: 5.02%
Average Return U.S. Long-Term Government Bonds for 90s: 9.23%
Average Return U.S. Large Company Stocks for 90s: 18.99%
Average Return U.S. Small Company Stocks for 90s: 15.87%
Highest was Large Company Stocks, Lowest was 3 Month T-Bills
6.
Standard Deviation. Calculate the standard deviation of the U.S. Treasury Bills,
Long-Term Government Bonds, and Large Company Stocks for the 90s from Table
5.1. Which had the highest and which had the lowest variance?
Answer from data is:
Standard Deviation for U.S. Treasury Bill for 90s: 1.37%
Standard Deviation for U.S. Long-Term Government Bonds for 90s: 12.38%
Standard Deviation for U.S. Large Company Stocks for 90s: 14.21%
Standard Deviation for U.S. Small Company Stocks for 90s: 21.78%
Highest was Small Company Stocks, Lowest was 3 Month T-Bills
13. Expected Return. Rob Hull Consultants, a famous think tank in the Midwest, has
provided probability estimates for the four potential economic states for the coming
year. The probability of a boom economy is 10%, the probability of a stable growth
economy is 15%, the probability of a stagnant economy is 50%, and the probability of
a recession is 25%. Estimate the expected return on the following individual
investments for the coming year.
INVESTMENT
Stock
Corporate Bond
Government Bond
Boom
25%
9%
8%
Forecasted Returns for Each Economy
Stable Growth
Stagnant
Recession
12%
4%
-12%
7%
5%
3%
6%
4%
2%
ANSWER
Expected Return Stock = 0.10 x 0.25 + 0.15 x 0.12 + 0.50 x 0.04 + 0.25 x (-0.12)
= 0.0250 + 0.0180 + 0.0200 - 0.0300 = 0.0330 or 3.3%
Expected Return Corp. Bond = 0.10 x 0.09 + 0.15 x 0.07 + 0.50 x 0.05 + 0.25 x 0.03
= 0.0090 + 0.0105 + 0.0250 + 0.0075 = 0.0520 or 5.2%
Expected Return Gov. Bond = 0.10 x 0.08 + 0.15 x 0.06 + 0.50 x 0.04 + 0.25 x 0.02
= 0.0080 + 0.0090 + 0.0200 + 0.0050 = 0.0420 or 4.2%
14. Variance and Standard Deviation (expected). Using the data from problem 13,
calculate the variance and standard deviation of the three investments, stock,
corporate bond, and government bond. If the estimates for both the probabilities of
the economy and the returns in each state of the economy are correct, which
investment would you choose considering both risk and return? Why?
ANSWER
Variance of Stock = 0.10 x (0.25 – 0.033)2 + 0.15 x (0.12 – 0.033)2
+ 0.50 x (0.04 – 0.033)2 + 0.25 x (-0.12 – 0.033)2
= 0.10 x 0.0471 + 0.15 x 0.0076 + 0.50 x 0.0000 + 0.25 x 0.0234
= 0.0047 + 0.0011 + 0.0000 + 0.0059 = 0.0117 or 1.17%
Standard Deviation of Stock = (0.0117)1/2 = 0.1083 or 10.83%
Variance of Corp. Bond = 0.10 x (0.09 – 0.052)2 + 0.15 x (0.07 – 0.052)2
+ 0.50 x (0.05 – 0.052)2 + 0.25 x (0.03 – 0.052)2
= 0.10 x 0.0014 + 0.15 x 0.0003 + 0.50 x 0.0000 + 0.25 x 0.0005
= 0.0001 + 0.0000 + 0.0000 + 0.0001 = 0.000316 or 0.00316%
Standard Deviation of Corp. Bond = (0.000316)1/2 = 0.017776 or 1.78%
Variance of Gov. Bond = 0.10 x (0.08 – 0.042)2 + 0.15 x (0.06 – 0.042)2
+ 0.50 x (0.04 – 0.042)2 + 0.25 x (0.02 – 0.042)2
= 0.10 x 0.0014 + 0.15 x 0.0003 + 0.50 x 0.0000 + 0.25 x 0.0005
= 0.0001 + 0.0000 + 0.0000 + 0.0001 = 0.000316 or 0.0316%
Standard Deviation of Gov. Bond = (0.000316)1/2 = 0.017776 or 1.78%
The best choice is the corporate bond. First comparing the corporate bond and the stock,
the corporate bond has a higher expected return and a lower variance (standard
deviation). Second comparing the corporate bond and the government bond the corporate
bond has a higher return and the same variance (standard deviation). This result is due to
the low probabilities of “good” economic states where the stock performs best.
Chapter Six
Use the following table for problems 1 through 4.
Par Value
$1,000.00
$1,000.00
$5,000.00
$5,000.00
Coupon Rate
8%
6%
9%
12%
Years to
Maturity
10
10
20
30
Yield to
Maturity
6%
8%
7%
5%
1. Price the bonds from the above table with annual coupon payments.
ANSWER:
Price = $1,000.00 x 1/(1.06)10 + $80.00 (1 – 1/(1.06)10)/ 0.06
Price = $1,000.00 x 0.5584 + $80.00 x 7.3601
Price
?
?
?
?
Price = $558.39 + $588.81 = $1,147.20
Price = $1,000.00 x 1/(1.08)10 + $60.00 (1 – 1/(1.08)10)/ 0.08
Price = $1,000.00 x 0.4632 + $60.00 x 6.7101
Price = $463.19 + $402.60 = $865.80
Price = $5,000.00 x 1/(1.07)20 + $450.00 (1 – 1/(1.07)20)/ 0.07
Price = $5,000.00 x 0.2584 + $450.00 x 10.5940
Price = $1,292.10 + $4,767.30 = $6,059.40
Price = $5,000.00 x 1/(1.05)30 + $600.00 (1 – 1/(1.05)30)/ 0.05
Price = $5,000.00 x 0.2314 + $600.00 x 15.3725
Price = $1,156.89 + $9,223.47 = $10,380.36
2. Price the bonds from the above table with semi-annual coupon payments.
ANSWER:
Price = $1,000.00 x 1/(1.03)20 + $40.00 (1 – 1/(1.03)20)/ 0.03
Price = $1,000.00 x 0.5537 + $40.00 x 14.8775
Price = $553.67 + $595.10 = $1,148.77
Price = $1,000.00 x 1/(1.04)20 + $30.00 (1 – 1/(1.04)20)/ 0.04
Price = $1,000.00 x 0.4564 + $30.00 x 13.5903
Price = $456.39 + $407.71 = $864.10
Price = $5,000.00 x 1/(1.035)40 + $225.00 (1 – 1/(1.035)40)/ 0.035
Price = $5,000.00 x 0.2526 + $225.00 x 21.3551
Price = $1,262.86 + $4,804.89 = $6,067.75
Price = $5,000.00 x 1/(1.025)60 + $300.00 (1 – 1/(1.025)60)/ 0.025
Price = $5,000.00 x 0.2273 + $300.00 x 30.9087
Price = $1,136.41 + $9,272.60 = $10,409.01
5. What is the yield of the above bonds if interest (coupons) is paid semi-annually?
ANSWER: (TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
20
?
-1000.00
40.00
1000.00
KEYS
N
I/Y
PV
PMT
FV
CPT
8.0
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
KEYS
CPT
20
N
?
I/Y
8.2300
-850.00
PV
30.00
PMT
1000.00
FV
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
40
?
-5400.00
225.00
KEYS
N
I/Y
PV
PMT
CPT
8.1807
5000.00
FV
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
60
? -4300.00
300.00
KEYS
N
I/Y
PV
PMT
CPT
13.9936
5000.00
FV
10. What are the coupon rates for the bonds listed below?
Par Value
$1,000.00
$1,000.00
$1,000.00
$1,000.00
Coupon
Rate
?
?
?
?
Years to
Maturity
30
25
20
10
Yield to
Maturity
6.0%
10.0%
9.0%
8.0%
Price
$1,412.94
$1,182.56
$907.63
$862.63
Coupon
Frequency
Annual
Semi-Annual
Quarterly
Monthly
ANSWER: (TVM Keys) Set Calculator to P/Y = 1 and C/Y = 1
INPUT
30
6.0
-1412.94
?
1000.00
KEYS
N
I/Y
PV
PMT
FV
CPT
90.00
Coupon payments are $5.00 every year so coupon rate is:
$1,000 x rate = $90.00
rate = $90 / $1,000 = 0.09 or 9%
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
50 10.0
-1,182.56
?
1000.00
KEYS
N
I/Y
PV
PMT
FV
CPT
60.00
Coupon payments are $5.00 every month so coupon rate is:
$1,000 x rate / 2 = $60.00
$1,000 x rate = $120.00
rate = $120 / $1,000 = 0.12 or 12%
(TVM Keys) Set Calculator to P/Y = 4 and C/Y = 4
INPUT
80
9.0
-907.63
?
1000.00
KEYS
N
I/Y
PV
PMT
FV
CPT
20.00
Coupon payments are $20.00 every four months so coupon rate is:
$1,000 x rate / 4 = $20.00
$1,000 x rate = $80.00
rate = $80 / $1,000 = 0.08 or 8%
(TVM Keys) Set Calculator to P/Y = 12 and C/Y = 12
INPUT
120
8.0
-862.63
?
1000.00
KEYS
N
I/Y
PV
PMT
FV
CPT
5.0000
Coupon payments are $5.00 every month so coupon rate is:
$1,000 x rate / 12 = $5.00
$1,000 x rate = $60.00
rate = $60 / $1,000 = 0.06 or 6%
11.
Moore Company is about to issue a bond with semi-annual coupon
payments, a coupon rate of 8% and par value of $1,000. The yield-tomaturity for this bond is 10%.
A. What is the price of the bond if the bond matures in 5, 10, 15, or 20 years?
B. What do you notice about the price of the bond in relationship to the
maturity of the bond?
ANSWER to A:
At five years to maturity
Price = $1,000.00 x 1/(1.05)10 + $40.00 (1 – 1/(1.05)10)/ 0.05
Price = $1,000.00 x 0.6139 + $40.00 x 7.7217
Price = $613.91 + $308.87 = $922.78
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
10 10.0
?
40.00
KEYS
N
I/Y
PV
PMT
CPT
-922.78
1000.00
FV
At ten years to maturity
Price = $1,000.00 x 1/(1.05)20 + $40.00 (1 – 1/(1.05)20)/ 0.05
Price = $1,000.00 x 0.3769 + $40.00 x 12.4622
Price = $376.89 + $498.49 = $875.38
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
20 10.0
?
40.00
KEYS
N
I/Y
PV
PMT
CPT
-875.38
1000.00
FV
At fifteen years to maturity
Price = $1,000.00 x 1/(1.05)30 + $40.00 (1 – 1/(1.05)30)/ 0.05
Price = $1,000.00 x 0.2314 + $40.00 x 15.3725
Price = $231.38 + $614.90 = $846.28
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
30 10.0
?
40.00
KEYS
N
I/Y
PV
PMT
CPT
-846.28
1000.00
FV
At twenty years to maturity
Price = $1,000.00 x 1/(1.05)40 + $40.00 (1 – 1/(1.05)40)/ 0.05
Price = $1,000.00 x 0.1420 + $40.00 x 17.1591
Price = $142.05 + $686.36 = $828.41
(TVM Keys) Set Calculator to P/Y = 2 and C/Y = 2
INPUT
40 10.0
?
40.00
KEYS
N
I/Y
PV
PMT
CPT
-828.41
1000.00
FV
ANSWER to B
The longer the maturity of a bond selling at a discount, all else held
constant, the lower the price of the bond!
13. Addison Company will issue a zero coupon bond this coming month. The
projected yield for the bond is 7%. If the par value of the bond is $1,000 what is
the price of the bond using a semi-annual convention if
a. The maturity is 20 years?
b. The maturity is 30 years?
c. The maturity is 50 years?
d. The maturity is 100 years?
ANSWER to A:
Price = $1,000 x 1 / (1.035)40 = $1,000 x 0.2526 = $252.57
ANSWER to B:
Price = $1,000 x 1 / (1.035)60 = $1,000 x 0.1269 = $126.93
ANSWER to A:
Price = $1,000 x 1 / (1.035)100 = $1,000 x 0.0321 = $32.06
ANSWER to A:
Price = $1,000 x 1 / (1.035)200 = $1,000 x 0.0010= $1.03
19.
In Problem 18, the conversion option is for 50 shares of Joe Phillips
Manufacturing Company for every bond. If the current bond price is $1,240 at
what share price would a bondholder be better off converting to stock?
ANSWER: Any price above $1,240 / 50 = $24.80.
Chapter 7
1. Murphy Motors, Inc. has just set the company dividend policy at $0.50 per year.
The company plans on being in business forever. What is the price of this stock if
a. An investor wants a 5% return?
b. An investor wants an 8% return?
c. An investor wants a 10% return?
d. An investor wants a 13% return?
e. An investor wants a 20% return?
SOLUTION: Use the constant dividend infinite dividend stream model:
Price = Dividend / r
a. Price = $0.50 / 0.05 = $10.00
b. Price = $0.50 / 0.08 = $6.25
c. Price = $0.50 / 0.10 = $5.00
d. Price = $0.50 / 0.13 = $3.85
e. Price = $0.50 / 0.20 = $2.50
2. Rice Electronics wants its shareholders to earn a 15% return on their investment
in the company. At what price would the stock need to be priced today if Rice
Electronics had the following cash dividend policy:
a. $0.25 constant annual dividend forever?
b. $1.00 constant annual dividend forever?
c. $1.75 constant annual dividend forever?
d. $2.50 constant annual dividend forever?
