Chapter1. An Overview of Financial Management
* Why Business?
* What are needed?
* What is Finance? Financial Management? (p.4 – p.6)
* Relationship with economics and accounting (p.4)
* Major Financial Decisions (p.4 – p.6)
* Firm’s objectives and goals (P.8)
* Career opportunities: Corporate officer, Investments, Financial institutions, Sales, Education –
requirements (math, stat, econ, etc) licensing (NASD Series 6, 64, 7, Actuary exams),
certification exams (CFA, CFP, CLU, etc) (p.6)
* Real assets vs. Financial assets
* Major issues in Finance: Time value of money, risk-return trade-off, security valuation, capital
budgeting, short-term and long-term asset management, inflation, interest rates, exchange rates,
etc (p.5, p.10 – p.13)
* New world : Globalization, Technology (P.14 – p.15)
* And New Problems and Issues (Contagion effects, fraud, confidentiality and privacy issues)
(P.14 – p.15)
* Types of Business Organization (p.6 – p.8)
1) Sole Proprietorship: business owned by one person.
Advantages: Single taxation-schedule C, prompt decisions, Disadvanatges: unlimited liability
(you are personally liable for business obligations)=difficult to raise capital, limited life, difficult
to transfer partial ownership,
2) Partnership: 2 or more owners, similar to sole proprietorship, different varieties (general
partners, limited partners, LLC, LLP - -)
3) Corporation (choosemayrland.com): a legal entity created by a state law
When we talk about a corporation, we are referring to C-corporation.
To have a business incorporated, you need to file an application, corporate bylaws, articles of
incorporation, etc.
Adv: Limited liability (owners are not personally liable for business obligations) = maximum loss
is limited to the amount invested = easier to raise capital, easier to transfer ownership,
theoretically unlimited life span, Disadv: double taxation=corporate income tax for net earnings
and personal income tax for dividends
C. vs. Sub S. Corp=single taxation and limited liability, just file an application with IRS
Nonprofit
* Firm’s Objectives
=Normative obj in a capitalistic society should be making the most for owners=shareholders
=maximize the shareholders wealth= maximize the value of the firm=maximize the stock price
Aside: Some people argue that the objective to be stakeholder welfare maximization
Some other people argue that these two objectives could be consistent.
and Agency Conflicts (p.18 – p.21)
between owners=-shareholders and manager=employees, Managers may not work in the best
interest of shareholders=maximizing shareholders wealth=stock price max.
Solutions to Agency conflicts: performance based incentives like stock options, monitoring,
(hostile) takeover possibility
*Intrinsic value=true value=maximum potential value of the business. If the current stock price is
less than the intrinsic value, someone may be interested in taking over the business, fire existing
managers, and run business better to increase the stock price close to its intrinsic value. Managers,
of course, would like to see that any (hostile) takeover more difficult so that they can secure their
jobs regardless of their performance.
Corporate Governance (act or system of governing, control) – major issue since the
collapse of Enron, WorldCom, etc – check and balance between BODs and Management
* Social responsibility and Ethical behavior (p.15 – p.18)
- Shareholder wealth vs. stakeholder welfare maximization, Sequenced goal approach (Walmart
vs. Costco) . Think outside!
Chapter3. Financial Statements, Cash Flow, and Taxes
* Financial Statements (p.55 – p.56) prepared based on GAAP guidelines
Aside) Accounting is a historical report based on events occurred, it is based on a accrual method,
different from cash flow based approach. Accounting often fails to capture future contingencies
=> financial crisis like sub-prime.
Balance Sheet (p.57 – p.61): Assets = Liability (=Debt) + Equity
Or A=L+last year end’s Equity + Change in Equity this year
- B/S shows uses & sources of funding, how much short-term & long-term assets and
debt you may have,
Aside) ALM (Asset Liability Management)? Bill Gates, well endowed, but still borrow?
Stock concept=what you have at a particular point in time. Snapshot of the firm’s
financial position at a point in time (e.g., as of Dec. 31, 2008).
The structure of B/S (based on the liquidity)
Current Assets (Cash, Marketable securities like stocks and bonds, A/R, Inventory)
Net? (Long-term) Fixed Assets (Net plant and equipment, etc)
--Current Liability (A/P, Accruals, Notes Payable, etc)
Long-term Liability
Equity (Paid-in-capital, Retained Earnings)
Aside) Current vs. Long-term?
Income Statement (p.61 – p.63): Flow concept, shows how profitable,
(Net) sales = revenue
- CGS (the book example p.62 does not have this! This is not good.)
-----------Gross Margin=Gross Profit
- Operating expenses (administrative, salary, rent, etc) including depreciation &
amortization
-----------EBIT, Note that some people are also interested in EBITDA=EBIT+D/A(noncash exp)
- Interest Expenses
----------EBT ($150)
-Taxes (33%)?
----------(Net) earnings=Net Income = shareholder’s money ($100)
- Dividends ($35, $100?)
----------Addition to retained earnings (?), (if R/E end of last year=$70, then what is R/E now?)
(EX. Can you determine NE once I provide all these numbers? If I give you all the
numbers including NE, can you back-figure Sales?)
Aside1) Shareholders are the residual claimants=are the last to claim on the income or
assets of the business. Other stakeholders get their shares first.
Aside2) Margin (based on your selling price, sales, rev) vs. mark up (based on your cost),
$80+$20 = $100, margin ratio=20%, mark up ratio=25%
Aside3) Working capital=Current Assets, Net working capital=CA-CL, Working capital
management=management of CAs and CLs.
Aside4) Market value=Market capitalization vs book value, EPS, DPS, BPS =Equity/#shs
Statement of Cash Flows (p.63 – p.67) = Cash (and equivalents(MMA, CP=commercial
paper, T Bills)) at the end of the last year from the B/S + Net change in cash for this
year= Cash at the end of this year.
 3 channels: 1) operating cash flows, 2) (long-term) investment activities (buying and
selling long-term assets (fixed, securities, lending)), 3) financing (funding) activities
Aside) this shows everything about CASH (do we have enough cash, where is the cash from, etc)
1) Operating cash flows=Net earnings + D/A – Increase in CA + Increase in CL
(Do not include investing in Marketable Securities and Notes payable, why?)
(EX, NE=$100, DA=$30, and no change in CA & CL, Operating cash flow?)
2) Cash flows from investment activities= - Change in Net fixed assets-Change in investing
in Marketable securities and Lending (loan)
3) Financing activities=Issuing stocks (common, preferred) + Increase in notes payable +
Increase in Long-term liability - Dividends
4) => Net change in cash for this year = 1)+2)+3)
Statement of Retained Earnings
Previous period ending retained earnings (2008 12/31 B/S)+ this period addition to retained
earnings (from 2009 I/S) = this period ending retained earnings (2009 12/31 B/S)
Aside1) Statement of Stockholders’ Equity (p.67): Just add Paid in capital to the Statement of
Retained Earnings.
Aside2) A=L+E, A=L + old E+Change in E = L + old E+Addition to R/E = L + old E+(NE-Div)
That is, A = L + old E+(NE-Div)
NE=Sales(Rev) – CGS – Exp – Int – Taxes
 A+CGS+Exp+Int+Taxes+Div = L+old E+Sales(Rev)
Any increase (decrease) in LHS item appears in the debit (credit) column
Any increase (decrease) in RHS item appears in the credit (debit) column
* Free Cash Flow (p.68 – p.70) – concept and measurement
= Amount of cash that can be withdrawn without affecting firm’s ability to continue operating at
the same capacity (generating the same cash flows, now and the future)
= EBIT*(1-T) + D/A – {Capital Expenditure + Change in Net Working Capital}
Aside) Capital Expenditure=D/A + Change in Net fixed assets
Change in Net Working Capital=Increase in CA-Increase in CL (do not include Notes
Payable)
= EBIT*(1-T) – Change in Net fixed assets –Increase in CA + Increase in CL, ( “)
Aside) A growing business can have negative FCFs as it has a large capital expenditure (investing
in net fixed assets).
