# Present Value and the Opportunity Cost of Capital Fundamental Question by ramhood4

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Present Value and the Opportunity
Cost of Capital
Fundamental Question: How are asset prices
determined?
•   Companies invest in a variety of real assets.
•   Objective is to find real assets which are worth more than
they cost.
•   Essence of the capital budgeting process.
•   Asset valuation's relationship to a well-functioning capital
market: If there is a good market for an asset, its value is
exactly the same as its market price.
Present Value Example (B&M):
Suppose your house burns down leaving you with a lot worth
\$50,000 and a check for \$200,000.
Option 1: Rebuild
Option 2: Build an office building; cost is \$350,000; you predict you
can sell for \$400,000 in one year.
•    Rule: You should go ahead if the present value of the expected
\$400,000 payoff is greater than the investment of \$350,000.

Question: What's the value today of \$400,000 one year from now?
PV = Discount Factor x C1
where,
Discount Factor = 1/1+r , where r is the reward
investors demand for accepting delayed payment.

Assume that the \$400,000 payoff one year from now is a sure thing.

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Now, how else could you make \$400,000 one year from now?
•    Invest in government securities (assume 7% ROR)
•    How much must you invest?
\$400,000/1.07 = \$\$373,382
•  Now assume you've committed land and begun construction -
now you decide to sell. How much would you sell it for?
•  Since it produces \$400,000, well-informed investors would be
willing to pay \$373,832.
•  NOTE: This is the only feasible price that satisfies buyer and
seller. Present Value is also the market price.

TO CALCULATE PRESENT VALUE, WE DISCOUNT
EXPECTED FUTURE PAYOFFS BY THE RATE OF RETURN
OFFERED BY COMPARABLE INVESTMENT ALTERNATIVES.
RATE OF RETURN (ROR) IS OFTEN REFERRED TO AS THE
"DISCOUNT RATE", "HURDLE RATE" OR "OPPORTUNITY
COST OF CAPITAL".

Net Present Value

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Found by subtracting required investment from present value of
cash flows.
NPV = C0 + C1/(1+r)

Net Present Value Rule:
Accept investments that have a positive NPV.
Rate of Return Rule:
Accept investments that offer rates of return in
excess of their opportunity cost of capital.
NOTE:
The NPV rule and the IRR rule can conflict when
we have multiple period cash flows.
Present Value Techniques
•   Valuation of Cash Flows (components)

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1.   Magnitude
2.   Timing

•   Timeline
Example: We wish to calculate the PV of the cash flow stream,
where r = 10%

\$100                 \$200

-------|------------------|-------------------|--------------------
t =0             t=1                   t=2

PV = \$100/(1+.10) + \$200/(1+.10)2 = \$256

•     Discount Factors (Appendix Table 1 in B&M) - Very useful
when the same discount or interest rate is applied over the life of
the project.
Example:

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Discount              Cash             Present
Period             Factor                Flow             Value
----------         ------------          ------------     -----------
0                  1.0                   -\$150,000        -\$150,000
1                  1/1.07 = .935         -\$100,000        -\$ 93,500
2                  1/(1.07)2 = .873      +300,000         +261,900
--------------
Total NPV =      + \$18,400

Intuition Behind Present Value
•       Think about the problem in terms of future value.

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•   If you have \$100 and put it in the bank for one year at 6%,
how much do you have after one year?
one3 year.
•   Thus, to translate money from its value at t=0 to its value at
t=1, we multiply by (1+r)
•   Correspondingly, to translate value from t=1 to t=0, we
divide by (1+r).
•   This notion is easily extended to multiple time periods.
•   Provides a powerful means to value long-lived assets.
Oil and gas reserves
Value of a mine

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Perpetuities and Annuities
Perpetuities
• Securities issued by the British government
• No obligation to repay

• Offer fixed income for each year to perpetuity.

• Rate of return is equal to promised annual payment divided

by PV -       Return = Cash flow/PV
• Rearrange, and find the PV, given discount rate and annual

cash payment
EXAMPLE: Suppose you have \$1000 in bank drawing 5%; how
much can you withdraw at year end and still have same
amount in bank as at the beginning of the year? This process
can continue forever or in "perpetuity".
EXAMPLE: Endowed chair at CSM; r = 10% and annual cash
payment for chair is \$100,000.
PV of perpetuity = C/r = \$100,000/0.10 = \$1,000,000

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Growing Perpetuity - Allows for growth in annual
cash payment.