SOLUTION: Use the constant dividend infinite dividend stream model:
Price = Dividend / r
a. Price = $0.25 / 0.15 = $1.67
b. Price = $1.00 / 0.15 = $6.67
c. Price = $1.75 / 0.15 = $11.67
d. Price = $2.50 / 0.15 = $16.67
3. Tremblay Fine Foods has a current annual cash dividend policy of $2.25. The
price of the stock is set to yield a 12% return. What is the price of this stock if the
dividend will be paid for:
a. 10 years?
b. 15 years?
c. 40 years?
d. 60 years?
e. 100 years?
f. Forever?
SOLUTION: Use the finite constant dividend model except with f (use infinite constant
dividend model)
Price = Dividend x (1 – 1/(1+r)n) / r
a. Price = $2.25 x (1 – 1/(1.12)10 / 0.12 = $2.25 x 5.6502 = $12.71
b. Price = $2.25 x (1 – 1/(1.12)15 / 0.12 = $2.25 x 6.8109 = $15.32
c. Price = $2.25 x (1 – 1/(1.12)40 / 0.12 = $2.25 x 8.2438 = $18.54
d. Price = $2.25 x (1 – 1/(1.12)60 / 0.12 = $2.25 x 8.3240 = $18.73
e. Price = $2.25 x (1 – 1/(1.12)100 / 0.12 = $2.25 x 5.6502 = $18.75
f. Price = $2.25 / 0.12 = $18.75
5. King Waterbeds has an annual cash dividend policy that raises the dividend each
year by 4%. Last year’s dividend was $0.40 per share. What is the price of this stock
if
a. An investor wants a 5% return?
b. An investor wants an 8% return?
c. An investor wants a 10% return?
d. An investor wants a 13% return?
e. An investor wants a 20% return?
SOLUTION: Use the constant growth dividend model with an infinite dividend
stream:
Price = Last Dividend x (1 + g) / (r – g)
a. Price = $0.40 x (1.04) / (0.05 – 0.04) = $0.4160 / 0.01 = $41.60
b. Price = $0.40 x (1.04) / (0.08 – 0.04) = $0.4160 / 0.04 = $10.40
c. Price = $0.40 x (1.04) / (0.10 – 0.04) = $0.4160 / 0.06 = $6.93
d. Price = $0.40 x (1.04) / (0.13 – 0.04) = $0.4160 / 0.09 = $4.62
e. Price = $0.40 x (1.04) / (0.20 – 0.04) = $0.4160 / 0.16 = $2.60
7. Miles Hardware has an annual cash dividend policy that raises the dividend each
year by 3%. Last year’s dividend was $1.00 per share. Investors want a 15% return on
this stock. What is the price of this stock if
a. The company will be in business for 5 years and not have a liquidating
dividend?
b. The company will be in business for 15 years and not have a liquidating
dividend?
c. The company will be in business for 25 years and not have a liquidating
dividend?
d. The company will be in business for 35 years and not have a liquidating
dividend?
e. The company will be in business for 75 years and not have a liquidating
dividend?
f. Forever?
SOLUTION: Use the constant growth dividend model with a finite dividend stream:
Price = Last Dividend x (1 + g) / (r – g) x [1 – ((1+g) / (1+r))n]
a. Price = $1.00 x (1.03) / (0.15 – 0.03) x [1 – ((1.03) / (1.15))5]
= $1.03 / 0.12 x [1 - 0.5764] = $8.58 x [0.4236] = $3.64
b. Price = $1.00 x (1.03) / (0.15 – 0.03) x [1 – ((1.03) / (1.15))15]
= $1.03 / 0.12 x [1 - 0.1915] = $8.58 x [0.8085] = $6.94
c. Price = $1.00 x (1.03) / (0.15 – 0.03) x [1 – ((1.03) / (1.15))25]
= $1.03 / 0.12 x [1 - 0.0636] = $8.58 x [0.9364] = $8.03
d. Price = $1.00 x (1.03) / (0.15 – 0.03) x [1 – ((1.03) / (1.15))35]
= $1.03 / 0.12 x [1 - 0.0211] = $8.58 x [0.9789] = $8.40
e. Price = $1.00 x (1.03) / (0.15 – 0.03) x [1 – ((1.03) / (1.15))75]
= $1.03 / 0.12 x [1 - 0.0003] = $8.58 x [0.9997] = $8.58
f. Price = $1.00 x (1.03) / (0.15 – 0.03) = $1.03 / 0.12 = $8.58
11. Huber Athletic Club is going to offer preferred stock to its members with the
following characteristics; par value is $100 and annual dividend rate of 6%. If a
member wants the following returns, what price should he be willing to pay:
a. Brad wants a 10% return.
b. Mike wants a 12% return
c. Rick wants a 15% return
d. Julius wants a 18% return
SOLUTION: Use the constant dividend model with finite horizon
Price = Dividend / r
a. Brad’s Price = $100 x 0.06 / 0.10 = $60.00
b. Mike’s Price = $100 x 0.06 / 0.12 = $50.00
c. Rick’s Price = $100 x 0.06 / 0.15 = $40.00
d. Julius’s Price = $100 x 0.06 / 0.18 = $33.33
Chapter 8
Use the information in the following to answer questions 1-4 below:
State of
Economy
Boom
Probability
of State
.30
Return on J
in State
0.050
Return on K
in State
0.240
Return on L
in State
0.300
Growth
Stagnant
Recession
.40
.20
.10
0.050
0.050
0.050
0.120
0.040
-0.100
0.200
0.060
-0.200
1. Expected Return. What are the expected returns of the three different assets?
ANSWER
Expected Return J = 0.30 x 0.05 + 0.40 x 0.05 + 0.20 x 0.05 + 0.10 x 0.05
= 0.0150 + 0.0200 + 0.0100 + 0.0050= 0.0050 or 5.0%
Expected Return K = 0.30 x 0.24 + 0.40 x 0.12 + 0.20 x 0.04 + 0.10 x (-0.10)
= 0.0720 + 0.0480 + 0.0080 - 0.0100 = 0.1180 or 11.80%
Expected Return L = 0.30 x 0.30 + 0.40 x 0.20 + 0.20 x 0.06 + 0.10 x (-0.20)
= 0.0900 + 0.0800 + 0.0120 + 0.0200 = 0.1620 or 16.20%
2. Variance and Standard Deviation. What are the variances and standard deviations of
each of the three different assets?
ANSWER
σ2 (J) = 0.30 x (0.04 – 0.04)2 + 0.40 x (0.04 – 0.04)2 + 0.20 x (0.05-0.05)2
+ 0.10 x (0.04 – 0.04)2
= 0.30 x 0.0000 + 0.40 x 0.0000 + 0.20 x 0.0000 + 0.10 x 0.0000
= 0.0000+ 0.0000 + 0.0000 + 0.0000 = 0.0000 or 0.00%
Standard Deviation of J = (0.0000)1/2 = 0.0000 or 0.00%
σ2 (K) = 0.30 x (0.24 – 0.1180)2 + 0.40 x (0.12 – 0.1180)2 + 0.20 x (0.04 - 0.1180)2
+ 0.10 x (-0.10 – 0.1180)2
= 0.30 x 0.0149 + 0.40 x 0.0000 + 0.20 x 0.0061 + 0.10 x 0.0475
= 0.0045 + 0.0000 + 0.0012 + 0.0048 = 0.0104 or 1.04%
Standard Deviation of K = (0.0104)1/2 = 0.1022 or 10.22%
σ2 (L) = 0.30 x (0.30 – 0.1620)2 + 0.40 x (0.20 – 0.1620)2 + 0.20 x (0.06 - 0.1620)2
+ 0.10 x (-0.20 – 0.1620)2
= 0.30 x 0.0190 + 0.40 x 0.0014 + 0.20 x 0.0104 + 0.10 x 0.1310
= 0.0057 + 0.0006 + 0.0021 + 0.0131 = 0.0215 or 2.15%
Standard Deviation of L = (0.0215)1/2 = 0.1465 or 14.65%
3. Portfolio. What is the expected return of a portfolio with 10% in asset J, 50% in asset
K, and 40% in asset L?
ANSWER
Expected Return Portfolio = 0.10 x 0.05 + 0.50 x 0.118 + 0.40 x 0.162
= 0.0050 + 0.0590 + 0.0648 = 0.1288 or 12.88%
OR
First determine the portfolio’s return in each state of the economy with the
allocation of assets at 10% in J, 50% in K, and 40% in L.
Expected Return Portfolio in Boom= 0.10 x 0.05 + 0.50 x 0.24 + 0.40 x 0.30
= 0.0050 + 0.1200 + 0.1200 = 0.2450 or 24.50%
Expected Return Portfolio in Growth = 0.10 x 0.05 + 0.50 x 0.12 + 0.40 x 0.20
= 0.0050 + 0.0600 + 0.0800 = 0.1450 or 14.50%
Expected Return Portfolio in Stagnant = 0.10 x 0.05 + 0.50 x 0.04 + 0.40 x 0.06
= 0.0050 + 0.0200 + 0.0240 = 0.0490 or 4.90%
Expected Return Portfolio in Recession = 0.10 x 0.05 + 0.50 x (-0.10) + 0.40 x (-0.20)
= 0.0050 - 0.0500 - 0.0800 = -0.1250 or -12.50%
Now take the probability of each state times the portfolio outcome in that state:
Expected Return Portfolio = 0.30 x 0.2450 + 0.40 x 0.1450 + 0.20 x 0.0490
+ 0.10 x (-0.1250)
= 0.0735 + 0.0580 + 0.0098 - 0.0125 = 0.1288 or 12.88%
Note that either way produces the same expected return but that for the variance
calculation the portfolio returns in the three economic states are needed.
4. Variance and Standard Deviation of a Portfolio. What is the portfolio’s variance and
standard deviation using the same asset weights from problem 3?
ANSWER
Variance of Portfolio = 0.30 x (0.2450 – 0.1288)2 + 0.40 x (0.1450 – 0.1288)2
+ 0.20 x (0.0490 – 0.1288)2 + 0.10 x (-0.1250 – 0.1288)2
= 0.30 x 0.0135 + 0.40 x 0.0003 + 0.20 x 0.0064 + 0.10 x 0.0644
= 0.0041 + 0.0001 + 0.0013 + 0.0064 = 0.0119 or 1.19%
Standard Deviation of Portfolio = (0.0119)1/2 = 0.1090 or 10.90%
Use the information in the following to answer questions 5-8 below:
State of
Economy
Boom
Growth
Stagnant
Recession
Probability
of State
.15
.25
.35
.25
Return on R
in State
0.040
0.040
0.040
0.040
Return on S
in State
0.280
0.140
0.070
-0.035
Return on T
in State
0.450
0.275
0.025
-0.175
9. Benefits of Diversification. Sally Rogers has decided to invest her wealth equally
across the three following assets. What is her expected return increase and the risk
reduction benefit by investing in the three assets versus putting all her wealth in asset M?
HINT: Find the standard deviation of asset M and of the portfolio equally invested in M,
N, and O.
States
Boom
Probability
30%
Asset M Return Asset N Return
12%
19%
Asset O Return
2%
Normal
Recession
50%
20%
8%
2%
11%
-2%
8%
12%
ANSWER
First find the expected return of the equally weighted portfolio in the three economic
states:
Return of Portfolio in Boom = 1/3 (12%) + 1/3 (19%) + 1/3 (2%) = 11.00%
Return of Portfolio in Normal = 1/3 (8%) + 1/3 (11%) + 1/3 (8%) = 9.00%
Return of Portfolio in Recession = 1/3 (2%) + 1/3 (-2%) + 1/3 (12%) = 4.00%
Now find the expected returns of Asset M and the Portfolio.
Expected Return Asset M = 0.30 x (12%) + 0.50 x (8%) + 0.20 (2%)
E(rM) = 3.6% + 4.0% + 0.4% = 8%
Expected Return Portfolio = 0.30 x (11%) + 0.50 x (7%) + 0.20 (4%)
E(rM) = 3.3% + 4.5% + 0.8% = 8.6%
Now find the standard deviation of Asset M and the Portfolio.
Standard Deviation of Asset M = [0.30 x (0.12 – 0.08)2 + 0.50 x (0.08 – 0.08)2
+0.20 x (0.02 – 0.08)2]1/2
= [0.30 x 0.0016 + 0.20 x 0.0036]1/2
= [0.00048 + 0.00072]1/2 = [0.0012]1/2 = 0.0346 or 3.46%
Standard Deviation of Portfolio = [0.30 x (0.11 – 0.086)2 + 0.50 x (0.09 – 0.086)2
+0.30 x (0.4 – 0.086)2]1/2
= [0.30 x 0.0006 + 0.50 x 0.0000 + 0.20 x 0.0021]1/2
= [0.0002 + 0.0000 + 0.0004]1/2 = [0.0006]1/2 = 0.0246 or 2.46%
The benefit is an increase in return of 0.6% and a simultaneous reduction in total risk of
1%.