*Taxes (p.70 – p.75)
- Individual taxes: income (wages, salaries, interest, dividend, rent, etc) and capital gains (the
price difference, a favorable long-term capital gains tax rate), progressive tax (higher tax rate for
higher income), marginal tax rate (tax rate for the last one $), average tax rate (=total tax
amount/total taxable income), Alternative minimum tax (=minimum tax amount to pay regardless
of tax benefits).
- Corporate taxes: Very much the same, but the tax rates could be different and only 30% of
dividend income is taxable. Capital gains tax rates are the same as its income rates.
Ex. Tax amount for $65k taxable income with the tax schedule 15% up to $50k, 25% up to $75k,
etc? Taxes=$7,500 + $15k*0.25 = $11,250. Average and Marginal tax rates? Avg=11,250/65,000,
Marginal = 25%
**Financial Planning and Budgeting (as part of raising money) (p.511 – p.512)
Financial planning is primarily focusing on future sales (e.g., 25% increase in sales next year). In
order to achieve the sales goal, we need to increase assets to support the sales. If you look at the
right hand side of the B/S, there are two sources of funding, L & E. A change in E comes from
addition to retained earnings. A change in L comes from a chance in spontaneous liabilities (most
CLs as they increase as sales increases, except Notes Payable) as you may be able to finance an
increased in assets with no immediate cash outflows. A shortfall, a projected increase in assets
not covered by addition to retained earnings and a change in spontaneous liability, is covered by
Additional Funds Needed (or External Funds Needed).
The equation given in the book (16.1) on p.515 is:
AFN=Projected increase in Assets–Increase in Spontaneous Liability–Addition to Retained
Earnings
Aside1) We often use the percentage-of-sales method to determine all the three components
above.
Ex. This year: Sales=$100, Total Assets=$50, Spontaneous liability=$20, Addition to Retained
Earnings=$5. Assuming that assets are fully utilized (if not, then we may not need to increase
assets as much to support the sales increase), what is the AFN to increase the future sales by 25%?
= 50*(0.25) – 20*(0.25) – 5*(1.25)=$1.25 Note that 25% is used to determine the changes in
Assets and Spontaneous Liability. Since Addition to Retained Earnings is already a chance. A 25%
increase in addition to retained earnings should be 5*1.25.
Aside2) An increase in dividends => reduces addition to retained earnings => increases AFN.
Chapter4. Analysis of Financial Statements
*Financial manager is responsible for the financial health of a business. Need data to diagnose
(analyze) and make “good” financial decisions.
* Types of data
-Caveats: important, but imperfect. Need theory – why? Since we need guidelines to
analyze the data. Otherwise, we do not know what we are doing.
1) Accounting data – financial (ACCT201) about the financial aspects of the firm, most of the
information can be made available to the public, and managerial (ACCT202) is about the firm’s
operation
2) Other data – about economy, industry, people, etc
* Financial Accounting Data – used to produce financial statements, which are prepared subject
to FASB, SEC constraints
1) GAAP Limitations
(1) Different valuation methods between monetary (cash value) and non- items
(historical costs)
(2) Different numbers for the same event depending on the choice of accounting methods.
E.g. LIFO and FIFO.
(3) Important information omitted. E.g., quality of business, human resources
=> despite all its imperfections, excellent source of info.
2) Need to put into a good use (use the numbers in an analysis) – Otherwise?
=> Financial ratios are the simplest, yet a very powerful approach.
* Financial Ratios (Net sales are credit sales, Income statements) (p.104)
1) Profitability (p.96 – p.98)
Gross margin = Gross Margin/ (net) Sales
Operating (profit) margin=EBIT/Sales
(Net) profit margin (PM) = NE/sales
ROA=Return on Assets, NE/Assets = (NE/Sales)*(Sales/Assets)=PM*TAT, du Pont equation
ROE=NE/Equity = (NE/Assets)*(Assets/E)=ROA*EM, If ROA is positive, increased debt would
result in a greater ROE=> leverage effect However, if ROA is negative, you lose more with an
increased debt. Debt produces more volatile performance results => leverage effect.
Q) high numbers are good or bad? => generally good, but may not be desirable to have too high?
Aside) Mark-up vs. Margin
2) Liquidity (p.88 – p.89) – You must have enough liquid assets to cover your short-term
financial obligations, but not too much! Why? Liquid assets are not usually profitable.
- Current ratio= CA/CL > 1 => CA is greater than CL, meaning that you have enough CAs to
cover CLs=short-term debt.
Quick ratio=(CA-Inventory)/CL, why? Since inventory is the least liquid current assets.
Q) high or low? A number a little greater than 1.0 is good, but you do not want to have this
number too high.
Aside) factoring~ selling A/R
3) Effective Management (p.89 – p.92)
(1) Working Capital Management=management of CAs and CLs
Aside) most of B2B sales are credit sales
-Accounts receivable turnover=Sales/(Average) A/R, a higher number indicates that you are
managing your A/R effectively. However, you don’t want to have this number too high. Why?
Because your A/R may be too tight and limiting your sales and the profits as a result.
-Average collection period = (average) A/R / average daily sales
Average daily sales = (Annual) Sales/365 or 360 = how many days to collect the A/R. You would
want to have ACP shorter, but not too short.
-Inventory turnover (may use sales instead of CGS)
=Sales/Inventory, or CGS/Inventory, In general , you want to have a higher IT, but not too high
Payable period
Aside) Cash conversion cycle
PO => Delivered, Invoice issued with a payment term (e.g., 30 days) usually around the delivery
point, the products are stored as an inventory until they get sold => you have to wait until you
will get paid. Typically, your payment term with your supplier is already up and you have already
made the payment.
CCC=> the time difference between the moment you pay and you will get paid = inventory
period + receivable period – payment period
Ex) inventory period=6 months, both payment period and receivable period = 30 days.
CCC=6+1-1=6 months. If you have to borrow 10m, 8% annual => 10m*0.08/2=$400,000
(2) Fixed and Total Assets
Fixed asset turnover = sales/(N)FA Aside NFA=Total Fixed Asset – Accumulated Depreciation
TAT=Sales/TA,
Aside) TA=CA+(N)FA
4) Debt: too much debt is not good, why? Vulnerable, maybe difficult to cover the liability=debt.
However, if you are very certain about the success of your business, you may want to have “some”
debt (manageable) to increase the size of business => make more money!
Debt ratio = Debt/(Total)Assets
Equity Multiplier=TA/E, Aside)Note that E=TA-L or Debt => increased debt=> smaller Equity
TIE (p.92 – p.96) Times Interest Earned = EBIT/Interest Expenses : showing whether the
business is making enough profits (EBIT) to cover interest expenses. If TIE<1 => they do not
make enough money to be able to cover their interest payments. Increased debt=> increased
interest expenses => the ratio, TIE gets smaller. So this ratio moves in the opposite directions of
the other two ratios.
5) Dividend payout=Dividend/Net Earnings
Retention ratio=Addition to Retained Earnings/Net Earnings = 1 – dividend payout ratio
6) Market Value: P/E, P/B, P/S
- P/E=Stock Price (for one share)/EPS. EPS=Net Earnings/# of shares outstanding
Ex) current stock price =$20, NE=$2m, # of shares outstanding=1m =>P/E=$20/$2=10.
Aside) If the EPS is expected to be the same in the future, how long does it take to recover you
$20 investment to buy the stock? 10 years is the payback period. If earnings are expected to grow
in the future, then it would take less than 10 years to recover your $20 investment.
Aside) (P/EPS) * EPS= Share Price, using this relationship, some people try to project true
value=intrinsic value of a stock. Or try to estimate future stock price. Ex) Say, P/E=10 stays the
same and the EPS is expected to be say, $2.50 => estimated price becomes $25.
- P/B=Stock Price/BPS, BPS=Book Value/# shares outstanding
- P/S=Stock Price/Sales per share
Aside) P/E is a preferred choice, however, Net Earnings (and EPS) numbers change quite a bit
and could be even negative. Therefore, we also use P/B and P/S ratios and there are more stable.
* Du pont equations (p.101 – p.102)
Remark: Optimal ratio numbers? How to compare numbers? (p.103, p.105)
(1) Benchmark = try to change your ratios close to the benchmark numbers.