PV = C1/(1+r) + C1(1+g)/(1+r)2 + C2(1+g)2/(1+r)3 + . . .

Simple formula for this is the sum of a geometric series:
PV of growing perpetuity = C1/(r-g)

EXAMPLE: Endowed chair where g = 0.04.
PV = C/(r-g) = \$100,000/(0.10-0.04) = \$1,666,666

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Annuities
• An asset that pays a fixed sum each year for a specific
number of years, i.e. house mortgage.
• An annuity that makes payments in each of years 1 to t is

equal to the difference between two perpetuities.
PV of Annuity (for year 1 to year t):
C/r - [(C/r)(1/(1+r)t)]
or
C[(1/r) - (1/(r(1+r)t)]
NOTE: Expression in brackets is the annuity discount factor,
which is the PV at discount rate, r, for an annuity of \$1
paid at the end of each of t periods.
EXAMPLE: Endowed chair - cost to endow chair for 20
years at \$100,000 per year?
PV = \$100,000[(1/.10) - (1/(.10(1.10)20)]
= \$100,000 x 8.514
= \$851,400

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Compund vs. Simple Interest
•   Compund Interest - each interest payment is reinvested to
earn more interest in subsequent payments.
•   Simple Interest - no opportunity to earn interest on interest.

NOTE: Discounting is a process of compound interest.
EXAMPLE: What is the PV of \$100 to be received 10 years
from now, if the opportunity cost of capital is 10%?
PV = 100/(1.10)10 = \$38.55

•   Simple interest and continuously compounded interest are rarely
used in the business world. For virtuallly every application,
compound interest is the accepted technique.

Rule of 70: Number of years that it takes for an investment to
double in value at an annually compounded interest rate of r, is
approximately 70/r. So, if interest rate is 10%, then 7 years is
the amount of time.

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Valuing Stocks and Bonds
Key Issues
•   Focus on cash flows (magnitude and timing)
•   Caclculate the PV of those cash flows

Bonds
• Fixed set of cash payoffs - usually semi-annual.
• Interest payments and face value at maturity.

• Treasury bonds, municipal bonds, corporate bonds, foreign

bonds, mortgage bonds
EXAMPLE: Suppose in August of 1989, you invest in a 125/8%
1994 U.S. Treasury bond.
Coupon rate = 125/8%
Face Value = \$1000
Each year you receive .1265 * 1000 = \$126.50
In August, 1994 you receive \$1126.25
CASH FLOWS

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1990             1991               1992          1993            1994
\$126.25          \$126.25            \$126.25       \$126.25         \$1126.25
WHAT IS THE 1989 MARKET VALUE OF THIS STREAM?Compare
return to similar securities.Medium term Treasury bonds at that time offered ROR
of 7.6%
NOTE: 7.6% ROR is what investors gave up to invest in bond.
5 Ct
PV = ∑            t = \$1202.77
t =1(1+ r )
NOTE: Bond price quotes are expressed in a percentage of face value; i.e.
\$1202.77 = 120.28 percent
Consider the alternative view: If the price of the bond is \$1202.77,
what return do investors expect?
1202.77 = \$126.25 + \$126.25 + \$126.25 + \$126.25 + \$1126.25
1+ r       (1+ r )2 (1+ r )3 (1+ r )4    (1+ r )5
So, r = 7.6%
• r is yield to maturity or internal rate of return

NOTE: Bond yields are usually quoted as semi-annual compond rates.

Valuation of Common Stock

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•   Cash payoffs to owners of common stock
- cash dividends
- capital gains or losses
Suppose:
PO = current price
P1 = expected price
Div1 = expected divdend

Rate of return, r, that investors expect from a share over the next
year is defined as the expected dividend per share, Div1, plus
the expected price appreciation per share, P1 - P0, all divided by
the beginning year price.
Div1 + P1 − P0
ER = r =
P0
•   r is the market capitalization rate or expected return
on a security.