11. Beta of a Portfolio. The beta of four stocks, G, H, I, and J are respectively 0.45, 0.8,
1.15, and 1.6. What is the beta of a portfolio with the following weights in each asset?
Portfolio 1
Portfolio 2
Portfolio 3
Weight in G
25%
30%
10%
Weight in H
25%
40%
20%
Weight in I
25%
20%
40%
Weight in J
25%
10%
30%
ANSWER
Beta of Portfolio 1 = 0.25 x 0.45 + 0.25 x 0.8 + 0.25 x 1.15 + 0.25 x 1.6
βportfolio - 1 = 0.1125 + 0.2 + 0.2875 + 0.4 = 1.0
Beta of Portfolio 2 = 0.30 x 0.45 + 0.40 x 0.8 + 0.20 x 1.15 + 0.10 x 1.6
βportfolio - 2 = 0.135 + 0.32 + 0.23 + 0.16 = 0.845
Beta of Portfolio 3 = 0.10 x 0.45 + 0.20 x 0.8 + 0.40 x 1.15 + 0.30 x 1.6
βportfolio - 3 = 0.045 + 0.16 + 0.46 + 0.48 = 1.145
12. Expected Return of a Portfolio using Beta. Using the same four assets from above
(problem 11) in the same three portfolios. What are the expected returns of the four
individual assets and the three portfolios if the current SML is plotting with an intercept
of 4% (risk-free rate) and a market premium of 10% (slope of the line)?
ANSWER
Expected Return of Asset G = 4% + 0.45 (10%) = 8.5%
Expected Return of Asset H = 4% + 0.8 (10%) = 12%
Expected Return of Asset I = 4% + 1.15 (10%) = 15.5%
Expected Return of Asset J = 4% + 1.6 (10%) = 20%
Expected Return of Portfolio 1 = 4% + 1.0 (10%) = 14%
Expected Return of Portfolio 2 = 4% + 0.845 (10%) = 12.45%
Expected Return of Portfolio 2 = 4% + 1.145 (10%) = 15.45%
Chapter 9
1. Payback Period – Given the cash flows of the four projects, A, B, C, and D, and
using the Payback Period decision model, which projects do you accept and which
projects do you reject with a three year cut-off period for recapturing the initial cash
outflow? Assume that the cash flows are equally distributed over the year for Payback
Period calculations.
Projects
Cost
Cash Flow Year One
Cash Flow Year Two
Cash Flow Year Three
Cash Flow Year Four
Cash Flow year Five
Cash Flow Year Six
A
$10,000
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
B
$25,000
$2,000
$8,000
$14,000
$20,000
$26,000
$32,000
C
$45,000
$10,000
$15,000
$20,000
$20,000
$15,000
$10,000
D
$100,000
$40,000
$30,000
$20,000
$10,000
$0
$0
Solution
Project A:
Year One: -$10,000 + $4,000 = $6,000 left to recover
Year Two: -$6,000 + $4,000 = $2,000 left to recover
Year Three: -$2,000 + $4,000 = fully recovered
Year Three: $2,000 / $4,000 = ½ year needed for recovery
Payback Period for Project A: 2 and ½ years, ACCEPT!
Project B:
Year One: -$25,000 + $2,000 = $23,000 left to recover
Year Two: -$23,000 + $8,000 = $15,000 left to recover
Year Three: -$15,000 + $14,000 = $1,000 left to recover
Year Four: -$1,000 + $20,000 = fully recovered
Year Four: $1,000 / $20,000 = 1/20 year needed for recovery
Payback Period for Project B: 3 and 1/20 years, REJECT!
Project C:
Year One: -$45,000 + $10,000 = $35,000 left to recover
Year Two: -$35,000 + $15,000 = $20,000 left to recover
Year Three: -$20,000 + $20,000 = fully recovered
Year Three: $20,000 / $20,000 = full year needed
Payback Period for Project B: 3 years, ACCEPT!
Project D:
Year One: -$100,000 + $40,000 = $60,000 left to recover
Year Two: -$60,000 + $30,000 = $30,000 left to recover
Year Three: -$30,000 + $20,000 = $10,000 left to recover
Year Four: -$10,000 + $10,000 = fully recovered
Year Four: $10,000 / $10,000 = full year needed
Payback Period for Project B: 4 years, REJECT!
3. Discounted Payback Period – Given the following four projects and their cash
flows, calculate the discounted payback period with a 5% discount rate, 10% discount
rate, and 20% discount rate. What do you notice about the payback period as the discount
rate rises? Explain this relationship.
Projects
Cost
Cash Flow Year One
Cash Flow Year Two
Cash Flow Year Three
Cash Flow Year Four
Cash Flow year Five
Cash Flow Year Six
A
$10,000
$4,000
$4,000
$4,000
$4,000
$4,000
$4,000
B
$25,000
$2,000
$8,000
$14,000
$20,000
$26,000
$32,000
C
$45,000
$10,000
$15,000
$20,000
$20,000
$15,000
$10,000
D
$100,000
$40,000
$30,000
$20,000
$10,000
$10,000
$0
Solution at 5% discount rate
Project A:
PV Cash flow year one -- $4,000 / 1.05 = $3,809.52
PV Cash flow year two -- $4,000 / 1.052 = $3,628.12
PV Cash flow year three -- $4,000 / 1.053 = $3,455.35
PV Cash flow year four -- $4,000 / 1.054 = $3,290.81
PV Cash flow year five -- $4,000 / 1.055 = $3,134.10
PV Cash flow year six -- $4,000 / 1.056 = $2,984.86
Discounted Payback Period: -$10,000 + $3,809.52 + $3,628.12 + $3,455.35 = $892.99
and fully recovered
Discounted Payback Period is 3 years.
Project B:
PV Cash flow year one -- $2,000 / 1.05 = $1,904.76
PV Cash flow year two -- $8,000 / 1.052 = $7,256.24
PV Cash flow year three -- $14,000 / 1.053 = $12,093.73
PV Cash flow year four -- $20,000 / 1.054 = $16,454.05
PV Cash flow year five -- $26,000 / 1.055 = $20,371.68
PV Cash flow year six -- $32,000 / 1.056 = $23,878.89
Discounted Payback Period: -$25,000 + $1,904.76 + $7,256.24 + $12,093.73 +
$16,454.05 = $12,708.78 and fully recovered
Discounted Payback Period is 4 years.
Project C:
PV Cash flow year one -- $10,000 / 1.05 = $9,523.81
PV Cash flow year two -- $15,000 / 1.052 = $13,605.44
PV Cash flow year three -- $20,000 / 1.053 = $17,276.75
PV Cash flow year four -- $20,000 / 1.054 = $16,454.05
PV Cash flow year five -- $15,000 / 1.055 = $11,752.89
PV Cash flow year six -- $10,000 / 1.056 = $7,462.15
Discounted Payback Period: -$45,000 + $9,523.81 + $13,605.44 + $17,276.75 +
$16,454.05 = $11,860.05 and fully recovered
Discounted Payback Period is 4 years.
Project D:
PV Cash flow year one -- $40,000 / 1.05 = $38,095.24
PV Cash flow year two -- $35,000 / 1.052 = $31,746.03
PV Cash flow year three -- $20,000 / 1.053 = $17,276.75
PV Cash flow year four -- $10,000 / 1.054 = $8,227.02
PV Cash flow year five -- $10,000 / 1.055 = $7,835.26
PV Cash flow year six -- $0 / 1.056 = $0
Discounted Payback Period: -$100,000 + $38,095.24 + $31,746.03 + $17,276.75 +
$8,227.02 + $7,835.26 = $3,180.30 and fully recovered.
Discounted Payback Period is 5 years.
Solution at 10% discount rate
Project A:
PV Cash flow year one -- $4,000 / 1.10 = $3,636.36
PV Cash flow year two -- $4,000 / 1.102 = $3,307.79
PV Cash flow year three -- $4,000 / 1.103 = $3,005.26
PV Cash flow year four -- $4,000 / 1.104 = $2,732.05
PV Cash flow year five -- $4,000 / 1.105 = $2,483.69
PV Cash flow year six -- $4,000 / 1.106 = $2,257.90
Discounted Payback Period: -$10,000 + $3,636.36 + $3,307.79 + $3,005.26 + $2,732.05
= $2,681.46 and fully recovered
Discounted Payback Period is 4 years.
Project B:
PV Cash flow year one -- $2,000 / 1.10 = $1,818.18
PV Cash flow year two -- $8,000 / 1.102 = $6,611.57
PV Cash flow year three -- $14,000 / 1.103 = $10,518.41
PV Cash flow year four -- $20,000 / 1.104 = $13,660.27
PV Cash flow year five -- $26,000 / 1.105 = $16,143.95
PV Cash flow year six -- $32,000 / 1.106 = $18,063.17
Discounted Payback Period: -$25,000 + $1,818.18 + $6,611.57 + $10,518.41 +
$13,660.27 = $7,608.43 and fully recovered
Discounted Payback Period is 4 years.
Project C:
PV Cash flow year one -- $10,000 / 1.10 = $9,090.91
PV Cash flow year two -- $15,000 / 1.102 = $12,396.69
PV Cash flow year three -- $20,000 / 1.103 = $15,026.30
PV Cash flow year four -- $20,000 / 1.104 = $13,660.27
PV Cash flow year five -- $15,000 / 1.105 = $9,313.82
PV Cash flow year six -- $10,000 / 1.106 = $5,644.74
Discounted Payback Period: -$45,000 + $9,090.91 + $12,396.69 + $15,026.20 +
$13,660.27 = $5174.07 and fully recovered
Discounted Payback Period is 4 years.
Project D:
PV Cash flow year one -- $40,000 / 1.10 = $36,363.64
PV Cash flow year two -- $35,000 / 1.102 = $28,925.62
PV Cash flow year three -- $20,000 / 1.103 = $15,026.30
PV Cash flow year four -- $10,000 / 1.104 = $6,830.13
PV Cash flow year five -- $10,000 / 1.105 = $6,209.21
PV Cash flow year six -- $0 / 1.106 = $0
Discounted Payback Period: -$100,000 + $36,363.64 + $28,925.62 + $15,026.30 +
$6,830.13 + $6,209.21 = -$6,645.10 and never recovered.
Initial cash outflow is never recovered.
Solution at 20% discount rate
Project A:
PV Cash flow year one -- $4,000 / 1.20 = $3,333.33
PV Cash flow year two -- $4,000 / 1.202 = $2,777.78
PV Cash flow year three -- $4,000 / 1.203 = $2,314.81
PV Cash flow year four -- $4,000 / 1.204 = $1,929.01
PV Cash flow year five -- $4,000 / 1.205 = $1,6075.10
PV Cash flow year six -- $4,000 / 1.206 = $1,339.59
Discounted Payback Period: -$10,000 + $3,333.33 + $2,777.78 + $2,314.81+ $1,929.01 =
$354.93 and fully recovered
Discounted Payback Period is 4 years.
Project B:
PV Cash flow year one -- $2,000 / 1.20 = $1,666.67
PV Cash flow year two -- $8,000 / 1.202 = $5,555.56
PV Cash flow year three -- $14,000 / 1.203 = $8,101.85
PV Cash flow year four -- $20,000 / 1.204 = $9,645.06
PV Cash flow year five -- $26,000 / 1.205 = $10,448.82
PV Cash flow year six -- $32,000 / 1.206 = $10,716.74
Discounted Payback Period: -$25,000 + $1,666.67 + $5,555.56 + $8,101.85 + $9,645.06
+ $10,448.82 = $10,417.96 and fully recovered
Discounted Payback Period is 5 years.
Project C:
PV Cash flow year one -- $10,000 / 1.20 = $8,333.33
PV Cash flow year two -- $15,000 / 1.202 = $10,416.67
PV Cash flow year three -- $20,000 / 1.203 = $11,574.07
PV Cash flow year four -- $20,000 / 1.204 = $9,645.06
PV Cash flow year five -- $15,000 / 1.205 = $6,028.16
PV Cash flow year six -- $10,000 / 1.206 = $3,348.97
Discounted Payback Period: -$45,000 + $8,333.33 + $10,416.67 + $11,574.07 +
$9,645.06 + $6,028.16 = $997.29 and fully recovered
Discounted Payback Period is 5 years.
Project D:
PV Cash flow year one -- $40,000 / 1.20 = $33,333.33
PV Cash flow year two -- $35,000 / 1.202 = $24,305.56
PV Cash flow year three -- $20,000 / 1.203 = $11,574.07
PV Cash flow year four -- $10,000 / 1.204 = $4,822.53
PV Cash flow year five -- $10,000 / 1.205 = $4,018.78
PV Cash flow year six -- $0 / 1.206 = $0
Discounted Payback Period: -$100,000 + $33,333.33 + $24,305.56 + $11,574.07 +
$4,822.53 + $4,018.78 = -$21,945.73 and initial cost is never recovered.
Discounted Payback Period is infinity.
As the discount rate increases, the Discounted Payback Period also increases. The reason
is that the future dollars are worth less in present value as the discount rate increases
requiring more future dollars to recover the present value of the outlay.
7. Net Present Value – Swanson Industries has a project with the following projected
cash flows:
Initial Cost, Year 0: $240,000
Cash flow year one: $25,000
Cash flow year two: $75,000
Cash flow year three: $150,000
Cash flow year four: $150,000
a. Using a 10% discount rate for this project and the NPV model should
this project be accepted or rejected?
b. Using a 15% discount rate?
c. Using a 20% discount rate?