(2) time-series=looking at the ratios of the same company over time to determine how things
change.
(3) cross-sectional = industry averages, SIC (Standard Industry Codes can be used to
determine different industries.
* Other important issues for accounting data
1) Cash flows vs. accrual accounting data
=> Show me the money! vs. event (sale, etc) based records
2) Different types of costs
Total costs, Average=Total costs/total # of units,
Marginal=Incremental, extra cost for the last unit
Sunk=costs already incurred=let bygones be bygones as we focus on the future,
Opportunity cost (the best opportunity you may have to give up because of your choice)-example
A=7% (9%), B=8% (9%), C=9%(8%) => Choose C since what you gain (9%) is greater than the
opportunity cost of 8%.
* Other Data (other than accounting data): 1) Economics data, 2) Data about people
(stakeholders), 3) Process Data (quality of the product, efficiency)
* EVA (P.108, p.290) = Economic Value Added, a measure of how much shareholders’ wealth is
increased beyond what they can earn elsewhere. EVA=EBIT(1-T) – Total Investors’
Capital*After -Tax Cost of Capital p.108
Chapter2. Financial Markets & Institutions
* Roles and Functions (p.28 – p.29)
1) Major role: Surplus ->$-> Deficit, create Financial Assets (stocks, bonds, loans, etc)
Why imbalance? = different cash flow streams and needs for cash over time
Three types of money transfer (p.28) = direct (no middlemen, but finding your counterpart is
difficult), indirect using a broker (just a facilitator, commission), indirect using a dealer (carrying
inventories, profits from bid-asked difference, spread)
Aside) Asked=price to sell, Bid=price to buy from a dealers’ perspective,
Asked price ($25) – bid ($24.5) = spread ($0.50). If 100 shares, then the dealer profit $50.
* Money and capital markets (p.30): Money market is a short-term security (money market
instrument) market, where short-term debt securities are traded. Capital market is where longterm debt instruments and equity securities (common stock) are traded. Short-term? Maturities
less than or equal to one year.
*Another way to divide financial markets into two different groups is Primary vs. Secondary
Markets
* Primary Markets: Brand new securities are issued for the first time. New car market, an influx
of capital to the issuer
Explain? (p.30)
1) Investment banker (p.34) ~ Goldman Sachs, J P Morgan,
Analysis and advice, Underwriting (best effort vs. firm commitment), Selling, Market
stabilization
2) Flotation cost = cost of issuing securities. Ex. Amount to raise $100m, Floatation cost 5% =>
$5m.
3) IPO (auction, eg. Dutch)=Initial Public Offering=Private company going public by selling their
ownership to the public. Seasoned Public Offering=more shares issued by already a public
company
4) Private placement: inviting only a few major investors (many of them are institutional
investors like banks, insurance companies, mutual funds, etc)
-Advantages (less government regulations, easy, smaller flotation costs, etc) and
disadvantages (limiting your investor pool and get smaller receipts, still deal with professional
investors and end up costing more to raise money)
* Secondary Markets: place where existing securities are traded. Used car market. No additional
influx of money to the issuer. Linkage between secondary market and the primary market.
Explain? (p.30)
1) Functions
2) Exchanges (p.39), NYSE, ASE ~ organized markets. Physically exist.
3) versus OTC (Over-The-Counter, unorganized markets) NASD (Bernard Madoff) and
NASDAQ (National Assn of Securities Dealers Automatic Quotation system)~ a computer
system serving the OTC market.
Aside: Series Exams
Aside: SEC registration requirements vs. listing requirements
4) Other trading mechanisms
* Behavior of Financial Markets
1) Market indexes (p.45)
2) Models of stock price behavior (p.46 – p.50)
Technical
Fundamental
Efficient market hypothesis: Intrinsic value=> buy & sell
Random walk
* Other Markets: Currency, Derivative Markets including Futures (fix the price today for future
trading), Options, etc.
Chapter6. Interest Rates
*Money Rates
- Interest rate: price (=cost) of money (p.163) = compensation for making an investment today,
would like to have more money back in the future!
- Exchange rate: relative value of two currencies = ($) price of a FC (that is, how many $s for one
unit of the FC), Aside) price is an exchange rate, too.
* How to compute interest rate or Rates of return
= (End Balance – Beg Balance + Holding Period Income)/Beg Balance
= (Pt – Pt-1 + C)/Pt-1, C=dividend, interest, rent, - Pt-1=$100, Pt=$110, C=$5, Rt = (110 – 100 + 5)/100 = .15 or 15%
Aside) Gains from the price change (Pt – Pt-1) or the appreciation of the value of investment is
called Capital Gains. Sometimes, the value of the investment could depreciate and you may have
a capital loss.
* Interest rates = rate of return
1) Interest Rate has an Inverse relationship with PV (Present Value) or Price => you pay more,
you get less in return (assuming the future value and the income being the same).
(1) Why? At least, need to know that interest rates can be used to determine the value of
financial assets!
p.132 Figure 5.2 why convex?
2) The Components of interest rates (Irving Fisher) ~ what are the factors determining the interest
rates?
Rk = Real risk free rate + Expected inflation rate (IP) + Risk premium (for security k)
Return(interest rate for) on security k is determined by the 3 factors - (1) Make sense? Yes, return is a compensation for 1) giving up my purchasing power today, 2)
for losing value of money, 3) taking the risk.
(2) Real risk free rate determinants: how patient consumers are, how productive the economy is.
If the economy is more patient (impatient) and/or less (more) productive => real interest rates
should be lower (higher). Real=Purchasing Power of real goods/services.
Note: I need to add expected inflation rate to protect me against an erosion of the purchasing
power of money due to inflation.
(3) Ex-post (after the fact) vs. ex-ante (before the realization of the event) ~ what we talk about
here is ex-ante in the sense how much you should ask for when you make an investment.
However, what you really get from the investment is determined ex-post based on your decision
and your luck!
(4) Nominal risk free=T-Bill (short-term government security) rate, risk pm for this is ZERO
(5) Interest rates in different countries
Aside: There are some private ratings agencies determining their evaluations of risks. Moody’s,
S&P’s, etc. AAA, AA, A, BBB (Baa), BB, B, - 3) Term Structure of Interest Rates (p.175 – p.176) = relationship between interest rates and (time
to ) maturity. Snapshot at any given point in time. A table is a way to describe.
Example: BOA Today’s CD rates. Note that the interest rates quoted are APRs (annualized
percentage rates).
(1) WSJ example
(2) Yield curve p.175 A graphical representation of term structure of interest rates.
(3) Three theories (or hypotheses) trying to explain what determines the shape of the yield
curve, i.e., the relationship between long-term and short-term interest rates. In other words, why
we sometimes have rising, downward sloping, or flat yield curves? (Remark: if we make a longterm investment, we usually have a larger return. The question is not for the extra length of the
investment, but what happens for the return in each year. Example, 10 year CD vs 2 year CD. Yes,
you get more on 10 year CD for a longer)
a) Expectations hypothesis: says that our expectation of future interest rates has an impact
on the long-term interest rates in such a way that if we expect a higher interest rates in the future,
then the long-term rates (say, 10 year CD) tend to be higher than short-term rates (say, 1 or 2 year
CD). Why? If the market is competitive, short-term rollover and long-term strategies are expected
to produce the same overall returns.
That is, oR1 + E(1R2) = oR2 + oR2 = 2*oR2 => oR2 = average of current short-term and
expected short-term future rates. If E(1R2) > oR1, then oR2 > oR1 => rising (normal) yield curve.
=> (1+E(1R2))*(1+ oR1) =(1+ oR2)^2 Exact one in the book.
Example: If oR1=4%, oR2=5%, What is E(1R2)? 4% + X = 5+5=10% X=? 6%
1+E(1R2) = (1.05)^2/1.04 =1.06009 => E(1R2) = 0.06009 or 6.009%
b) Liquidity preference hypothesis: Other things being the same, people do not want to
make a long-term investment. This means that the long-term rate should be higher (this is called
Liquidity Risk Premium or Maturity Risk Pm) to make it equally attractive.