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EXAMPLE: Company X is selling for \$100/share; investors
expect a \$5 dividend and the stock to sell for \$110 one year
from now. The expected return, r, then is:

r = \$5+ \$110 − \$100 = 0.15
\$100

Correspondingly, given investors' forecasts of dividend and price and the
expected return offered by other equally risky stocks, then today's price:
Div1 + P1
Price = P0 =             If r, the expected return on securities
1+ r
in the same risk class as Firm X is 15 percent, then today's price should
be:
P0 = \$5+ \$110 = \$100NOTE: All securities in an
.
115
equivalent risk class are priced to offer the same return. No other price
could survive in competitive capital markets.
Multiple Period Valuation

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Just as price at P0 is dependent on investors expectations about
year 1's dividends and stock price appreciation, so also can we
compute P1, based on expectations about year 2.
Div2 + P2
P1 =
1+ r

EXAMPLE: Suppose a year from now investors will be looking
at dividends of \$5.50 in year 2 and a subsequent price of \$121.
This would imply a price at the end of year 1 of:

P1 = \$5.50 + \$121 = \$110
.
115

Today's price then can be computed either as:

Div1 + P1 \$5.00 + \$110
P0 =            =             = \$100
1+ r          .
115
or

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Div1 Div2 + P2 \$5.00 \$5.50 + \$121
P0 =       +         =     +             = \$100We can
1+ r (1+ r )2    .
115       .
(115) 2

extend this result to multiple periods in the following manner:
H     Divt         PH
P0 = ∑              +
t = 1 (1+ r )     (1+ r ) H
t

where H is the final period and the summation is the
discounted present value of the dividend stream from year
1 to H.

NOTE: Stock valuation is nothing more than the sum of the
present value of the expected cash flows from dividend
streams during the period and the present value of the end-
of-period stock price.

In the case where H goes to infinity, we can ignore P because
this value goes to 0.
So, then we can think of P0 as the present value of a perpetual
stream of cash dividends, where

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∞   Divt
P0 = ∑
t = 1 (1 = r )
t

Growth Rate and the Gordon Model
Dividend growth Rate
Incorporation of growing perpetuities

Div1
P0 = r − g

g = anticipated growth rate (must be < r)
r = market capitalization rate
NOTE: As g approaches r, stock price becomes infinite - r
must be greater than g if growth is perpetual.
Estimating Capitalization Rate

Market capitalization rate, r, equals the dividend yield (Div1/P0)
plus the expected rate of growth in dividends (g), where

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Div1
r=        +g
P0

EXAMPLE (B&M): Sears, Roebuck & Company is selling for
\$42/share early in 1989; dividend payments for 1989 are expected to
be \$2.00 per share.

Div1 \$2.00
Dividend Yield =       =      = 0.048
P0 \$42.00

What about g, the rate of growth in dividends?

Methodology:

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1. Observe Historical payout ratio, ratio of dividends to earnings per
share. for Sears, historically been about 45%; 55% of earnings is
reinvested: plowback ratio.

2. Sears' return on equity, ROE, or ratio of earnings per share to book
equity per share is about 12%.
EPS1
ROE =                      = 0.12
BookEquity / Share

3. Assume fairly stable ROE and payout ratios.
4. If we forecast 12% ROE and reinvest 55%, then book equity
should increase by 0.55 x 0.12 = 0.066. (Since we assume that
ROE and payout are constant, earnings and dividends per share
will also increase by 6.6%). Therefore dividend growth rate is:
g = plowback ratio x ROE = 0.55 x 0.12 = 0.066

So, utilizing the Gordon Model, we may now compute the market
capitalization rate, r.

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Div1
r=         + g = 0.048 + 0.066 = 0.114
P0
or about 11.5% is the market capitalization rate.

Methodological shortcomings of the Gordon Model:
1. Constant growth?
2. Constant Plowback?
3. Constant ROE?
4. Single stock analysis may be inappropriate - may need to
look at a class of stocks, i.e. FERC sets market
capitalization rates for utility industry.
5. Rule of thumb only.
6. Avoid use when firm is in a high growth period
(Remember, g is a long-term growth rate.)

Stock Price and Earnings per Share

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•   Growth Stock - those stocks purchased primarily for the
expectation of capital gains; interested in future growth or earnings
rather than next year's dividends.
•   Income Stock - purchased primarily for the cash dividends.

Consider the case of a company that does not grow at all, i.e. no
plowback of earnings - simply produces a constant stream of
dividends. Special case where:
Expected return = dividend yield = earnings-price ratio
Div1 EPS1
Expected Return =                 =
P0   P0
For example, if the dividend is \$10/sher and stock price is \$100,
then market capitalization rate, r, is 0.10.
Similarly, price equals:

Div1 EPS1 \$10. 00
P0 =       =    =        = \$100
r    r    0.10

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NOTE: E(r) for growing firms can also equal the earnings-price
ratio. Key is whether earnings are reinvested to provide a return
greater or less than the market capitalization rate.
EXAMPLE (B&M): Effect on stock price of investing an additional \$10
in Year 1 at different rates of return. Project Costs are \$10.00 - EPS1.
NPV = -10 + C/r, where r = 0.10
Project's Impact
Project Rate        Incremental           Project NPV          on share Price         Share Price
of Return           Cash Flow, C          in Year 1            in Year 0              in Year 0, P0        EPS/P0          r
-----------------   -------------------   ------------------   --------------------   ------------------   -------------   -----
0.05                \$0.50                 -\$5.00               -\$4.55                 \$95.45               .105            .10
0.10                \$1.00                        0                    0               \$100.00              .10             .10
0.15                \$1.50                 +\$5.00               +\$4.55                 \$104.55              .096            .10
0.20                \$2.00                 +\$10.00              +\$9.09                 \$109.09              .092            .10
0.25                \$2.50                 +\$15.00              +\$13.64                \$113.64              .088            .10

NOTE: The earnings-price ratio equals the market capitalization rate (r)
only when the new project's NPV = 0. Managers frequently make poor
financial decisions because they confuse earnings-price ratios with the
market capitalization rate.

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PVGO - Present Value of Growth Opportunities
• Think of stock price as the capitalized value of avaerage earnings under

a no-growth policy, plus PVGO, where
EPS
P0 = r 1 + PVGO

Rearranging, we see the earnings-price ratio is equal to:
EPS1
= r(1− PVGO )
P0           P0

•   Earnings-price ratio will underestimate r if PVGO is positive and
overestimate it if PVGO is negative.

Valuation of PVGO
• We can compute the PVGO using the simplified DCF formulation,

replacing dividends with forecasted NPV1, where
NPV
PVGO = r − g1

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SUMMARY:

•   For "growth" stocks, PVGO is high and P/E ratio is high (or
earnings-price ratio is low.
•   Growth stocks are those which PVGO is large relative to the
capitalized value of earings per share - not because it's rate of
growth is high.

EXAMPLE: P0 = \$30, EPS = \$1.00, r = 0.10
1. Capitalized value of earnings equals \$10
2. PVGO = \$20.
3. PVGO is very large relative to the price of the stock.

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Price-Earnings Ratio (or Multiple)
•   Market price divided by its current earnings per share.
•   Measures how much investors are willing to pay for a company with
that level of earnings.
•   Importance:
1. changes in P/E ratio directly impacts stock prices.
2. current price is just the product of a stock's P/E ratio and EPS
Current Price = P/E Ratio x EPS
3. P/E ratio translates earnings into value; as the P/E ratio
expands or contracts, so does price.
4. P/E ratios tend to accelerate changes (in either direction) as
earnings/share changes.

•   P/E Determinants - in general, P/E's increase when:
1. Growth rate of earnings are expected to increase.
2. Dividend payout ratio is expected to increase.
3. Riskiness of a stock decreases.

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Three important factors associated with P/E ratios:
1. Earnings potential
2. Dividends
3. Investment quality

NOTE: Since firms have relatively stable dividend policies, the
variables most likely to affect P/E are risk and expected
growth.

High P/E Ratio
• Good growth opportunities

• Earnings are relatively safe

• Deserves low capitalization rate (r).

Low P/E Ratio
• Low or no growth opportunities

• Unstable earnings

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•   Firms can have high P/E ratios and almost 0 earnings - generates
exptremely high P/E ratio.
•   No reliable association between P/E ratio and the market
capitalization rate, r; ratio of EPS to P0 measures r only if
PVGO = 0; EPS must represent earnings with no growth.
•   Earnings per share means different things to different firms
because of arbitrary accounting practices, i.e., depreciation
methods, valuation of inventory, capitalizing vs. expensing, etc.

P/E Ratios - Wall Street Journal (10/7/92)

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Company         P/E Ratio      Company           P/E Ratio
-------------   ------------   -------------     ------------
Exxon           17             Coca-Cola         29
Mobil           23             Hewlett-Packard   14
Chevron         25             Goodyear          12
Texaco          17             General Mills     20
Amoco           25             Phillip-Morris    3
Shell           16             Paine-Webber      4
ARCO            32             Shell Oil         16

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Investment Criteria               •   Net Present Value
•   Discounted/Undiscounted Payback (Payout)
•   Average Return on Book Value
•   Internal Rate of Return
•   Profitability Index

Net Present Value

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•    Any investment rule which does not recognize the time
value of money is useless.
•    A dollar today is worth more than a dollar tomorrow.
•    Depends solely on forecasted future cash flows and
opportunity costs of capital
•    Additivity Rule: Because present values are all measured in
units of today's dollars, you can add them up.
NPV(A+B) = NPV(A) + NPV(B)