Solution
a. NPV = -$240,000 + $25,000/1.10 + $75,000/1.102 + $150,000/1.103 +
$150,000/1.104
NPV = -$240,000 + $22,727.27 + $61,983.47 + $112,697.22 + $102,452.02
NPV = $59,859.98 and accept the project.
b. NPV = -$240,000 + $25,000/1.15 + $75,000/1.152 + $150,000/1.153 +
$150,000/1.154
NPV = -$240,000 + $21,739.13 + $56,710.76 + $98,627.43 + $85,762.99
NPV = $22,840.31 and accept the project.
c. NPV = -$240,000 + $25,000/1.20 + $75,000/1.202 + $150,000/1.203 +
$150,000/1.204
NPV = -$240,000 + $20,833.33 + $52,083.33 + $86,805.56 + $72,337.96
NPV = -$7,939.82 and reject the project.
11. Internal Rate of Return – What are the IRRs of the four projects for
Swanson Industries in problem #9?
Solution, this is an iterative process but can be solved quickly on a calculator or
spreadsheet.
Enter the keys noted for each project in the CF of a Texas BA II Plus calculator
Cash Flows
CFO
CO1, F1
CO2, F2
Year three
Year four
Year five
CPT IRR
Project M
-$2,000,000
$500,000, 1
$500,000, 1
$500,000, 1
$500,000, 1
$500,000, 1
7.93%
Project N
-$2,000,000
$600,000, 1
$600,000, 1
$600,000, 1
$600,000, 1
$600,000, 1
15.24%
Project O
-$2,000,000
$1,000,000, 1
$800,000, 1
$600,000, 1
$400,000, 1
$200,000, 1
20.27%
Project P
-$2,000,000
$300,000, 1
$500,000, 1
$700,000, 1
$900,000, 1
$1,100,000, 1
17.72%
15. Profitability Index -- Given the discount rates and the future cash flows of each
project, which projects should they accept using profitability index?
Cash Flows
Year zero
Year one
Year two
Year three
Project U
-$2,000,000
$500,000
$500,000
$500,000
Project V
-$2,500,000
$600,000
$600,000
$600,000
Project W
-$2,400,000
$1,000,000
$800,000
$600,000
Project X
-$1,750,000
$300,000
$500,000
$700,000
Year four
Year five
Discount Rate
$500,000
$500,000
6%
$600,000
$600,000
9%
$400,000
$200,000
15%
$900,000
$1,100,000
22%
Solution, find the present value of benefits and divide by the present value of the
costs for each project.
Project U’s PV Benefits = $500,000/1.05 + $500,000/1.052 + $500,000/1.053
+ $500,000/1.054 + $500,000/1.055
Project U’s PV Benefits = $476,190.48 + $453,514.74 + $431,918.80 +
$411,351.24 + $391,763.08 = $2,164,738.34
Project U’s PV Costs = $2,000,000
Project U’s PI = $2,164,738.34 / $2,000,000 = $1.0824 accept project.
Project V’s PV Benefits = $600,000/1.09 + $600,000/1.092 + $600,000/1.093
+ $600,000/1.094 + $600,000/1.095
Project V’s PV Benefits = -$2,000,000 + $550,458.72 + $505,008.00 +
$463,331.09 + $425,055.13 + $389,958.83 = $2,333,790.77
Project V’s PV Costs = $2,500,000
Project V’s PI = $2,333,790.77 / $ 2,500,000 = 0.9335 and reject project.
Project W’s PV Benefits = $1,000,000/1.15 + $800,000/1.152 +
$600,000/1.153 + $400,000/1.154 + $200,000/1.155
Project W’s PV Benefits = $869,565.22 + $604,914.93 + $394,509.74 +
$228,701.30 + $99,435.34 = $2,197,126.53
Project W’s PV Costs = $2,400,000
Project W’s PI = $2,197,126.53 / $2,400,000 = 0.9155 and reject project.
Project X’s PV Benefits= -$2,000,000 + $300,000/1.22 + $500,000/1.222 +
$700,000/1.223 + $900,000/1.224 + $1,100,000/1.225
Project X’s PV Benefits= -$2,000,000 + $245,901.64 + $335,931.20 +
$385,494.82 + $406,259.18 + $406,999.18 = $1,780,586.02
Project X’s PV Cost = $1,750,000
Project X’s PI = $1,780,586.02 / $1,750,000 = 1.0175 and accept project.
19. NPV Profile of a Project – Given the following cash flows of Project L-2, draw
the NPV profile. Hint use a discount rate of zero for one intercept (y-axis) and solve for
the IRR for the other intercept (x-axis).
Cash flows:
Year 0 = -$250,000
Year 1 = $45,000
Year 2 = $75,000
Year 3 = $115,000
Year 4 = $135,000
NPV (discount rate = 0) = -$250,000 + $45,000 + $75,000 + $115,000 +
$135,000 = $120,000 (y-axis intercept)
NPV (discount rate = 5%) = -$250,000 + $45,000/1.05 + $75,000/1.052 +
$115,000/1.053 + $135,000/1.054 = $71,290.51
NPV (discount rate = 10%) = -$250,000 + $45,000/1.10 + $75,000/1.102 +
$115,000/1.103 + $135,000/1.104 = $31,500.58
NPV (discount rate = 15%) = -$250,000 + $45,000/1.15 + $75,000/1.152 +
$115,000/1.153 + $135,000/1.154 = -$1,357.74
NPV (discount rate = 20%) = -$250,000 + $45,000/1.20 + $75,000/1.202 +
$115,000/1.203 + $135,000/1.204 = -$28,761.57
IRR = 14.77%
NPV Dollars
$120,000
NPV Profile
Of Project L-2
$90,000
$60,000
$30,000
$0
5%
10%
15%
20%
-$30,000
Discount Rates
Chapter 10
1. From the balance sheet accounts listed below:
a. list all the working capital accounts,
b.find the net working capital for the years ending 2003 and 2004, and
c. calculate the change in net working capital for the year 2004.
Balance Sheet Accounts of Romula Corporation
Account
Balance 12/31/2003
Balance 12/31/2004
Accumulated Depreciation
$2,020
$2,670
Accounts Payable
$1,800
$2,060
Accounts Receivable
$2,480
$2,690
Cash
$1,300
$1,090
Common Stock
$4,990
$4,990
Inventory
$5,800
$6,030
Long-Term Debt
$7,800
$8,200
Plant, Property & Equipment
$8,400
$9,200
Retained Earnings
$1,370
$1,090
Solution:
a. The Working Capital Accounts are:
Cash, Accounts Receivable, Inventory, and Accounts Payable
b. The Net Working Capital for 2003 and 2004:
Net Working Capital = Cash + Accounts Receivable + Inventory – Accounts
Payable
2003 Net Working Capital = $1,300 + $2,480 + $5,800 - $1,800 = $7,780
2004 Net Working Capital = $1,090 + $2,690 + $6,030 - $2,060 = $7,750
c. The Change in Net Working Capital for 2004 is, $7,750 - $7,780 = -$30 or a
decrease in Net Working Capital of $30.
d.
3. Find the operating cash flow for the year for Spacely Sprockets if they had sales
revenue of $300,000,000, cost of goods sold of $140,000,000, sales and administrative
costs of $40,000,000, depreciation expense of $65,000,000 and a tax rate of 40%.
Solution: Using income statement format we have,
Sales
$300,000,000
COGS
$140,000,000
SG&A
$ 40,000,000
Depreciation
$ 65,000,000
EBIT
$55,000,000
Taxes (@ 40%)
$22,000,000
Net Income
$33,000,000
Operating Cash Flow = EBIT + Depreciation – Taxes
Operating Cash Flow = $55,000,000 + $65,000,000 - $22,000,000 = $98,000,000
For problems 5 through 10 use the data from the following financial statements:
Partial Income Statement Year Ending 2004
Sales Revenue
$350,000
COGS
$140,000
Fixed Costs
$ 43,000
SG&A Expenses
$ 28,000
Depreciation
$ 46,000
Partial Balance Sheet 12/31/2003
Assets:
Liabilities:
Cash
$ 16,000
Notes Payable
$ 14,000
Accounts Rec.
$ 28,000
Accounts Payable
$ 19,000
Inventories
$ 48,000
Long-Term Debt
$190,000
Fixed Assets
$368,000
Acc. Depreciation
$142,000
Owner’s Equity
Retained Earnings
$ ???????
Intangible Assets
$ 82,000
Common Stock
$130,000
Partial Balance Sheet 12/31/2004
Assets:
Liabilities:
Cash
$ 26,000
Notes Payable
$ 12,000
Accounts Rec.
$ 19,000
Accounts Payable
$ 24,000
Inventories
$ 53,000
Long-Term Debt
$162,000
Fixed Assets
$448,000
Acc. Depreciation
$ ???????
Retained Earnings
$ ??????
Intangible Assets
$ 82,000
Common Stock
$180,000
Owner’s Equity
5. Complete the partial income statement and balance sheet if the company paid
interest expense of $18,000 for 2004, dividends of $30,000 and had an overall tax rate
of 40% for 2004.
Solution:
Income Statement for the Year Ending 12/13/2004
Sales Revenue
$350,000
COGS
$140,000
Fixed Costs
$ 43,000
SG&A Expenses
$ 28,000
Depreciation
$ 46,000
EBIT
$ 93,000
Interest Expense
$ 18,000
Taxable Income
$ 75,000
Taxes @ 40%
$ 30,000
Net Income
$ 45,000
And with a Dividend payment of $30,000 the remainder of Net Income goes to Retained
Earnings, $15,000. To complete the balance sheet add up all the asset accounts and
subtract off the accumulated depreciation (contra asset account) for a total of $400,000.
Now balance the balance sheet by determining the total liabilities and owner’s equity
accounts ($353,000) and filling in the difference between this total and total assets as the
balance in Retained Earnings, $47,000.
Balance Sheet 12/31/2003
Assets:
Liabilities:
Cash
$ 16,000
Notes Payable
$ 14,000
Accounts Rec.
$ 28,000
Accounts Payable
$ 19,000
Inventories
$ 48,000
Long-Term Debt
$190,000
Fixed Assets
$368,000
Acc. Depreciation
$142,000
Retained Earnings
$ 47,000
Intangible Assets
$ 82,000
Common Stock
$130,000
Total Assets
$400,000
Total Liab. & OE
$400,000
Owner’s Equity
Do the same for the year 2004 but now we must first find accumulated depreciation total.
The prior year was $142,000 and the current year’s depreciation from the income
statement is $46,000 so the accumulated depreciation for 2004 is $188,000. Also,
Retained Earnings went up by Net Income minus dividends paid out so we have an
increase of $15,000 ($45,000 - $30,000).
Balance Sheet 12/31/2004
Assets:
Liabilities:
Cash
$ 26,000
Notes Payable
$ 12,000
Accounts Rec.
$ 19,000
Accounts Payable
$ 24,000
Inventories
$ 53,000
Long-Term Debt
$162,000
Fixed Assets
$448,000
Acc. Depreciation
$188,000
Retained Earnings
$ 62,000
Intangible Assets
$ 82,000
Common Stock
$180,000
Total Assets
$440,000
Owner’s Equity
Total Liab. & O.E.
$440,000
6.Find the Cash Flow from Assets for 2004 and break down into it its three parts,
Operating Cash Flow, Change in Net Working Capital, and Capital Spending.
Solution:
Find the three parts that make up Cash Flow from Assets, Operating Cash Flow,
Change in Net Working Capital and Capital Spending.
Operating Cash Flow is EBIT – Taxes + Depreciation so,
OCF = $93,000 - $30,000 + $46,000 = $109,000
Change in Net Working Capital is 2004 NWC – 2003 NWC
2003 Net Working Capital is Current Assets minus Current Liabilities
2003 NWC = $16,000 + $18,000 + $48,000 - $14,000 - $19,000 = $59,000
2004 NWC = $26,000 + $19,000 + $53,000 - $12,000 - $24,000 = $62,000
Change in NWC = $62,000 - $59,000 = $3,000
Capital spending for 2004 is the Change in Net Fixed Assets (Fixed Assets minus
Depreciation) plus 2004 Depreciation Expense. Note there is no change in Intangible
Assets so we need only Fixed Assets and Accumulated Depreciation.
Capital Spending = ($448,000 - $188,000) – ($368,000 - $142,000) + $46,000 =
$80,000
And Cash Flow from Assets is:
CF from Assets = OCF - Increase in NWC - Increase in Capital Spending
CF from Assets = $109,000 - $3,000 - $80,000 = $26,000
7. Find the Cash Flow to Creditors for 2004 by parts and total with the parts Interest
Income Paid and Increases in Borrowing.
Solution:
First the Interest Paid to Creditors comes from the income statement and is
$18,000 for the year. Second, the change in Long-Term Debt reflects an increase or
decrease in cash flows to creditors. Here we have a decrease from 2003 to 2004 reflecting
a reduction or retirement of debt, a cash flow to creditors:
Decrease in Long-Term Debt 2004 = $190,000 – $162,000 = $28,000
Cash Flow to Creditors for 2004 = $18,000 + $28,000 = $46,000
8. Find the Cash Flow to Owners for 2004 by parts and total with the parts being
Dividends Paid and Increase in Borrowing.