Example: LP=MP=1%,
From the equation for the expectations hypothesis, we have
(1+E(1R2))*(1+oR1)=(1+oR2-MP)^2
oR1 + E(1R2) = 2*(oR2-LP) => 4% + E(1R2) = 2*(5%-1%)=8%
(1.04)*(1+E(1R2)) = (1+0.05 – 0.01)^2=(1.04)^2 => E(1R2) = 4% Note that we could have a 2
year long-term rate at oR2=4%, if oR1 = E(1R2) = 4% Flat Yield curve. However, oR2 in this
case is 5% to make the two strategies equally competitive.
c) Market segmentation: short-term markets and long-term markets are segmented.=>
two different markets. Therefore, short-term and long-term interest rates are independently
determined. For example, pension funds are inventing only in long-term securities.
4) Risk types (p.168 – p.174)
(1) Default risk & premium
(2) Liquidity risk & premium
(3) Maturity risk & premium (Interest rate risk, Reinvestment risk & Call risk)
Now,
Rk = rf + IP + RPk = Rf + IP + DPk + LPk + MPk
Example: 2 year AA (DP=0.5%) rated bond with MP=0.3%, LP=0.6%, IP=3% this year and 4%
next year, with rf=2%? Rk= 2%+(3+4)/2+ 0.5 + 0.6 + 0.3 = 2+3.5+1.4=6.9%, required rate of
return. If somebody offers 7.4% for this security, then what would you do? Take it.
5) Tax considerations
(1) Before-tax and after-tax returns
Ra = Rb*(1-t), Rb=10%, you are in a 30% tax bracket? Ra? 7%
If Ra=14% and t=30%, what is Rb? 14%=Rb*(1-0.3) => Rb=20%
(2) Tax equivalent before-tax rate of return?
Basically, determining the Rb, given Ra
Municipal bonds (bonds issued by State or Local governments) or Muni(s) – interest income from
munis are tax exempt. Which one (munis vs. taxable securities) do you think would have a lower
return (Rb)? Since our bottom line is Ra, munis offer lower Rb.
* Exchange rates
1) American (price, direct) vs. European (quantity, reciprocal) quotations
$/FC=American term => how many $ s would be equivalent to one unit of a FC, just like a price
of Twinkie. FC/$= How many units of FC for one $, just like how many twinkies for one $.
An inverse relationship between them. $/TW=0.5 => you can get 2 twinkies for one dollar.
2) WSJ
3) Cross rates
4) Spot and Forward rates
5) Exchange rate risk exposures
Chapter5. Time Value of Money
* The Money Rules
#1: The more, the better => $2 today better than $1 today
#2: The sooner, the better => $1 today better than $1 tomorrow
#3: Tradeoff between the amount and the time
=> $1 today is equivalent to say, $1.06 tomorrow or $.96 today is equivalent to $1 tomorrow
#4: Choose the point in time first, then try to come up with the equivalent $ amount
=> $100 today vs $109 tomorrow?
Today (Present Value): $100 today vs say, say$104 today’s value (PV) of $109 tomorrow
OR Tomorrow (FV): say, $106 FV of $100 today vs. $109 tomorrow.
=> NEED PV->FV or FV->PV conversions just like any conversions to compare, add, subtract.
e.g, 25 inches vs 2 feet, note an inverse relationship (note the inverse relationship
between the two conversion factors, x12 or x(1/12))
* TVM Fundamental Relationships
Note: (1) Interest rate per period vs. APR (nominal rate, rate quoted)
e.g., 6% for six months vs. 10% for a year? Which one is more? Maybe the second one?
That is why we want to have the interest rates quoted on the same time length, a year. However,
what is the actual interest earned? For all of our TVM calculations, we use interest rate per period.
How can I get the interest rate period? Answer=”APR/# of periods a year”
Ex: Quarterly Compounding, 10% APR, 10%/4=2.5% per period
(2) Simple interest vs. compound interest (interest on interest) in case of multiple prds?
Ex: Semi-annual example, 2 periods (two six months) with 12% APR?
What is the interest rate per period=12%/2=6%, What is your total interest for a year
based on simple interest calculation method? 6% x 2 =12%.
Based on compounding? (1+0.12/2)^2 = (1.06)^2=1.1236 => 12.36% actual rate of
return from compounding method. Yield=actual rate of return vs. APR (Rate)
(3) FV = PV*{(1+I)^N} => Given any 3 variables out of 4 variables (FV, PV, I, and N),
you can solve the equation for the 4th
Sometimes, we use i or r instead of I, and n instead of N, { }=FVIF(I%, N)
(4) Timeline! I=interest per period!, N=#periods! (p.124 – p.125)
1) Finding FV: $100 deposited for 3 years at 10%, semi-annual compounding? (p.125 – p.130)
(1) Using the formula (timeline!)
(2) Using the TVM(FV) table, FVIF(I%, N)=Conversion factor of[1$ today->FV] : note!
(3) Financial calculator: Check p/Y=1. Clear TVM each time before calculation.
Aside: Rule of 72! How long it takes to double your money,
#of periods to double my money=72/interest rate per period, Alternatively, you can
use this to determine the interest rate required for you to double the money
Ex. 6% per year => 72/6=12 years, 10 years? Approx 7.2%. 7.18% Exactly
2) Finding PV (discounting): How much to deposit to have $100 3 years later at 10%, semiannual compounding? (p.131 – p.133)
(1) Using the formula, Note that the inverse relationship, PV=FV*{1/(1+I)^N}
(2) Using the TVM(PV) table, PVIF(I%, N) = 1/(1+I)^N
(3) Financial calculator:
3) Finding a time period: $100 deposited today and wish to have $370 at 16% with semi-annual
compounding, # years? => get # of periods, then 8.5 years (p.134)
(1) Using the formula => 370=100*(1+.08)^N, # of years=N/2=17/2=8.5
(2) Using the TVM(maybe FV) table
(3) FC: Note “-“ . Presee CPT, then N
4) Finding an interest rate: $100 today and wish to have $1,700 in 12.5 years with semi-annual
compounding, interest rate (APR)? => APR=12%x2=24% (p.133 – p.134)
(1) Using the formula and Trial & Error, 100=1700*{1/(1+I)^25} or 1700=100*(1+I)^2525
(2) Using the TVM (maybe FV) table
(3) FC: Note “-“ . Press CPT, then and i/Y
* Multiple Cash Flows
1) Uneven Flows
=> Brutal Force (p.143 – p.146): Determine the PV( or FV) of each payment. Then add all the
PVs to determine the PV of all the payments.
FC: Enter CFo=0, CF1=100, CF2=200, CF3=300, CF4=400, CF5=600 together with I/Y=5%,
then determine NPV
Excel is an excellent choice in this case.
Enter each cell the payment, 100, 200, 300, 400, 600 then enter =npv(5%, address of 100: address
of 600), hit “enter” to get 1,335
We can also Excel to back-figure the interest rate to produce the PV given. In other words,
determine I given PV and cash flows. In this example, have -1,335 on top of the cash flows (righ
above 100), then “=IRR(address of -1,335: address of 600)” and hit “enter” to get 5%.
2) Annuity: equal amount for some consecutive periods (p.134 – p.141)
(1) Different types – Ordinary (p.135)=each payment is made at the end of each period, Annuity
Due (p.135)=each payment is made at the beginning of each period, Perpetuity(p.141 –
p.142)=ordinary annuity, but forever
(2) Annuity examples (annuity, mortgage payments, lease payments, etc. vs. apartment rent)
(2) Analogous example: 3 yards(1760), 3 feet(5280), 3 inches(63360) on the line
(3) How to compute FV, PV of an ordinary annuity? (p.135, p.138)
Ex1: Save $100 each month for 10 years, at 6%, FV at the end of the 10th year? $16,388
How much extra money you have from this = 16,388 – 12,000 =4,388 due to interest.