Year        Project 1   Project 2   Project 3    Proj. 1&3    Proj. 1&2   Proj. 2&3
0           -100        -100        -100         -200         -200        -200
1           0           225         450          450          225         675
2           550         0           0            550          550         0
IRR         135%        125%        350%         213%         131%        238%
NPV (10%)   354         105         309          663          459         414

Payback (Payout)•           Initial investment should be
recoverable within some specified cutoff period.• Computed by

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counting the number of years it takes before cumulated cash
flows equal initial investment.
EXAMPLE:

Cash Flow
Project   Period 0    Period 1    Period 2      Period 3    Payback        NPV (10%)
A         -2000       2000        0             0           1              -182
B         -2000       1000        1000          5000        2              3492

Payback rule says accept A over B;
NPV rule says reject A and accept B.
NOTE: Payback criterion gives equal weight to all cash flows
before payback date and no weight at all to subsequent cash
flows.

EXAMPLE:
Cash Flow

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Project    Period 0    Period 1  Period 2      Period 3     Payback             NPV (10%)
A          -2000       1000      1000          5000         2                   3492
B          -2000       0         2000          5000         2                   3409
C          -2000       1000      1000          100,000      2                   74,867
Firm accepts too many short-lived projects, possibly with
negative NPV's.

Choosing a Cutoff Period
•   Firms typically arbitrarily choose the cutoff period.
•   If one knows the typical pattern of cash flows, then you can
find the optimal cutoff period that maximizes NPV.

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•   CAUTION: Only works if cash flows are spread relatively
evenly over the life of the project.
Optimal Cutoff Period = 1 − 1 n
r r (1+ r )
where n = life of the project
EXAMPLE: 10% discount rate, 10 year project.
So, optimal cutoff is 6 years.

Discounted Payback
•   More appropriate because opportunity cost of capital is
integrated - but still ignores after payout cash flows.

Average Return on Book Value
•   Book rate of return

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• Divide average forecasted profits (after depreciation and
taxes) by the average book value of the investment.
• Ratio is then measured against book rate of return (ROR) of

the firm as a whole.
EXAMPLE: Assume \$9000 investment, depreciated at \$3000
per year; assume no taxes.
Cash Flow
Project                  Period 1    Period 2       Period 3     Book ROR
A         Cash Flow      6000        5000           4000
Net Income 3000            2000           1000         44%
B         Cash Flow      5000        5000           5000
Net Income 2000            2000           2000         44%
C         Cash Flow      4000        5000           6000
Net Income 1000            2000           3000         44%
Average Book Value of Investment:
Year 0         Year 1         Year 2          Year 3         Average
\$9000          \$6000          \$3000           \$0             \$4500

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NOTE: All projects have 44% book ROR (2000/4500), yet
Project A clearly has a higher NPV.

Limitations to Average Return on Book Value:
• No allowance for immediate cash flows being more valuable

than distant ones.
• Not based on cash flows, but accounting income; these are

often very different due to accounting practices.
• Yardstick for evaluating average book ROR is arbitrary.

Internal (or Discounted Cash Flow) Rate of Return
•   Rule: Accept investment opportunities offering rates of return
in excess of the opportunity cost of capital.
•   Single period model

ROR =     Payoff −1
Investment

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or

C1
NPV = C0 +         =0
1+ r

where discount rate that makes NPV = 0 is the internal rate of
return.

EXAMPLE:
Year 0               Year 1           Year 2
-\$4000               \$2000            \$4000
so,            NPV = −4000 + 2000 + 4000 2 = 0
(1+ IRR ) (1= IRR )
IRR = 0.28 (28%)
NOTE: IRR and the opportunity cost of capital are not the same.

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•   IRR gives the same answer as NPV rule whenever NPV os a
project is a smoothly declining function of the discount rate.

Pitfalls Associated with the IRR Rule
1. Lending versus Borrowing Situations

Project           Period 0          Period 1       IRR         NPV-10%
A                 -1000             1500           50%         \$364
B                 1000              -1500          50%         -\$364
•   Lending (A) versusBorrowing (B) -When we lend money, we
want a high rate of return; conversely, when we borrow, we want
a low rate of return.