Solution:
Dividends Paid for 2004 were $30,000 and the Common Stock account changed
from $130,000 in 2003 to $180,000 in 2004 for an increase of $50,000 so we have the
following Cash Flow to Owners:
2004 CF to Owners = $30,000 - $50,000 = -$20,000
9. Verify the Cash Flow Identity, Cash Flow from Assets ≡ Cash Flow to Creditors +
Cash Flow to Owners
Solution:
$26,000 ≡ $46,000 - $20,000
10. Produce the Sources and Uses of Cash (Statement of Cash Flows) for the year
2004.
Solution:
Using the information from questions 5 through 9 and noting that this Sources and
Uses of Cash ties out to the change in the cash balance for the year, we have a target of
$10,000 increase in cash or source for 2004.
Sources and Uses of Cash 2004
Sources and (Uses): Operating Activities
Operating Cash Flows
$109,000
Decrease in Current Assets (ex-Cash)
$
4,000
Increase in Current Liabilities
$
3,000
Sources and (Uses): Investing Activities
Capital Spending
Sources and (Uses): Financing Activities
($ 80,000)
Interest Expense
($ 18,000)
Dividends
($ 30,000)
Decrease in Long-Term Debt
($ 28,000)
Increase in Common Stock
$ 50,000
Net Sources and (Uses) of Cash
$ 10,000
11. Erosion Costs – Fat Tire Bicycle Company currently sells 40,000 bicycles per year.
The current bike is a standard balloon tire bike, selling for $90.00 with a production and
shipping cost of $35.00. The company is thinking of introducing an off-road bike with a
projected selling price of $410 and a production and shipping cost of $360. The projected
market is for 12,000 bikes in annual sales. However, they will loose sales in the fat tire
bikes of 8,000 per year if they introduce the new bike. What is the erosion cost from the
new bike? Should they start producing the off-road bike?
Solution:
Erosion Cost = ($90 - $35) x 8,000 = $520,000
Net Annual Cash Flow with one bike: ($90 - $35) x 40,000 = $2,600,000
Net Annual Cash Flow with two bikes:
($90 - $35) x (40,000 - 8,000) = $2,080,000
($410 - $360) x 12,000 = $600,000
Net Annual CF = $2,080,000 + $600,000 = $2,680,000
Increase of $80,000 per year so add new off-road bike to production.
15. Depreciation Expense –Brock Florist Company buys a new delivery truck for
$29,000. It is classified as a light duty truck.
d. Calculate the depreciation schedule using a five year life and straight
line depreciation and the half year convention for the first and last year.
e. Calculate the depreciation schedule using a five year life and MACRS
depreciation.
f. Compare the depreciation schedules from parts a and b before and after
taxes with a 30% tax rate for Brock Florists. What do you notice about
the difference in these two methods?
Solution
a. Annual depreciation is cost of truck divided by five; $29,000/ 5 = $5,800
And for the first and last year we have $5,800 / 2 = $2,900.
b. Depreciation schedule using MACRS;
Year One Depreciation = $29,000 x 0.2000 = $5,800
Year Two Depreciation = $29,000 x 0.3200 = $9,280
Year Three Depreciation = $29,000 x 0.1920 = $5,568
Year Four Depreciation = $29,000 x 0.1152 = $3,340.80
Year Five Depreciation = $29,000 x 0.1152 = $3,340.80
Year Six Depreciation = $29,000 x 0.0576 = $1,670.40
c. Comparing the two depreciation schedules before and after taxes (at 30%):
Year
One
Two
Three
Four
Five
Straight Line
$2,900
$5,800
$5,800
$5,800
$5,800
MACRS
$5,800
$9,280
$5,568
$3,340.80
$3,340.80
∆ Before Tax
$2,900
$3,480
-$232
-$2,459.20
-$2,459.20
∆ After Tax
$870
$1,044
-$69.60
-$737.76
-$737.76
$2,900
$29,000
Six
Total
$1,670.40
$29,000
-$1,229.60
$0
-$368.88
$0
The difference is that the MACRS moves up the tax shield to the early years
of depreciation yet the total tax shield is the same under both depreciation
schedules.
19. Project Cash Flows & NPV – The managers of Classic Autos Incorporated plan to
manufacture classic T-Birds (1957 replicas). The necessary foundry equipment will cost a
total of $4,000,000 and will be depreciated using a five-year MACRS life. Projected sales
in annual units for the next five years are 300 per year. If sales price is $27,000 per car,
variable costs are $18,000 per car, and fixed costs are $1,200,000 annually, what are the
annual operating cash flows if the tax rate is 30%? The equipment is sold for salvage for
$500,000 at the end of year five. What is the after tax cash flows of the salvage? Net
working capital increases by $600,000 at the beginning of the project (Year 0) and is
reduced back to its original level in the final year. What is the incremental cash flows of
the project? Using a discount rate of 12% for the project, should the project be accepted
or rejected with the NPV decision model?
Solution
Annual depreciation of foundry equipment is:
Year One, $4,000,000 x 0.20 = $800,000
Year Two, $4,000,000 x 0.32 = $1,280,000
Year Three, $4,000,000 x 0.192 = $768,000
Year Four, $4,000,000 x 0.1152 = $460,800
Year Five, $4,000,000 x 0.1152 = $460,800
Operating Cash Flows are:
Annual Sales, 300 x $27,000 = $8,100,000
Annual COGS, 300 x $18,000 = $5,400,000
In thousands (rounded)
Year 1
Sales Revenue
- COGS
- Fixed Costs
- Depreciation
EBIT
- Taxes
Net Income
+ Depreciation
Operating Cash Flows
Year 2
$8,100
$5,400
$1,200
$ 800
$ 700
$ 210
$ 490
$ 800
$1,290
$8,100
$5,400
$1,200
$1,280
$ 220
$ 66
$ 154
$1,280
$1,434
Year 3
Year 4
Year 5
$8,100
$5,400
$1,200
$ 768
$ 732
$ 220
$ 512
$ 768
$1,280
$8,100
$5,400
$1,200
$ 461
$1,039
$ 312
$ 727
$ 461
$1,188
$8,100
$5,400
$1,200
$ 461
$1,039
$ 312
$ 727
$ 461
$1,188
The equipment is sold for salvage for $500,000 at the end of year five. It has a book value
of $4,000,000 - $800,000 - $1,280,000 - $768,000 - $460,800 - $460,800 = $230,400
Gain on Sale is $500,000 - $230,400 = $269,600
Tax on Gain is $269,600 x 0.30 = $80,880
And after-tax cash flow on disposal is $500,000 - $80,880 = $419,120.
Incremental Cash Flows for Project (Answer in Thousands, $000)
Account/Activity
Investment
Year 0 Year 1
-$4,000
NWC
-$ 600
OCF
Salvage Value
Year 2
Year 3
Year 4
Year 5
$ 600
$1,290
$1,434
$1,280
$1,118
$1,118
$ 419
Total Cash Flows
(Incremental)
-$4,600 $1,290
$1,434
$1,280
$1,118
$2,137
NPV @ 12% = -$4,600 + $1,290/1.12 + $1,434/1.122 + $1,280/1.123 + $1,118/1.124 +
$2,137/1.125 = -$4,600 + 1,241 + 1,199 + $911 + $711 + $1,213 = $529
Accept the project because NPV is positive $529,209 (without any rounding).
Chapter 11
1. WACC – Eric Cartman has another get rich quick idea but needs funding to support
the idea. Eric will borrow $2,000 from his mom and she will charge Eric 6% on the loan.
Eric will borrow $1,500 from Chef and he will charge 8% on the loan. Eric will borrow
$800 from Mr. Garrison and he will charge Eric 14% on the loan. What is the weighted
average cost of capital for Eric?
Solution:
Total funds borrowed = $2,000 + $1,500 + $800 = $4,300
WACC = ($2,000 / $4,300) x 0.06 + ($1,500 / $4,300) x 0.08 + ($800 / $4,300) x 0.14
WACC = 0.4651 x 0.06 + 0.3488 x 0.08 + 0.1860 x 0.14
WACC = 0.0279 + 0.0279 + 0.0260 = 0.0819 or 8.19%
5. Cost of Debt with Fees -- Kenny Enterprises will issue the same debt in problem #3
but now will use an investment banker that charges $25 per bond for their services. What
is the new cost of debt for Kenny Enterprises at a market price of $920, $1000, and
$1080?
Solution:
A. If the bond sells for $920 and Kenny pays $25 per bond the net proceeds are $895
$895 = $1,000 / (1+ (YTM/2))40 + $40 x (1 – 1/(1 + (YTM/2))40)/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS
40
?
-895
40
1000
Variables
N
I/Y
PV
PMT
FV
OUTPUT
9.15%
B. If the bond sells for $1000 and Kenny pays $25 per bond the net proceeds are $975
$975 = $1,000 / (1+ (YTM/2))40 + $40 x (1 – 1/(1 + (YTM/2))40)/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS
40
?
-975
40
1000
Variables
N
I/Y
PV
PMT
FV
OUTPUT
8.26%
C. If the bond sells for $1080 and Kenny pays $25 per bond the net proceeds are $1055
$1055 = $1,000 / (1+ (YTM/2))40 + $40 x (1 – 1/(1 + (YTM/2))40)/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS
40
?
-1055
40
1000
Variables
N
I/Y
PV
PMT
FV
OUTPUT
7.47%
7. Cost of Equity: SML – Stan is expanding his business and he will sell common stock
for the needed funds. If the current risk-free rate is 4% and the expected market return is
12%, what is the cost of equity for Stan if the beta of the stock is:
A. 0.75
B. 0.90
C. 1.05
D. 1.20
Solution:
A. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity = E(ri) = 0.04 + 0.75 (0.12 – 0.04)
Cost of Equity = 0.04 + 0.75 (0.08) = 0.04 + 0.06 = 0.10 or 10%
B. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity = E(ri) = 0.04 + 0.90 (0.12 – 0.04)
Cost of Equity = 0.04 + 0.90 (0.08) = 0.04 + 0.072 = 0.112 or 11.2%
C. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity = E(ri) = 0.04 + 1.05 (0.12 – 0.04)
Cost of Equity = 0.04 + 1.05 (0.08) = 0.04 + 0.084 = 0.124 or 12.4%
D. Using the security market line we have,
E(ri) = rf + βi (E(rm) – rf)
Cost of Equity = E(ri) = 0.04 + 1.20 (0.12 – 0.04)
Cost of Equity = 0.04 + 1.20 (0.08) = 0.04 + 0.096 = 0.136 or 13.6%
9. Cost of Preferred Stock – Kyle is raising funds for his company by selling preferred
stock. The preferred stock has a par value of $100 and a dividend rate of 6%. The stock is
selling for $80 in the market. What is the cost of preferred stock for Kyle?
Solution:
The dividend is $100 x 0.06 = $6.00
And with a price of $80 the cost of preferred stock is $6/$80 = 0.075 or 7.5%
13. Adjusted WACC – Lewis runs an outdoor adventure company and wants to know
what impact a tax change will have on his WACC. Currently Lewis has the following
borrowing pattern:
Equity 35% and cost of 14%
Preferred Stock 15% and cost of 11%
Debt 50% and cost of 10% before taxes.
What is the adjusted WACC for Lewis if the tax rate is
a. 40%
b. 30%
c. 20%
d. 10%
e. 0%?
Solution:
a. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.40) =
Adjusted WACC = 4.9% + 1.65% + 3.0% = 9.55%
b. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.30) =
Adjusted WACC = 4.9% + 1.65% + 3.5% = 10.05%
c. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.20) =
Adjusted WACC = 4.9% + 1.65% + 4.0% = 12.55%
d. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.10) =
Adjusted WACC = 4.9% + 1.65% + 4.5% = 11.05%
e. Adjusted WACC = 0.35 x 14% + 0.15 x 11% + 0.50 x 10% x (1 – 0.00) =
Adjusted WACC = 4.9% + 1.65% + 5.0% = 13.55%
15. Beta of a Project – Magellan is adding a project to the company portfolio and has the
following information, the expected market return is 14%, the risk-free rate is 3%, and
the expected return on the new project is 18%. What is the beta of the project?
Solution:
E(rproject) = 18% = 3% + βproject x (14% - 3%) and Beta = 1.3636
Chapter 12
3. Benefit of Borrowing – Wilson Motors is looking at expanding its operations by
adding a second manufacturing location. If successful the company will make $400,000
but if it fails the company will loose $250,000. Wilson Motors has decided to borrow the
$250,000 but the bank is charging 15% on the loan. Should Wilson Motors borrow the
money if
g. The probability of success is 90%?
h. The probability of success is 80%?
i. The probability of success is 70%?
Solution:
A. Return on 90% success rate = 0.9 x $400,000 - $250,000 x 1.15 = $72,500,
so borrow the money.
B. Return on 80% success rate = 0.8 x $400,000 - $250,000 x 1.15 = $32,500,
so borrow the money.
C. Return on 70% success rate = 0.7 x $400,000 - $250,000 x 1.15 = -$7,500,
So do not borrow the money.