Ex; I would like to receive $100 each month for the next 10 years at 6%. How much do I
have to save today? $9,007.35
a) Brutal Force = even for annuity, you can deal with each payment, then sum
them up to get the total PV or FV. This is inefficient.
b) FVIFA(I%, N), PVIFA(I%,N): In our example above, I=0.5%, N=120
c) FC: note “-“ PMT, N, I
(4) How to compute FV, PV of an annuity due? (p. 137: FV of an annuity due)
a) Brutal Force
b) FVIFA*(1+I), PVIFA*(1+I) => since you have each period one period earlier
c) FC: Change the setting to BEG => maybe, don’t do it
d) Ex2: everything is the same as Ex1, except you pay (or get) $100 at the
beginning of each month? PV=100*PVIFA(.5%, 120)*(1.05)=9,052.38.
Alternatively, you can look at this as an ordinary annuity with 119 periods and
$100 extra today =100*(.5%, 119)+100=9,052.38. How about FV?
FV=100*FVIFA(.5%, 120)*(1.05). Alternatively, you can determine the FV
based on the PV you have already determined using the relationship between PV
and FV, FV=PV*(1.05)^120.
(5) How to compute FV, PV of perpetuity? (p.141 – p.142: PV of perpetuity)
PV of perpetuity = C/I, C=payment per period, I=interest rate per period
Ex: PV of $100 monthly perpetuity at 12% APR= 100/0.01=10,000
3) Constant growth rate model
(1) What is it? Cn=Cn-1*(1+g), Timeline
(2) PV equation and the formula =C1/(I-g)
(3) Perpetuity is a special case with g=0% = C/I as we saw earlier
EX: Co=$2, g=5%. Then C1=Co*1.05=$2.10, C2=C1*(1+g)=Co*(1=g)^2, - Cn=Co*(1+g)^n=2*(1.05)^n - - > exponential growth.
PV of the constant growth rate payments = C1/(I-g)
EX: If I=10%? PV= $2.10/(0.10 – 0.05) =$42. What if everything is the same, but g=0%
(perpetuity)?, then C1=Co*(1+0.0)=2, PV=2/0.1=$20. The extra $22 is for the growth of
the future payments.
* APR / EAR (p.148 – p.150), effective annual rate = (annual percentage) yield (APY)
APR is a rate quoted, EAR is taking into the compounding effect
EAR=(1 + APR/n)^n – 1, n=# of periods a year
EX: APR=10%, Semiannual,
Semiannual => n=2 => EAR=APY=(1.05)^2 – 1 = 0.1025 or 10.25%
Quarterly => n=4 =>EAR=(1.025)^4-1 = 0.10381 or 10.381%
Frequent compounding produces a higher APY? Because of more interest on interest
* Loan Amortization (p.151 – p.152)
EX: House price=$300,000, 20% down, 30 year fixed at 6%, $10,000 closing cost (for paperwork,
the point (? = extra payment upfront to get lower interest rate), etc)
How much to borrow? 300,000*(1-0.2)=240,000 + 10,000 = 250,000
Monthly payment=$1,498.88 (Note that you have an equal monthly amount, the composition
between interest portion and the repayment of the principal varies over time. Initially, more for
interest payments Table 5-4 on p.151).
Total payment=1,498.88*360=$539,597
Total interest payment=539,597 – 250,000 =289,597
What if I choose to have a 15 year loan instead?
Monthly payment=2,109.64
Total payment=2109.64*180 =379,735
Total interest payment = 379,735-250,000=129,735
 Much lower interest payment for a 15 year loan. Is the 15 year loan better? Well, you need to
look at your cash flow situation. Actually, the PVs of both are the same!
For TVM, it is important to have a time line first. Unfortunately, Aplia does not provide a
time line presentation, makes it unnecessarily difficult to us to understand what is going on.
Please also remember, interest rate per period and # periods. “-“ for cash outflows.
However, need to convert your answers to APR and # years.
Finally, note that the “relative positions” of the cash flows are what matter. Ex1: FV3 of
FV4=$100 at 10% is equivalent to PV of FV1=$100, say at 10%. Ex2: How to determine PV
of cash flows FV2=100, FV3=100? BF, FV1 using an ordinary annuity PV to get FV1, then
discount FV1 to get a PV similar to get a total length of two strings 100 f and 100 inches.
Chapter7. Bonds and Their Valuation
What is a bond? A well structured IOU with a Face Value (FV), maturity date, and typically
(equal) coupon payments.
Coupon (Interest) rate is rather specified. Each coupon payment=FV*coupon rate per period
Ex: $1,000, coupon rate=8%, semi-annual coupon paying bond, 10 year bond => Time line?
Each coupon payment=$40, the last payment $40+$1,000=$1,040
Who issues? Federal government (treasury bonds=securities), municipal bonds (munis) issued by
state and local governments, corporate bonds, foreign governments and corporations.
Bond characteristics: Par value=Face value=Principal, Coupon (fixed, variable, zerocoupon=deep discount), Maturity date,
(Indenture) Provisions=fine prints: examples of provisions are Call (callable bonds)-issuer has the
option to retire the bond prior to its maturity at a specified value. It is not good for investors and
the price (return on this bond) should be lower (higher). Sinking fund=fund set aside to pay off
the bonds, giving bond investors a piece of mind=> higher bond price/lower returns, Puttableinvestor has an option to terminate the bond prior to its maturity=>good for investors, higher
bond price/lower returns, Convertibility (CB): investors can covert a bond into equity. Investors
like this. Other issues: income bond=only interest payments, if possible, indexed bonds=coupon
payments are based on an inflation index, - - Bond Valuation:
What is value?=worth, ultimately subjective, but we try to teach you learn an “educated” way to
come up with a “reasonable” value
Why important? Our basic economic (investment) decision whether to buy (investing=buying the
asset) is based on the comparison between the value & the (market) price, which is given to an
individual.
How? Many different approaches. In basic finance, the best approach is the PV model. Given a
prospective stream of future cash flows, we determine the (present) value at a (given) investor’s
required rate of return (discount rate, opportunity cost (returns or interest rates from the
best alternative)
Example:
PV=C*PVIFA(r%, n) + F*FVIF(r%, n)
or C PMT, F FV, r i/y, n N, CPT => PV
Ex: 15 year annual coupon paying bond with 10% coupon rate, FV=$1000. What is the PV at
r=10%? Note that C=1000*0.1=$100, 15 N, 1000 FV, 10% i/Y CPT PV=$1,000
What if r=7%? PV=$1,273.24
What if r=15%? PV=$707.63
 Note that there is an inverse (negative) relationship between the discount rate (r) and the
PV. Does it make sense? Given a bond (or the all payments from the bond), how much
you may think about the bond varies inversely as what other opportunities available. If
there is a great opportunity out there with r=opportunity cost is high, the value you have
for the bond could be less - - -. Alternatively, you can think of the PV of $100 you expect
to receive in 3 years. As the interest rate becomes high, you can get $100 with less money
saved.
Aside) Value may not depend on the holding period. This is possible since we assume that the
person buying it from Steve is expected to have the same value of the remaining cash flows. =>
the value is independent of how long an investor plans to hold it.
* Value vs. Price
If the market is “efficient”, then Price should be close to the “average” Value of most investors,
and Price moves close to Value pretty quickly. Once you determine a PV, you compare the PV
with the price of the bond (which is given) to make an investment decision. If PV>Po, then the
bond is undervalued (or underpriced) and you want to buy (invest in) the bond. Otherwise, the
bond is overvalued (or overpriced).
* Bond Valuation (p.200 – p.203, p.209 – p.210): Negative relationship between interest
(=discount) rates and bond values.
A typical bond makes interest (coupon) payments semi-annually. In the book, annually. For a
semi-annual coupon bond, C=INT = Face Value*APR coupon rate/2, N=2*#years, required rate
of return (=discount rate), rd =APR rate/2
WARNING: some books use the “price” instead of “value”!!! An individual cannot determine
the (market) price. The price is already given. Everything they are doing in this chapter is to
determine the value, not price. However, the price is very close to value for a bond.
Aside) Bond sells at a discount (premium, par) => the PV or price is less (higher, equal to) than
the Face Value. Examples on p.203 and p208 are about different discount rates (rd=10%, 15%,
5%) for the same bond (coupon rate=10%), and about different values at different coupon rates
(coupon rate=13%, 10%, 7%) with the same discount rate=10%.
 Note that when the coupon rate is high (higher than the discount rate or yield), then the
bond sells at a par and the bond PV curve will be placed above the face value. For this
bond, you will have a negative capital gains (or capital loss) as the PV > Face Value (Face
value can be thought of the payment you will get when you return (resell) the bond back to
the issuer. Whether the bond is at a par (PV=FV), or at a premium (PV>FV), or at a
discount (PV<FV), the expected total return should be the same as you get a competitive
return as the market return. However, the composition of the total return between income
return and the capital gains return may change. See below in our discussion about YTM.
* YTM (yield to maturity): (Given the price), a special discount rate which makes PV=price.
Example (p.203 – P.205) – Return on bond investment if the bond is held until maturity. For this,
all you need to do is enter all the information including the price of the bond (entered into PV),
then try to compute the discount rate, i/Y
Ex. 9.5% semi-annual coupon 20 year maturity bond with 15 years remaining. FV=1000 and the
current price is $1,137.76. What is the YTM? => 47.5 PMT, 30 N, 1000 FV & -1137.76 PV, then
CPT i/Y = 3.96*2=7.92%
Aside: What is the current yield (coupon income rate) of the bond = annual coupon
payment/current bond price=$95/$1137.76=8.35%. What is then the expected capital gains rate
from the current price of $1137.76 to $1000 Face Value? Total return measured by YTM=7.92%
minus the current yield of 8.35% = -0.43%.
YTC (yield to call)? If the bond is callable, you can determine the yield based only on the coupon
payments you expect to get until the bond gets called and the call value. Ex: the bond can be
called within 5 years from now and the call value (the lump-sum the issue will pay when called)
is $1,040. Everything is the same except 10 N (5 years *2 periods a year), 1040 FV => CPT
i/Y=6.88%
NOTE: Yield = return for investors, but it is a cost of financing from an issuer’s perspective.
Since YTC is less than YTM, the issuer is expected to call to save at 6.88% instead of keep
paying more at 7.92%.
Remark: %change in the value due to changes in interest rates varies for different bonds. The
bond with longer time to maturity and/or lower coupon rates have greater % changes => long
term bonds and smaller coupon paying bonds are more sensitive to changes in interest rates. (p.
210 – p.214) – We need to talk about this in class. However, with this fact, you can work on the
Aplia HW at the moment. When investors are seeking a steady income, they are more concerned
about reinvestment rate risk in case interest rates fall. They really hate when the bonds get called
so that they have to reinvest and there are no good investment opportunities.
* Bond Investment Risks
- Interest Rate Risk
- Reinvestment (Rate) Risk
- Default Risk
1) different types of corporate bonds
2) bond ratings
* Bond Markets and Quotations p.220
Chapter8. Risk and Rates of Return
* What is “risk” and why does it matter?
Finance/Investing dealing with the future -> uncertainty -> risk
Given uncertainty, the risk is that we may earn less than anticipated.
Different investments have different levels of risk.
Different people have different attitudes to risk. And the same person can have different risk
attitudes depending on what is at stake. => Risk aversion is assumed.
Risk Premium and required rate of return
Risk increases => Higher required return => Lower Financial Value
Sources or risk : macroeconomic, social, business, financial, etc
* Probability distribution
(p. 233, p. 234 Table 8-1, p. 235, Figure 8-2)
Vs. Historical return data
Expected value vs. historical (=sample)average
Variance and standard deviation (p.236) vs. sample stat
Semi-variance
Coefficient of variation
Portfolio risk and return – define and measure
CML
* Variance (or Standard Deviation) for Total risk about our total wealth (team’s performance)
versus Another risk for an individual asset as a part of your wealth (individual player’s
performance measured as his/her contribution to the team’s performance: how to pick a player for
your team-NFL draft?) => Concept of a portfolio
=> See p.242, Figure 8-4 for a complete diversification effect, the total risk is completely
eliminated? Very rare, but can still got the picture about diversification or the risk offsetting
effect like in Figure 8-5 on p.244
Then, how do you measure the risk contribution of each security? – Market risk measured by beta!
- Systematic (market, non-diversifiable) vs. unsystematic (idiosyncratic, beta, individual security)
risk: see fig 8-6 on 246 Which one is relevant risk?
Beta is to measure the systematic risk!
CAPM, SML (P. 240, P. 251 – P. 258)
Example on p.253
Chapter9. Stocks and Their Valuation
* What is a stock? Represents ownership, receive dividends
* Characteristics of common stock & shareholder rights
- residual claims, limited liability, preemptive rights
- proxy, proxy fights
* Stock Price vs. Intrinsic Value (p.273 – p.275)
- Price < Value => Buy/Invest, Don’t buy otherwise
* Stock Valuation
- DDVM (Discount Dividend Valuation Model) Discount all dividends and determine the sum of
all dividend PVs
We cannot do this for a general situation as we need to estimate infinite many dividends.
- Thus, we use Gordon’s constant growth rate model (dividends grow at the constant rate, g)
Dt = Dt-1 * (1 + g)
Then, the PV = D1 /(rs – g), where D1 = projected next dividend, rs = discount rate, required return,
or opportunity cost, g=projected dividend growth rate
Aside: rs is typically given. However, you sometimes need to estimate rs. 1) Use the best return
from all the “competing” investment choices (opportunity cost concept), or 2) Use CAPM=SML,
where rs = rf + (rm – rf)*βs, where rf = risk-free rate (e.g., T bill rate), rm = projected market return,
(rm – rf) = market risk premium, βs = security s’s systematic risk or beta risk.
Ex, if Do = $2.00, rs = 8%, g = 5%, then PV = 2.10/(0.08 – 0.05) = $70 (note, D1 = 2*1.05=2.10
If Po = $66, you want to buy/invest as PV > Po
Aside: If the market is competitive, then Po moves closer to PV (as a lot of people want to buy
this stock and the price of stock increases with a strong demand). Eventually, Po = PV in the
market equilibrium.
* Alternatively, we can make an investment decision by comparing rs (the minimum you are
seeking, the required rate of return), and 𝑟̂𝑠 (security s’ projected return on investment). If Rs >
𝑟̂𝑠 , then buy/invest as you may be able to make more than you are asking for. Now, the question
is how to compute 𝑟̂𝑠 ? The return on investment is based on how much you invest (here, Po) and
how much you expect to receive in return from the investment (here, all the projected dividends,
D1, D2, - - -). Again, we are using a PV=D1 / (rs – g). The difference is, instead of rs, which is
already given or somehow you determined, you are trying to backfigure what is the special rs,
which satisfies this PV equal to Po. In other words, we try to solve the equation, $2.10/(rs – o.o5)
= $66. Let us call that special rs, 𝑟̂𝑠 = 2.10/66 + 0.05 = 0.0318 + 0.05 = 0.0818 or 8.18%.
Note that 𝑟̂𝑠 =8.18% > rs =8% (given) and you want to buy/invest in this example.
Remark 1: The two alternatives (comparing the price and (present) value or comparing the
projected return and the required return) would always produce the same consistent
buying/investment decision.
Remark 2: 𝑟̂𝑠 = D1/Po + g, where D1/Po = projected dividend yield and g=projected dividend
growth rate=projected capital gains yield. Note that the price of the constant growth rate stock is
expected to increase at the rate of g%, the same as the dividend growth rate.
* Market Efficiency
* Preferred Stock Valuation and Preferred Stock Yield (don’t worry about Variable-Rate
Preferred)
Recall the PV of perpetuity => PV of a Preferred Stock = Dp / rp
(Note that this is practically the same as PV of a stock, PV = D1 /(rs – g) with g=0%
Examples p.291 – p.292
What is the projected return on preferred stock? Find out rp, which produces PV equal to the
current price of the preferred stock, Po.
𝑟̂𝑝 = Dp / Po (=projected dividend yield)
(Note: the projected capital gains yield for a preferred stock = 0% since the dividend growth
rate=g=0%. The price of the preferred stock is expected to remain constant like dividends over
time.)