6. Pecking Order Hypothesis – Rachel has the following places she can borrow:
Source of Funds
Parents
Friends
Bank Loan
Credit Card
Interest Rate
0%
5%
9%
14.5%
Borrowing Limit
$10,000
$2,000
$15,000
$5,000
What is Rachel’s weighted average cost of capital if she needs to borrow
a. $10,000
b. $20,000
c. $30,000
Solution:
a. for $10,000 she would borrow all of it from her parents and pay 0%
interest so her WACC is 0.
b. For $20,000 she would borrow $10,000 from her parents, $2,000 from
her friends and $8,000 from the bank for a WACC of,
WACC = 10,000 / $20,000 x 0% + $2,000 / $20,000 x 5% +
$8,000 / $20,000 x 9%
WACC = 0% + .5% + 3.6% = 4.1%
c. For $30,000 she would borrow $10,000 from her parents, $2,000 from
her friends, $15,000 from the bank and $3,000 against her credit card for
a WACC of,
WACC = 10,000 / $30,000 x 0% + $2,000 / $30,000 x 5% +
$15,000 / $30,000 x 9% + $3,000 / $30,000 x 14.5%
WACC = 0% + .333% + 4.5% + 1.45% = 6.283%
9. Finding WACC – Monica is the CFO of Cooking World and uses Pecking Order
Hypothesis (POH) philosophy when she borrows for company projects. Currently the
she can borrow up to $400,000 from her bank at a rate of 8.5%, float a bond for
$750,000 at a rate of 9.25%, or issue additional stock for $1,300,000 at a cost of 17%.
What is the WACC for Cooking World if Monica chooses to invest
a. $1,000,000 in new projects
b. $2,000,000 in new projects
c. $3,000,000 in new projects?
Solution:
a. WACC if she borrows $1,000,000 is
WACC = 0.4 x 8.5% + 0.6 x 9.25% = 3.40% + 5.55% = 8.95%
b. WACC if she borrows $2,000,000 is
WACC = 0.2 x 8.5% + 0.375 x 9.25% + 0.425 x 17%
WACC = 1.7000% + 3.4688% + 7.2250% = 12.3938%
c. She can not borrow $3,000,000 her maximum borrowing is $2,450,000.
WACC at $2,450,000 is,
WACC = 0.1633 x 8.5% + 0.3061 x 9.25% + 0.5306 x 17%
WACC = 1.3878% + 2.8316% + 9.0204% = 13.2398%
11. M&M, World of No Taxes – Air America is looking at changing its capital structure
from an all equity firm to a leveraged firm with 50% debt and 50% equity firm. Air
America is a not for profit company and therefore pays no taxes. If the required rate
on the assets of Air America is 20% (RA), what is the current required cost of equity
and what is the new required cost of equity if the cost of debt is 10%?
Solution:
RE = RA + (RA – RD) x (D/E)
All Equity Firm: RE = RA + (RA – RD) x (D/E), where D = 0
All Equity Firm: RE = 20% + (20% - 10%) x 0/1 = 20%
New Leveraged Firm at 50-50 Debt to Equity
RE = 20% + (20% - 10%) x 1/1 = 30%
Chapter 13
Problems and Solutions
1. Business Operating Cycle – Kolman Kampers has a production cycle of 35 days,
an collection cycle of 21 days, and payment cycle of 14 days. What is Kolman’s
business operating cycle and cash conversion cycle? If Kolman reduces the
production cycle by one week what is the impact on the cash conversion cycle? If
Kolman decreases the collection cycle by one week what is the impact on the cash
conversion cycle? If Kolman increases the payment cycle by one week what is the
impact on the cash conversion cycle?
Solution:
Business Cycle = Production Cycle + Collection Cycle
Business Cycle = 35 Days + 21 Days = 56 Days
Cash Conversion Cycle = Business Cycle – Payment Cycle
Cash Conversion Cycle = 56 Days – 14 Days = 42 Days
Reducing Production Cycle by one week (7 days) reduces cash conversion
cycle by one week (7 Days) to 35 days.
Reducing Collection Cycle by one week (7 days) reduces cash conversion
cycle by one week (7 Days) to 35 days.
Increasing Payment by one week (7 days) reduces cash conversion cycle
by one week (7 Days) to 35 days.
2. Business Operation Cycle – Stewart and Company currently has a production
cycle of 40 days, a collection cycle of 20 days, and a payment cycle of 15 days.
What Stewart’s current business operating cycle and cash conversion cycle? If
Stewart and Company wants to reduce its cash conversion cycle to 35 days what
action can Stewart take?
Solution
Business Cycle = Production Cycle + Collection Cycle
Business Cycle = 40 Days + 20 Days = 60 Days
Cash Conversion Cycle = Business Cycle – Payment Cycle
Cash Conversion Cycle = 60 Days – 15 Days = 45 Days
Options on reducing the cash conversion cycle to 35 days:
1) reduce production cycle by 10 days
2) reduce collection cycle by 10 days
3) increase payment cycle by 10 days
4) combination of reductions to production cycle and collection
cycle and increase of payment cycle totaling 10 days.
Use the following account information for problems 3 through 8.
2003 Selected Income Statement Items for Rian Company
Cash Sales
$298,000
Credit Sales
$672,000
TOTAL SALES
$970,000
COGS
$570,000
2003 Selected Balance Sheet Accounts of Rian Company
12/31/03
12/31/02
Change
Accounts Receivable
$38,000
$46,000
$8,000
Inventory
$55,000
$59,000
$4,000
Accounts Payable
$27,000
$25,000
$2,000
3. Average Production Cycle – Find the average production cycle for Rian Co.
Solution
Average Inventory = (Beginning Inventory + Ending Inventory) / 2
Average Inventory for Corporate Seasonings = ($55,000 + $59,000) / 2 = $57,000
The second step is to determine how quickly we turn over the inventory. To do
this, we take the cost of goods sold for the year, COGS, and divide by the average
inventory:
Inventory Turnover = COGS / Average Inventory
Inventory Turnover for Corporate Seasonings = $570,000 / $57,000 = 10 times
Average Production Cycle = Days in Year / Inventory Turnover
Average Production Cycle = 365/10 = 36.5 Days
4. Average Production Cycle – For the coming year Rian Co. wants to reduce its
average production cycle by 6.5 days to 30 days. If the target ending inventory for
2004 is $61,000 what COGS will the company need to reach their goal?
Solution
Working backwards through the equations for average production cycle we have,
Average Production Cycle = 365/ x = 30 Days where x is the inventory turnover.
X = 12.1667
Average Inventory = 12.1667 = COGS / [($59,000 + $61,000)/2]
COGS = 12.1667 x $60,000 = $730,000
5. Average Collection Cycle – What is the average collection cycle for Rian Co.?
Solution
Average Accounts Receivable = (Beginning A/R + Ending A/R) / 2
Average A/R for Corporate Seasonings = ($38,000 + $46,000) / 2 = $42,000
Step two is to determine the Accounts Receivable turnover rate:
Accounts Receivable Turnover Rate = Credit Sales / Average Accounts Receivable
A/R Turnover for Corporate Seasonings = $672,000 / $42,000 = 16 times
The third and final step is to estimate the collection cycle by dividing the number of
days in a year by the Accounts Receivable turnover rate:
Collection Cycle = 365 / Accounts Receivable Turnover Rate
Rian’s Collection Cycle = 365 / 16 = 22.8125 Days
6. Average Collection Cycle – Rian Company had a target of 20 Days for collection
cycle for the year 2003. If total sales had remained at $970,000 how much of the
sales revenue would have needed to be cash sales for Rian to meet the collection
goal?
Solution
Working backwards to find credit sales we have,
Collection Cycle = 20 Days = 365 / Average Receivable Turnover
Average Receivable Turnover = 365 / 20 Days = 18.25 Days
Average Receivable Turnover = 18.25 Days = Credit Sales / $42,000
Credit Sales = $42,000 x 18.25 = $766,500
Cash Sales = Total Sales – Credit Sales = $970,000 - $766,500 = $203,500
7. Average Accounts Payable Cycle – Calculate Rian Co. average accounts payable
cycle.
Solution
Average Accounts Payable = (Beginning of the year A/P + End of Year A/P) / 2
Average A/P = ($27,000 + $25,000) / 2 = $26,000
The second step is to determine the Accounts Payable Turnover and here we use the
COGS as the cost of production.
Accounts Payable Turnover = COGS / Average A/P
Rian’s A/P Turnover = $570,000 / $26,000 = 21.9231 times
The third and final step is to determine the number of days that Corporate Seasonings
takes to pay its suppliers:
Accounts Payable Cycle = 365 / Accounts Payable Turnover
Rian’s A/P Cycle = 365 / 21.9231 = 16.6491 days
8. Average Accounts Payable Cycle – Rian Co. had a target of 15 days for payment
(accounts payable) cycle. What would the ending balance in the accounts payable
account needed to be to reach this target holding all other accounts the same?
Solution
Working backwards we have,
Rian’s A/P cycle = 15 days = 365 / Accounts Payable Turnover
Accounts Payable Turnover = 365 / 15 days = 24.3333 days
Accounts Payable Turnover = 24.3333 days = $570,000 / Average Accounts Payable
Average Accounts Payable = $570,000 / 24.3333 = $23,424.66
Average Accounts Payable = $23,424.66 = [$27,000 + Ending A/P] / 2
Ending A/P = $23,424.66 x 2 - $27.000 = $19,849.32
9. Cash Flow of Accounts Receivable – Myers and Associates, a famous law office
in Southern California bills it clients on the first of each month. However clients
pay in the following fashion; 40% pay at the end of the first month, 30% pay at
the end of the second month, 20% pay at the end of the third month, 5% pay at the
end of the fourth month and 5% default on their bills. Myers wants to know the
anticipated cash flows for the first quarter of 2004 if the past billings and
anticipated billings follow this same pattern.
Fourth Quarter
Actual Billings
First Quarter
Anticipated Billings
Oct
$392,000
Nov
$323,000
Dec
$296,000
Jan
$340,000
Feb
$360,000
Mar
$408,000
Solution
End of January Anticipated Cash Flow from Billings =
5% of Oct + 20% of Nov + 30% of Dec + 40% of Jan =
0.05 x $392,000 + 0.20 x $323,000 + 0.30 x $296,000 + 0.40 x $340,000 =
$19,600 + $64,600 + $88,800 + $136,000 = $309,000
End of February Anticipated Cash Flow from Billings =
5% of Nov + 20% of Dec + 30% of Jan + 40% of Feb =
0.05 x $323,000 + 0.20 x $296,000 + 0.30 x $340,000 + 0.40 x $360,000 =
$16,150 + $59,200 + $102,000 + $144,000 = $321,350
End of March Anticipated Cash Flows
5% of Dec + 20% of Jan + 30% of Feb + 40% of Mar =
0.05 x $296,000 + 0.20 x $340,000 + 0.30 x $360,000 + 0.40 x $408,000 =
$14,800 + $68,000 + $108,000 + $163,200 = $354,000
10. Ageing Accounts Receivable – Thomas Bicycles has the following outstanding
account receivables at the close of the month. The monthly late fee is 1% of the
outstanding balance at the end of the billing month following the sale (February
sales receive a late fee in April if not paid by March 31, 2004). Determine the
current amount due for each bill and age the receivables. Today is May 31, 2004.
Invoice #
01-1145
02-0390
02-1101
Billing Date Customer
01-11-04
DHL
02-03-04
KPM
02-11-04
JBB
Original $
$125.00
$315.00
$200.00
Late Fees $
Current Due
03-14-04
03-17-04
04-09-04
04-21-04
04-22-04
05-06-04
05-11-04
03-1448
03-1773
04-0985
04-2104
04-2201
05-0698
05-1143
GLC
WNK
ERN
DLB
QSV
JMG
BMM
$350.00
$850.00
$310.00
$240.00
$565.00
$400.00
$725.00
Solution:
Late Fees are for invoices from January for three months (March, April, and May),
February for two months (April and May), and invoices from March for one month
(May). The April and May bills are not yet late enough for late fees.
Late Fees per bill;
01-1145 Late Fee = $125.00 x 1.013 - $125.00 = $2.51
02-0390 Late Fee = $315.00 x 1.012 - $315.00 = $6.33
02-1101 Late Fee = $200.00 x 1.102 - $200.00 = $4.02
03-1448 Late Fee = $350.00 x 1.10 - $350.00 = $3.50
03-1773 Late Fee = $850.00 x 1.10 - $850.00 = $8.50
Invoice #
01-1145
02-0390
02-1101
03-1448
03-1773
04-0985
04-2104
04-2201
05-0698
05-1143
Billing Date Customer
01-11-04
DHL
02-03-04
KPM
02-11-04
JBB
03-14-04
GLC
03-17-04
WNK
04-09-04
ERN
04-21-04
DLB
04-22-04
QSV
05-06-04
JMG
05-11-04
BMM
Original $
$125.00
$315.00
$200.00
$350.00
$850.00
$310.00
$240.00
$565.00
$400.00
$725.00
Late Fees $
$2.51
$6.33
$4.02
$3.50
$8.50
$0.00
$0.00
$0.00
$0.00
$0.00
The ageing of accounts receivable by period and total amount due:
Current Due
$127.51
$321.33
$204.02
$353.50
$858.50
$310.00
$240.00
$565.00
$400.00
$725.00
0-30 days (#05-0698 and #05-1143) $1,125.00
31-60 days (#04-0985, #04-2104, and #04- 2201) $1,115.00
61-90 days (#03-1448 and #03-1773) $1,212.00
91-120 days (#02-0390 and #02-1101) $525.35
Over 120 days (#01-1145) $127.51
13. Credit Screening – Fred and Barney manufacture kid peddle cars. They currently
have 4,000 cash paying customers and make a profit of $60 per car. Fred and Barney
want to expand their customer base by allowing customers to buy on credit. They
estimate a credit sales will bring in an additional 1200 customers per year but that
they will also have a default rate on credit sales of 5%. It costs $260 to make a peddle
car and they retail for $320. If all customers (old and new) buy on credit, what is the
cost of bad debt without a credit screen? What is the most Fred and Barney would pay
for a credit screen that accurately identifies bad debt customers prior to the sale?