Aside: If the market is in equilibrium, then the required rate of return, r, is equal to the projected
return on investment, 𝑟̂ , as well as Po = PV.
* Non-Constant Growth Model (Supernormal Growth Model)
In case the dividend grow rates change over time.
Ex, Do = $2, D1 = 2*(1.15) =$2.30 (15% increase), From D2, dividends are expected to grow at
the constant rate of 6.4%. That is, D2 = $2.30*(1.064) = $2.4472, D3 = 2.4472*(1.064), etc. If the
discount rate is 10.4%, What is the PV?
=> If you move the time period by one period, you can apply the constant growth rate model
to determine the value of the stock at the end of period 1 for the future dividends from D2
onwards (D2, D3, D4, - - -). For a person who may be buying this stock one year later, the value
of the stock for him could be FV1 = D2 / (rs – g) = 2.4472/(0.104 – 0.064) = $61.18. Now, you
can determine the PV of the stock based on D1 and FV1 (you may be able to sell the stock for
this amount one year later after you will receive D1) PV=2.3/1.104 + 61.18/1.104 = $57.50
Tips for Aplia:
#3 - between the common stock and preferred stock, you may want to compare their
projected total returns as the risk and return are positively related.
#4 – Once you determine the value of the stock, you can multiply it by the current number of
shares outstanding to determine the current market capitalization. Now, multiply the
additional shares issued by the price offered to determine how much amount the firm has
received from selling new shares. Add the two amounts to determine the firm’s new increased
market capitalization and divide this amount by the new total number of shares outstanding
(previous number of shares outstanding + additional shares issued) to determine the new
value of each share. The difference between the value of the stock prior to the new shares
being issued and the new value of each share is the dilution amount per share. The existing
shareholders may not be happy as the new shares given to new shareholders at a price less
than the market price.
The firm can avoid this conflict with existing shareholders by giving them a chance to buy
first those new shares to be issued at “good” prices on the ownership pro-rata basis. Give that
the fraction of new issues issued relative to existing total number of shares, say 20%, you are
entitled to increase your number of shares by that percentage amount, ie, up to 20% increase
in the number of shares you will be holding. By multiplying the new number of shares you
can hold by the new value of the share (you computed in the previous question), you can
determine $ value of your investment by exercising the preemptive right.
* Corporate Valuation Model (p. 286 – p. 291)
Stock Quotations
Chapter10. The Cost of Capital (Funding, Financing)
* Basic Definitions
- Marginal cost of raising extra one $! (the minimum rate of return (e.g., 8,6%) on the last one
$ to generate from the project to satisfy every investor (creditors, equity investors (=shareholders),
preferred stock investors, etc, since they would not invest if the firm fails to provide what they are
demanding at minimum)
- Here, we try to determine the cost of capital. A low cost of funding is good!
* The cash flows an investor faces and the cash flows from an issuer’s (firm’s) perspective are a
kind of mirror image; -Po followed by C1, C2, C3, - - - versus PoN followed by -C1, -C2, -C3, - - -.
The cash flow at 0 may be different due to PoN = Po – FC, FC=Flotation Cost. Note that
investors determine the ROI (return on investment) for various security investment from the
security projected cash flows: YTM (or YTC depending on whether it is likely to be called for a
callable bond), Projected Total Return on Stock ( 𝑟̂𝑠 from DCF or CAPM), Projected Total Return
on Preferred Stock (𝑟̂𝑝 ).
* Where are the money from (how to finance/fund)?
- Look at the Right Hand Side of the B/S
- Here, we are mainly focusing on the long-term financing (forget about current liabilities)
- Different funding sources:
Equity: Internal (using R/Es) & External (issuing new common stock shares)
Debt: Bonds (and long-term loans. We mainly talk about bonds in this class)
Preferred Stock
 Capital structure,
 What is optimal capital structure? e.g., 40%, 50%, 10%. This is a Fin439 topic, Here,
the capital structure is given in terms of % numbers of $ amount (=> we need to get %
structure)
* To raise capital, what do you need to do?
- Need to offer each group of investors (E, D, P), what they seek! => each group’s required rate
of return from Chapters 7, 8, and 9.
- Take into consideration extra costs & benefits (flotation costs, tax benefits, etc)
- E.g., Try to raise $10m for a new project, Given the capital structure above, and the cost of
Equity (10%), Debt (7%), Pref Stock (8%) => WA(M)CC = .4*10% + .5*7% + .1*8% = 8.3%
Real Life Example using Apples:
US: VA (5¢) with a limited qty of 30 apples, unlimited qty of WA (6¢)
Chile: (4¢) with a 40% quota (=> wus, wch ?)
Note: For US apples, always buy VA apples whenever possible! Why?
1) When buying 10 applies
How many from US (6)? how many from C (4)? How many from VA(6)?
Total Cost = 46¢ = 6*5¢ + 4*4¢
Average Cost = 4.6¢ = TC/total#
Marginal Cost when you buy the 11th = TC11 – TC10 = 50.6 – 46 = 4.6¢ or
= wus*MCus + wch*MCch = .6*5¢ + .4*4¢ = 4.6¢ (60% of the one last apple from
the US, actually from VA, 40% from Chile)
Note: AC = MC
2) When do I need to switch from VA to WA?
When the total # of apples from the US becomes 30, or the TOTAL # of apples becomes
X, where (.6)X = 30 => Backfigure X=?
3) At 250 apples
Where are the apples from? Since 250*0.6 = 150 US applies and 100 from Chile.
Among the US apples, 30 from VA (buy out all the VA apples), 120 WA
TC = 1270¢ or $12.70 = 30*5¢ + 120*6¢ + 100*4¢
AC = 5.08¢ = ?
MC = TC251 – TC250 or
= .6*6¢ + .4*4¢ =5.2¢ (from 250 to 251 apples, US applies are only from WA)
4) WA(M)CC schedule by looking at MCs,
In terms of US apples, the MC increases when we buy out all VA applies as we have to
start buying more expensive WA apples. The break point is at 30 US apples.
In terms of TOTAL # of apples. The break point is at 50 total number of applies.
=> Now, in terms of Equity (Internal and External) and Debt?
* Cost of Debt (bonds)
- Reviewing: Cash flow stream from investor’s perspective
{- P0, C, C, C, - - - , C, C+F}, n periods
=> YTM (return (yield) on the bond)
Ex: Po and FV=$1,000, coupon rate=8.75%, annual, 30 year bond? YTM=8.5%
=> Ex2: Po and FV=$1,000, coupon rate=10%, semi-annual, 20 year? YTM=10%
=> Ex3: Po = $1,025, FV=1,000, coupon rate=8%, semi-annual, 20 years?
(-1025 PV, 40 PMT, 1000 FV, 40 N, CPT i/Y=YTM=3.88%*2=7.76%)
- How about the cash flow stream from issuer (firm)’s perspective?
- Cash inflows and outflows are switched
- Instead of Po, (Po – FC)=PoN will be used, where FC=flotation cost
=> {PoN , -C, -C, -C, - - - , -C, -C-FV}
Aside) For the flotation costs and the interest (coupon) payments, the issuer can
enjoy TAX benefits. How much? (C+F/n)*t, where t is the tax rate
=> NOW, compute YTM before tax, kb from the cash flows { }(Using a financial
calculator, PoN PV, -C(coupon payment per period) PMT, -F FV, n (number of periods) N,
CPT i/Y). Then compute ka = kb *(1-T) to determine the after-tax cost of debt.
=> Ex3 above: F is a 4% of Po, PoN = 1025*(1-0.04)=$984, so {984, -40, - - , -40-1000}
(kb = 8.16%, and ka = 5.30% based on t=35%
* Cost of Equity (=cost of common stock)
=How much the firm has to deliver to shareholders to make them happy (delivering what they
asking for, required rate of return) + flotation costs, if exist.
- Internal Equity Financing using retained earnings. No floatation costs.
There are two approaches, one is using the DCF (discount cash flow) = DDM (discount
dividend model), the other one is CAPM
DCF(=DDM): In this case, ki = kre = 𝑟̂𝑠
Ex1: Po = $23.06, D1 = $1.25, g=8.3%, ki = 13.7%
CAPM: Ex2: Risk free rate is 5.6%, Expect Market Return (r m)=10.6%, Beta=1.48
 ki = 5.6% + (10.6% - 5.6%)*1.48 = 5.6% + 5%*1.48 = 13%
(note that the market risk premium = rm – rf = 5% )
- External Equity Financing by issuing new common equity shares (basically, we use DCF
approach. However, we need to use PoN because of the FC), ke = D1/PoN + g
Ex3: The same as Ex1 except the FC is 10% of the share price. PoN = 23.06*(1-0.1)=$20.75
ke = 1.25/20.75 + 0.083 = 14.3%
* Cost of Preferred Stock
kp = Dp /PoN
Ex: Dp = $10, Po = $100 with the FC is 2.5% of the pref stock price. kp = 10/97.5 = 10.3%
Note: unlike debt (bond) financing, no tax benefits for equity and preferred stock financing for
dividend payments and flotation costs.
* The Financing (Capital, Funding) Structure before the Break Point and after
- What causes the break point? Using more expensive External Equity Financing when you
switch from International Equity Financing (using retained earnings) to External Equity
Financing
- Where is the Break Point? In terms of Equity Financing Amount? When you use up all
retained earnings.
- Where is the Break Point in terms of total new financing amount? Try to find out the total
new financing amount based on the capital structure. For example, if you finance 35% of the
capital from equity and the size of retained earnings is $7 million, then the total new financing
would be $7m/0.35=$20m. You can confirm that 35% of $20m is indeed $7m. In general, the
breakpoint in terms of total new capital = Addition to retained earnings for the year/Equity
fraction p.320.
* Calculating the Overall Cost of Capital (WA(M)CC)
- Prior to the Break Point = wdka + wski + wpkp Note ka = kb*(1-T). wd, ws, and wp are
fraction of funding from debt, stock equity, and preferred stock.
Ex1: wd=45%, ws= 53%, and wp = 2% with ka = 5.3%, ki = 13.7%, and kp = 10.3%
WACC = 0.45*5.3% + 0.53*13.7% + 0.02*10.3% = 9.85%
- After the Break Point = wdka + wske + wpkp Note that ki = cost of internal equity financing
(or cost of retained earnings), ke = cost of external equity financing
WACC = 0.45*5.3% + 0.53*14.3% + 0.02*10.3% = 10.17%
- Cost of Capital Schedule: You can plot WACC against the total new capital amount. WACC
prior to the breakpoint would be flat at 9.85%, then WACC jumps to a new higher level at 10.17%
- Which projects to accept? Investment Opportunity Schedule: If the projected return of a
project is higher than WACC, you want to take the project. If not, you don’t want to take the
project.
Aplia #6-2: If the market is in equilibrium, the cost of equity=projected return on stock. You also
note that Note that 𝑟̂𝑠 = projected dividend yield + projected capital gains yield and projected
capital gains yield=the growth rate.
Note that the Growth rate = ROE*(1-dividend payout ratio) p.281. Comments: there is a trade-off
between current dividends and future dividends as the firm pays our more now, they have a
smaller addition to retained earnings and you expect a slower future growth of business, resulting
in less future dividends. Many of fast growing (IT) companies pay little or no dividends as they
want to plow back their earnings into their business for them to grow faster.
Chapter11.The Basics of Capital Budgeting
*Do you recall why we are in business? To make money
-What do we need? Idea(s), then capital (money)
*4 major decisions to be made?
1. Examine the idea(s) under consideration to take or reject, if chosen
-capital budgeting
2. Then need to come up with money, equity (internal vs. external?) or debt, how much each? capital structure
3. Short-term management (working capital mgt) and long-term management
4. How much paid out to shareholders in the form of dividends and how much to be kept within
the firm in the form of additional retained earnings–dividend policy
First, we have to estimate
1. The size of initial investment (initial outlay)
2. (NET) future cash flows on a timeline (note cash flows are different from (net) earnings as we
are interested in cash flows.)
3. Determine appropriate weighted cost of capital (WACC, which can be used as a discount rate)
Note: Different types of projects: independent (take all “good” projects), mutually exclusive (only
the “best” one among the “good” ones).
* 5 Alternative Methods (Payback, Discounted Payback, NPV, IRR, MIRR)
Example:
A: IO=10k
Future Cash Flows
C1=5k
C2=5k
C3=5k
B: IO=10k
C1=2k
C2=3k
C3=4k
C4=5k
C5=6k
1. Payback Period: How many periods to recover IO (your investment) - no discount rate used (it,
no PVs),
(Cumulative future cash flows) (p.353 – p.355)
PBa = 2 periods
PBb = 3.2 periods
Decision Rule: Accept the project if PB < Max period allowed or choose the one with a shorter
payback period for mutually exclusive projects. If Max allowed = 3 periods? (A only) 4 periods
(take both)?, If these are mutually exclusive with Max allowed=4 periods (A)?
Advantage: Intuitive and simple, popular choice
Disadvantage: Ignores cash flows beyond payback period, No TVM
2. Discounted Payback
Use discounted PVs.
3. Net Present Value (p. 338 – p. 341)
Recall from Chapter 7 and 9 to buy a security from an individual investor’s perspective,
PV>Price => Buy/Invest.
Here, IO is like a price of a project and we need to consider buying a project from a corporate
perspective.
Define NPV=PV-IO
Then, PV>IO (or price)  NPV>0 (or +NPV)
Decision Rule: Accept all +NPV projects or choose the project with the largest +NPV if mutually
exclusive.
Given K=10%, NPVa = 2.43k, NPVb = 4.44k => take both or only B
Given K=23.3%, NPVa = 0.011k, NPVb=-0.002k => take A (pretty weak, though) and reject B.
(Note: as r (discount rate) increases, PV and NPV declines. NPV profile is a trace of the NPV for
different discount rates)
(Note: NPV function on Excel is actually a PV function. Therefore you need to use
NPV(discount rate, C1 cell address: Cn cell address)-IO to determine NPV.)
4. Internal Rate of Return: Special discount rate which makes PV=IO (price) (p. 341 – p. 345) or
NPV=0. Note: YTM = Bond’s IRR
Decision Rule: Accept if IRR>hurdle rate (=discount rate, required rate, WACC) or choose the
one with the highest IRR in case of mutually exclusive projects.
PVa = 5*PVIFA(r%, 3) set equal to IO=10, what is the special r (discount rate) which satisfies
this equation? That special r is the IRR (return on the investment) for the project
=> PVIFA(r%, 3) = 2. Using the PVIF table, we can find out IRR should be approximately
23%~24%
=> Using the financial calculator -10 PV, 5 PMT, 3 N => i/Y= 23.38% (this is simple, since the
cash flow stream is an ordinary annuity)
PVb = 2*PVIF(r%, 1)+3*PVIF(r%, 2)+4*PVIF(r%, 3)
+5*PVIF(r%, 4)+6*PVIF(r%,5) set equal to IO=10, How to solve? Trial & Error
Or a Financial Calculator if you know how to deal of uneven cash flows
Or Excel Spreadsheet IRR(-IO cell address: Cn cell address) => 23.29%
Sometimes, IRR may not work well (how and when?). The best capital budgeting method is NPV
approach, although IRR is widely used in the real world (p. 349 – p.353).
* Crossover rate and its significance
* Modified Internal Rate of Return (MIRR) (p. 347 – p. 349) ~ use WACC to determine FV of
the all future cash flows. Then try to determine IRR based on Co ( - IO) and the FV of all future
cash flows.
Chapter12. Cash Flow Estimation and Risk Analysis
* Guidelines for capital budgeting
*Calculating a project’s free cash flows
- Initial investment
-Depreciation schedule
-Operating cash flows
-Terminal value
* Project evaluation and decision criteria
* Capital rationing
- Evaluating risk in capital budgeting (pp.374-379)
- Sensitivity analysis
- Scenario analysis
- Monte Carlo simulation
* Expansion Project (p. 369 – p. 372)
* Replacement Analysis (p. 372 – p. 374)
* The Optimal Capital Budgeting (p. 385)