What are the increased profits by adding credit sales for customers with and without a
credit screen? Should Fred and Barney offer credit sales if credit screen costs $10 per
customer?
Solution
Cost of bad debt is 0.05 x (4,000 + 1,200) x $260 = $67,600
Maximum cost of Credit Screen:
Old Profits = 4,000 x $60 = $240,000
$240,000 = 5200 x 0.95 x $60 – 5,200 x Cost of Screen per Customer
Cost per Customer = ($296,400 - $240,000) / 5200 = $10.85
New Profits of Credit Screen without = 5,200 x 0.95 x $60 – 0.05 x 5,200 x $260
= $296,400 - $67,600 = $228,800
New Profits with Credit Screen = 5,200 x 0.95 x $60 - $5200 x $10
= $296,400 - $52,000 = $244,400
Fred and Barney should offer credit sales if with credit screen cost of $10 per
customer.
15. Credit Terms -- As the manager of Fly-By-Night Airlines you decide to allow
customers 90 days to pay their bills. However, to encourage early payment you allow
customers to reduce their bill by 1.5% if paid within the first 30 days. At what implied
effective annual interest rate (EAR) are you loaning money to your customers? What if
you extend the discount to 60 days and allow full payment up to 180 days?
Solution:
Holding Period (60 Day) Return = $0.015 / $0.985 = 0.01523 or 1.523%
Now what is 0.1523% interest over 60 days stated on an annual basis?
Effective Annual Rate = (1 + 0.01523) 365/60 - 1 = 0.0963 or 9.63%
Holding Period (120 Day) Return = $0.015 / $0.985 = 0.01523 or 1.523%
Now what is 0.1523% interest over 120 days stated on an annual basis?
Effective Annual Rate = (1 + 0.01523) 365/120 - 1 = 0.0470 or 4.70%
17. Economic Order Quantity -- Economic Order Quantity -- Tyler’s Tinkering Toys
believes he will sell 4,000,000 Beany Babies this coming year (note this is annual
sales). He plans on ordering Beany Babies 40 times over the next year. The carrying
cost is $0.03 per baby per year. The order cost is $600 per order. What is the annual
carrying cost of the Beany Babies inventory? What is the annual ordering cost of the
Beany Babies? What is the optimal order quantity for the Beany Babies? Verify your
answer by calculating the new total inventory cost.
Solution
Annual Carrying Cost = average inventory x cost per unit per year
Average inventory = (4,000,000 / 40) / 2 = 50,000
Annual Carrying Cost = 50,000 x $0.03 = $1,500
Annual Ordering Costs = 40 x $600 = $24,000
EOQ = [2 x 4,000,000 x $600 / 0.03]1/2 = 400,000
New Carrying Costs = 400,000 / 2 x $0.03 = $6,000
New Ordering Costs = 4,000,000 / 400,000 x $600 = $6,000
EOQ of 400,000 is optimal order quantity (carrying costs = ordering costs).
Chapter 14
1. Timeline of Cash Dividend – Tiger Manufacturing Incorporated has the following
press release: “Tiger Manufacturing will pay a quarterly dividend of $0.50 per
share to record holders as of the 10th of this month on the 20th of this month.” This
announcement was made on July 3, 2005. Draw a time line of the dates around
this dividend payment assuming a two day settlement for stock trading.
Solution
Tiger Manufacturing Dividend Dates
Jul 3, 2005
Jul 8, 2005
Jul 10, 2005
Jul 20, 2005
Declaration
Ex-Date
Record Date
Payment Date
3. Stock Price around Dividend – Using the information in problem number 1, what
will the stock price of Tiger Manufacturing be after the cash dividend
announcement if the current price is $47.12 per share (assume the price does not
change between Sept. 3rd and Oct. 20th) and on what day does the price change?
What is the cost to a buyer after the announcement? What is the sales revenue to a
seller after the announcement?
Solution:
The price will drop by the size of the cash dividend on the morning following the
ex-date. The new price will be $47.12 - $0.50 = $46.62.
A new buyer after the announcement effectively pays $46.62 for the stock
regardless of the date of the purchase. If the buyer acquires the stock before the exdate the buyer pays $47.12 but is entitled to the $0.50 dividend so the net price is
$46.62. After the ex-date the buyer pays $46.62 but is not entitled to the $0.50
dividend.
The seller receives a net of $47.12 if the sale takes place before the ex-date
directly from the new buyer. If the sale takes place after the ex-date the seller receives
$46.62 directly from the buyer and the $0.50 dividend from the company for a net of
$47.12.
5. Dividend Pattern – Refer to Table 15-2 in the text (PepsiCo Dividend History)
and predict the next dividend using a percent change, a dollar change pattern, and
your expectation given the pattern change.
Solution
Using a percentage change we see the following changes each June:
June 2001
($0.145/$0.140) - 1 = 3.57%
June 2002
($0.150/$0.145) - 1 = 3.45%
June 2003
($0.160/$0.150) - 1 = 6.67%
Average percent change is (3.57% + 3.45% + 6.67%) /3 = 4.56%, so next change
would be 1.0456 x $0.16 = $0.1673
With a dollar (cent) change we have the following average, ($0.005 + $0.005 +
$0.01) / 3 = $0.00667 so the next change would be $0.16 + $0.0067 = $0.16667
Just looking at the pattern one would probably guess either $0.165 for a half-cent
increase or $0.17 with a full one-cent increase.
2. Creating Own Dividend Policy – Mickey owns 2,000,000 shares of Wisney
Entertainment. Wisney just declared a cash dividend of $0.05 per share. The stock
is currently selling for $5.00. If Mickey wants an annual “dividend income” from
his stock holdings of $50,000, $100,000, or $250,000 what must he do to get
these levels of income? What is his wealth in paper and cash for each level of
desired dividend income level?
Solution
The cash dividend he will receive if he does nothing is $0.05 x 2,000,000 =
$100,000 so if he wants this dividend income he just waits for the check. His wealth
after the distribution is:
Paper 2,000,000 x ($5.00 - $0.05) = $9,900,000
Cash 2,000,000 x $0.05 = $100,000
Total Wealth is $9,900,000 + $100,000 = $10,000,000
If Mickey wants only $50,000 then he must use half of the cash dividend to buy
back shares. Shares purchased = $50,000 / $4.95 = 10,101. His wealth after dividend
distribution and share purchase is:
Paper 2,010,101 x ($5.00 - $0.05) = $9,950,000
Cash 2,000,000 x $0.05 - $50,000 = $100,000 - $50,000 = $50,000
Total Wealth is $9,950,000 + $50,000 = $10,000,000
If Mickey wants $250,000 then he must sell some of his shares after the cash
dividend. Dividend is $100,000 and he needs $150,000 more.
Shares sold = $150,000 / $4.95 = 30,303. His wealth after dividend distribution and
share purchase is:
Paper (2,000,000 – 30,303) x ($5.00 - $0.05) = $9,750,000
Cash 2,000,000 x $0.05 + 30,303 x $4.95 = $100,000 + $150,000 = $250,000
Total Wealth is $9,750,000 + $250,000 = $10,000,000
11. Change Dividend Policy in World of Taxes – Looking back a problem #9 with
Benny; now assume that Benny is taxed 20% on dividend distribution and 20% on
capital gains. Assume also that Benny originally paid $18 for these shares. If
Benny only wants to receive $200 after tax, is his wealth impacted by changing
this dividend policy from a high payout policy to a low payout policy?
Solution
If Benny did not change the policy he would receive a cash dividend of 500 x
$2.00 = $1000 and pay taxes of $200 for a net cash flow of $800. His wealth would
be:
Paper wealth 500 x (18.00 - $2.00 x (1 - 0.20)) = 500 x $16.40 = $8,200
Cash wealth $1,000 - $200 = $800
Total wealth after cash dividend $8,200 + $800 = $9,000
If Benny only wants $200 in cash he will use the extra $600 to buy more shares of
Western Forest at $16.40 per share, or 36.5854 shares ($600/$16.40).
His wealth is now:
Paper wealth 535.5854 x $16.40 = $8,800
Cash wealth $800 - $600 = $200
Total wealth $8,800 + $200 = $9,000
17. Stock Repurchase Plan – Northern Railroad has announced it will buy back
1,000,000 of its 30,000,000 shares over the next year. If the stock is selling for
$23.40 what is the equivalent cash dividend that the company could pay? If you
owned 300 shares of stock, how many would you need to sell to get this cash
equivalent dividend?
Solution
The 1,000,000 shares will cost Northern Railroad $23,400,000 and the equivalent
cash dividend per share is: $23,400,000 / 30,000,000 = $0.78 per share. If you
own 300 shares you would have received $234.00 if a cash dividend had been
declared instead of the repurchase. So to get $234 you would need to sell
$234/$23.40 = 10 shares of stock.
Stock Repurchase Plan – Southern Railroad
Chapter 15
9. Pro Forma Financial Statements – Prepare Pro Forma Income Statements for Wal-Mart
and Starbucks using the 2004 information provided in problems 7 and 8. Which company
is doing a better job of getting sales dollars to net income? Where is the one company
having an advantage over the other company in turning revenue into net income?
Solution
Account
Sales
COGS
Depreciation
SG&A
EBIT
Interest
Taxes
Net Income
Wal-Mart
Jan. 31, 2004
Percent
$258,681
100.00%
$198,747
76.83%
$0
0.00%
$44,909
17.36%
$15,025
5.81%
$832
0.32%
$5,139
1.99%
$9,054
3.50%
Starbucks
Sep. 30, 2004
Percent
$5,294
100%
$2,198
41.52%
$206
3.89%
$2,266
42.80%
$624
11.79%
$0
0.00%
$232
4.38%
$392
7.40%
Starbuck brings 7.4 cents of sales revenue to the bottom line compared to 3.5 cents for
Wal-Mart. The advantage Starbuck’s has over Wal-Mart is in the cost of goods sold and
selling, general, and administrative expenses. Starbuck’s is able to generate nearly 12
cents on the sales dollar at EBIT whereas Wal-Mart is about 6 cents per sales dollar at
EBIT. Why Starbucks enjoys this advantage is a question that will take more financial
and economic investigation into the operations of the two companies and the industries in
which they operate.
11.Variance Analysis – Given the following budget and performance information on
Microbrew Incorporated, provide the following variances to the budget, sales price
variance, sales volume variance, production price variance, production volume variance,
overhead price variance and overhead volume variance. Verify the variances by using the
forecast EBIT and the actual EBIT.
Microbrew Incorporated Management Report #1
Budget
Actual
Sales Quantity
1,200 kegs
Price per gallon
$65.00 per keg
Sales Dollars
$78,000
Production costs (material and labor)
$48.00 per keg
COGS
Overhead
EBIT
Solution
1,382 kegs
$86,375
$68,064
$14,400
$12,980
$ 5,331
Sales Price Variance = Actual Price x Actual Quantity – Forecast Price x Actual
Quantity = $86,375 - $65.00 x 1,382 = $86,375 - $89,830 = $3,445 unfavorable
Sales Volume Variance = (1,382 – 1,200) x $65.00 = $11,830 favorable
Net Sales Variance = $11,830 favorable - $3.445 unfavorable = $8,385 favorable
12. Variance Analysis – Farbucks Coffee is looking at their regional store managers’
performance reports to determine which managers are controlling the sales, material,
labor, and overhead variances for their individual coffee shops. Each region has the same
projections, budgets, and standard costs and actual performance by category is listed for
each region:
Category
Sales Quantity
Sales Dollars
Labor Costs
Labor Rate
Materials
Material Rate
SG&A
EBIT
Forecast
Budget
4,000
$10,000
$2,400
$0.60
$2,200
$0.55
$4,200
$1,200
Actual
Region #1
3,878
$10,080
$2,375
Actual
Region #2
4,234
$10,244
$2,498
Actual
Region #3
3,902
$9,752
$2,283
Actual
Region# 4
4,164
$10,362
$2,519
$2,313
$2,312
$2,157
$2,177
$4,135
$1,257
$4,186
$1,248
$4,206
$1,106
$4,538
$1,128
Which Manager seems to be doing the best job based on favorable and unfavorable
variances in Net Sales Variance, Net Material Variance, Net Labor Variance, Net
Overhead Variance and Total Variance?
Solution
Sales Variances for the four regions:
Forecast Price = $10,000 / 4,000 = $2.50
Sales Price Variance = Actual Price x Actual Quantity – Forecast Price x Actual Quantity
Region #1 = $10,080 - $2.50 x 3,878 = $10,080 - $9,695 = $385 Favorable
Region #2 = $10,244 - $2.50 x 4,234 = $10,244 - $10,585 = $341 Unfavorable
Region #3 = $9,752 - $2.50 x 3,902 = $9,752 - $9,755 = $3 Unfavorable
Region #4 = $10,362 - $2.50 x 4,164 = $10,362 - $10,410 = $48 Unfavorable
Sales Volume Variance = Forecast Price x (Actual Quantity – Forecast Quantity)
Region #1 = $2.50 x (3,878 - $ 4,000) = $305 Unfavorable
Region #2 = $2.50 x (4,234 - $ 4,000) = $585 Favorable
Region #3 = $2.50 x (3,902 - $ 4,000) = $245 Unfavorable
Region #4 = $2.50 x (4,164 - $ 4,000) = $410 Favorable
Net Sales Variance:
Region #1 = $385 Favorable and $305 Unfavorable = $80 Favorable
Region #2 = $341 Unfavorable and $585 Favorable = $244 Favorable
Region #3 = $15 Unfavorable and $245 Unfavorable = $248 Unfavorable
Region #4 = $48 Unfavorable and $410 Favorable = $362 Favorable
Best Regional Manager on Sales is Regional Manager #4
Material Price Variance = Actual Cost x Actual Production – Actual Production x
Standard Cost
Standard Material cost = $2,200 / 4,000 = $0.55
Region #1 = $2,313 - $0.55 x 3,878 = $2,313 - $2,132.9 = $180.1 Unfavorable
Region #2 = $2,312 - $0.55 x 4,234 = $2,312 - $2,328.7 = $16.7 Favorable
Region #3 = $2,157 - $0.55 x 3,902 = $2,157 - $2,146.1 = $10.9 Unfavorable
Region #4 = $2,177 - $0.55 x 4,164 = $2,177 - $2,290.2 = $113.2 Favorable
Material Quantity Variance = (Actual Quantity– Standard Quantity) x Standard Costs
Region #1 = $0.55 x (3,878 - $ 4,000) = $67.1 Favorable
Region #2 = $0.55 x (4,234 - $ 4,000) = $128.7 Unfavorable
Region #3 = $0.55 x (3,902 - $ 4,000) = $53.9 Favorable
Region #4 = $0.55 x (4,164 - $ 4,000) = $90.2 Unfavorable
Net Material Variance
Region #1 = $180.1 Unfavorable and $67.1 Favorable = $113 Unfavorable
Region #2 = $16.7 Favorable and $128.7 Unfavorable = $112 Unfavorable
Region #3 = $10.9 Unfavorable and $53.9 Favorable = $43 Favorable
Region #4 = $113.2 Favorable and $90.2 Unfavorable = $23 Favorable
Best Regional Manager on Material Variance is Regional Manager #2
Labor Variance= Actual Cost x Actual Production – Actual Production x Standard Cost
Standard Labor cost = $2,400 / 4,000 = $0.60
Region #1 = $2,375 - $0.60 x 3,878 = $2,375 - $2,326.8 = $48.2 Unfavorable
Region #2 = $2,498 - $0.60 x 4,234 = $2,498 - $2,504.4 = $42.4 Favorable
Region #3 = $2,283 - $0.60 x 3,902 = $2,283 - $2,341.2 = $58.2 Favorable
Region #4 = $2,519 - $0.60 x 4,164 = $2,519 - $2,498.4 = $20.6 Unfavorable
Labor Quantity Variance = (Actual Quantity– Standard Quantity) x Standard Costs
Region #1 = $0.60 x (3,878 - $ 4,000) = $73.2 Favorable
Region #2 = $0.60 x (4,234 - $ 4,000) = $140.4 Unfavorable
Region #3 = $0.60 x (3,902 - $ 4,000) = $58.8 Favorable
Region #4 = $0.60 x (4,164 - $ 4,000) = $98.4 Unfavorable
Net Labor Variance
Region #1 = $48.2 Unfavorable and $73.2 Favorable = $25 Favorable
Region #2 = $42.4 Favorable and $140.4 Unfavorable = $98 Unfavorable
Region #3 = $58.2 Favorable and $58.8 Favorable = $117 Favorable
Region #4 = $20.6 Unfavorable and $98.4 Unfavorable = $119 Unfavorable
Best Regional Manager on Labor Variance is Regional Manager #3
Overhead Volume Variance = Actual Overhead – Standard Cost x Volume
Standard Overhead Cost = $4200/4,000 = $1.05
Region #1 = $4,135 - $1.05 x 3,878 = $4,135 - $4,071.9 = $63.1 Unfavorable
Region #2 = $4,186 - $1.05 x 4,234 = $4,186 - $4,445.7 = $259.7 Favorable
Region #3 = $4,206 - $1.05 x 3,902 = $4,206 - $4,097.1 = $108.9 Unfavorable
Region #4 = $4,538 - $1.05 x 4,164 = $4,538 - $4,372.2 = $165.8 Unfavorable
Overhead Quantity Variance = (Actual Quantity– Standard Quantity) x Standard Costs
Region #1 = $1.05 x (3,878 - $ 4,000) = $128.1 Favorable
Region #2 = $1.05 x (4,234 - $ 4,000) = $245.7 Unfavorable
Region #3 = $1.05 x (3,902 - $ 4,000) = $102.9 Favorable
Region #4 = $1.05 x (4,164 - $ 4,000) = $172.2 Unfavorable
Net Overhead Variance
Region #1 = $63.1 Unfavorable and $128.1 Favorable = $65 Favorable
Region #2 = $259.7 Favorable and $245.7 Unfavorable = $14 Favorable
Region #3 = $108.9 Unfavorable and $102.9 Favorable = $6 Unfavorable
Region #4 = $165.8 Unfavorable and $172.2 Unfavorable = $338 Unfavorable
Best Regional Manager on Overhead Variance is Regional Manager #1
Total Variance is the sum of the four areas and is the actual EBIT versus the budgeted
EBIT.
Region #1 = $1,257 - $1,200 = $57 Favorable
Region #2 = $1,248 - $1,200 = $48 Favorable
Region #3 = $1,106 - $1,200 = $94 Unfavorable
Region #4 = $1,128 - $1,200 = $72 Unfavorable
And Region #1 Manager is the overall “variance” winner for the reporting period, but
that does not mean Region #1 Manager did the best job. It will take more information to
come to that conclusion.
For the problems thirteen through sixteen use the following data:
Buzz Beer Incorporated Income Statement for
Period Ending
31 Dec 2003
31 Dec 2002
Revenue
$14,146,700
$13,566,400
COGS
8,449,100
8,131,300
SG&A
999,320
982,160
Depreciation
1,498,980
1,473,240
EBIT
3,199,300
2,979,700
375,000
356,100
1,093,300
1,041,500
$2,075,900
$1,933,800
Interest Expense
Taxes
Net Income
Balance Sheet for
Period Ending
Assets
31 Dec 2003
31 Dec 2002
Current Assets
Cash
$
191,000
$
188,900
Investments
182,300
121,800
Accts. Receivables
669,400
630,400
Inventory
587,500
563,600
1,630,300
1,504,700
Investments
3,052,000
2,827,900
Plant, Property and Equip.
8,498,900
8,481,500
349,000
348,700
1,159,300
956,700
$14,689,500
$14,119,500
$
1,545,700
$ 1,455,100
311,500
332,600
1,857,200
1,787,700
Debt
7,285,400
6,603,200
Other Liabilities
1,462,100
1,345,100
$ 11,977,800
$11,067,200
$ 1,457,900
$ 1,453,400
Total Current Assets
Long Term Assets
Goodwill
Intangible Assets
TOTAL ASSETS
Liabilities
Current Liabilities
Accounts Payable
Short Term Debt
Total Current Liabilities
Long-Term Liabilities
TOTAL LIABILITIES
Owner’s Equity
Common Stock
Retained Earnings
$ 1,253,800
$ 1,598,900
TOTAL OWNERS EQUITY
$ 2,711,700
$ 3,052,300
TOTAL LIAB. & OWNER’S EQ.
$ 14,689,500
$14,119,500
13. Financial Ratios, Liquidity – Calculate the Current Ratio, Quick Ratio, Cash Debt
Coverage Ratio and Cash Ratio for Buzz Beer for 2003 and 2002. Should any of these
ratios or the change in a ratio warrant concern for the managers of Buzz Beer or the
shareholders?
Solution
Current Ratio = Current Assets / Current Liabilities
2003 is, $1,630,300 / $1,857,200 = 0.8778
2002 is, $1,504,700 / $1,787,700 = 0.8417
Current Cash Debt Coverage Ratio = Cash Provided by Operations / Average
Current Liabilities
2003 is, ($3,199,300 + $1,498,900 - $1,093,300) / [($1,857,200 +
$1,787,700)/2] = $3,604,900 / $1,822,450 = 1.9781
Quick Ratio (or Acid Ratio Test) = Current Assets – Inventories / Current
Liabilities
2003 is, ($1,630,300 - $587,500) / $1,857,200 = 0.5615
2002 is, ($1,504,700 - $563,600) / $1,787,700 = 0.5264
Cash Ratio = Cash / Current Liabilities
2003 is, $191,100 / $1,857,200 = 0.1029
2002 is, $188,900 / $1,787,700 = 0.1057
The ratios are look reasonable and the change is in the right direction for better liquidity
for all ratios except the cash ratio.
17. DuPont Identity – For the following firms find the Return on Equity using the three
components of the DuPont Identity, the operating efficiency as measured by the profit
margin (Net Income/Sales), the asset management efficiency as measured by asset
turnover (Sales / Total Assets), and financial leverage as measured by the equity
multiplier (Total Assets / Total Equity).
All Dollars in millions (2003)
Company
Pepsi
Coca-Cola
Starbuck’s
Anh. Busch
Sales
$26,971
$21,044
$5,294
$14,146
Net Income
Total Assets
Liabilities
$3,568
$25,327
$13,453
$4,347
$27,342
$13,252
$392
$3,328
$841
$2,076
$14,689
$11,977
Solution:
First find the equity of each company:
Pepsi’s Equity = $25,327 - $13,453 = $11,874
Coca-Cola’s Equity = $27,342 - $13,252 = $14,090
Starbuck’s Equity = $3,328 - $841 = $2,487
Anheuser-Busch’s Equity = $14,689 - $11,977 = $2,712
Next calculate the three components
Company
Pepsi
Coca-Cola
Starbucks
Anh. Busch
Operating Efficiency
$3,568/$26,971
= 0.1323
$4,347 / $21,044 =
0.2066
$392 / $5,294 =
0.0740
$2,076 / $14,146 =
0.1468
Mgmt. Efficiency
$26,971/$25,327
= 1.0649
$21,044 / $27,342 =
0.7697
$5,294 / $3,328 =
1.5907
$14,146 / $14,689 =
0.9630
Financial Leverage
$25,327 / $11,874 =
2.1330
$27,342 / $14,090 =
1.9405
$3,328 / $2,487 =
1.3382
$14,689 / $2,712 =
5.4163
Last, take the three components to find the ROE,
Pepsi = 0.1323 x 1.0649 x 2.1330 = 0.3005 or 30.05% ROE
Coca-Cola = 0.2066 x 0.7697 x 1.9405 = 0.3085 or 30.85% ROE
Starbuck’s = 0.0740 x 1.5907 x 1.3382 = 0.1576 or 15.76% ROE
Anheuser-Busch = 0.1468 x 0.9630 x 5.4163 = 0.7655 or 76.55% ROE
While Coca-Cola is the most operationally efficient and Starbucks is the most efficient in
management, Anheuser-Busch is the best to its shareholders because it has effectively
utilized a very high financial leverage strategy, using debt and not shareholder earnings to
finance the profits of the firm.
19. Company Analysis – Go to a web site such as Yahoo.com and find the financial
statements of Disney, ticker symbol DIS, and McDonalds, ticker symbol MCD. Compare
these two companies using the following financial ratios:
Times Interest Earned, Current Ratio, Asset Turnover, Financial Leverage, Profit
Margin, and Return on Equity.
Which company would you invest in as either a bondholder or a stockholder?
Solution
Look up these values for each company,
Sales, EBIT, Interest Expense, Net Income, Current Assets, Total Assets, Current
Liabilities, and Equity
Sales
EBIT
Interest Expense
Net Income
Disney
$30,752
$4,368
$629
$2,345
McDonalds
$17,140
$2,734
$388
$1,471
Current Assets
Total Assets
Current Liabilities
Equity
$9,369
$53,902
$11,509
$26,081
$1,885
$25,525
$2,486
$11,982
Times interest Earned = EBIT / Interest Expense
Disney is, $4,368 / $629 = 6.9444
McDonalds is, $2,734 / $388 = 7.0464
Current Ratio = Current Assets / Current Liabilities
Disney is, $9,369 / $11,059 = 0.8472
McDonalds is, $1,885 / $2,486 = 0.7582
Asset Turnover = Sales / Total Assets
Disney is, $30,752 / $53,902 = 0.5705
McDonalds is, $17,140 / $25,525 = 0.6715
Financial Leverage = Total Assets / Total Equity
Disney is, $53,902 / $26,081 = 2.0667
McDonalds is, $25,525 / $11,982 = 2.1303
Profit Margin = Net Income / Sales
Disney is, $2,345 / $30,752 = 0.0763
McDonalds is, $1,471 / $17,140 = 0.0858
Return on Equity = Net Income / Total Owner’s Equity
Disney is, $2,345 / $26,081 = 0.0899
McDonalds is, $1,471 / $11,982 = 0.1228
The best company to invest in appears to be McDonalds with its higher ROE and strong
solvency position as most of the financial ratios are very similar.