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2. Multiple Rates of Return
• When there is more than one change in the sign of the cash

flows, there is generally not a unique internal rate of return.
EXAMPLE:
Project       Period 0       Period 1        Period 2           IRR              NPV-10%
C            -4000           25,000         -25,000      25% & 400%             -\$1,934
NPV = −4000 + 25,000 + −25,000 = 0
1.25      (1.25)2
NPV = −4000 + 25,000 + −25,000 = 0NOTE: There can
5.0      (5.0)2
be as many different IRR's for a project as there are changes in
the sign of the cash flows.3. No Internal Rate of Return
Project       Period 0       Period 1      Period 2       IRR         NPV-10%
D             1000           -3000          2500          None         \$339
4. Mutually Exclusive Projects
Project       Period 0        Period 1       IRR            NPV-10%
E              -10,000        20,000          100%         \$8,182
F              -20,000        35,000          75%          \$11,818

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NOTE: Maximizing NPV is inconsistent with IRR rule.

Incremental IRR -
• Dealing with differences in scale and timing.
• Evaluate IRR on incremental cash flows from mutually

exclusive projects.
EXAMPLE:
• Consider smaller project (E) where IRR is in excess of

opportunity cost of capital.
• Is it worth making an additional investment of \$10,000 in

F?

Incremental Flows:
Project           Period 0       Period 1          IRR                NPV-10%
F-E               -10,000        15,000            50%                \$3,636
NOTE: Incremental NPV is consistent with additivity rule.

1. Differences in Timing of Projects

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EXAMPLE:
Project
Year              A                     B         B-A
0                 -23,616               -23,616   0
1                 10,000                0         -10,000
2                 10,000                5,000     -5,000
3                 10,000                10,000    0
4                 10,000                32,675    22,675
IRR               25%                   22%       16.6%
NPV - 10%         \$8,083                \$10,347   \$2,264

2. Differences in Scale of Projects
EXAMPLE:
Project
Year                 X                     Y       Y-X

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0                  -10,000               -15,000             -5,000
1                  12,000                17,700              5,700
IRR                20%                   18%                 14%
NPV - 10%          \$908                   \$1089              \$181
• Compare incremental IRR to opportunity cost of capital; if

greater, take Y instead of X.• Incremental IRR will give same
investment decisions as NPV.

3. Other Issues associated with IRR
• Term structure of interest rates - short-term versus long-

term interest rates for short and long-lived projects.
• Difficult to set benchmark for acceptance of project when

opporunity cost of capital changes over time.
• Project Ranking - should we use IRR? Maximizing NPV

subject to capital constraints is better approach.

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Profitability Index
•    Present value of forecasted future cash flows divided by
initial investment.
PI = PV/C0
•    Rule: Accept all projects with a PI > 1 because this implies
they must have NPV >0.
•    This rule most closely resembles the NPV rule.
•    Inconsistency in PI Rule

EXAMPLE:
Project      Period 0           Period 1        PV-10%         PI           NPV-10%
K            -100               200             182            1.82         \$82
L            -10,000            15,000          13,636         1.36         \$3,636
• Profitability Index suggests that K should be selected over L;

however, L's NPV is greater than K's.•     Solution: Look at
P.I. on incremental investment.

Project          Period 0          Period 1        PV-10%          PI            NPV-10%

EB545 – Corporate Finance                                                             95
L-K          -9,900            14,800         13,454          1.36       \$3,554
• Profitability Index on the additional investment is greater

than 1, so you know that L is a better project.

EB545 – Corporate Finance                                                          96
Net Present Value Rule and
Investment Decisions
1. Only Cash flow is Relevant
•   Dollars received minus dollars paid.
•   NOT accounting profits.
•   Estimate cash flows on AFIT basis

2. Estimate Cash Flows on Incremental Basis
•   Don't confuse average cash flows with incremental cash
flows.
EXAMPLE: Decisions about investing in a losing
division where "turnaround" opportunities exist should
be made based on incremental analysis, not average
analysis.
•   Forget sunk costs

EB545 – Corporate Finance                                                     97
"spilled milk"
past and irreversible outflows
cannot be affected by accept/reject decision

•   Include opportunity costs- cost of a resource may be
relevant to the investment decision.
EXAMPLE: Decision to construct a new plant on land
that could be sold for \$1 million (opportunity cost)
NOTE: Very difficult to assess when no freely

•   Treat Inflation Consistently
Do not confuse nominal and real dollars
When using nominal dollars, use nominal discunt rates
When using real dollars, utilize real discount rates.

1+ nominal discount rate
Real Discount Rate =                            − 1
1+ inf lation rate

4. Separating Investment and Financing Decisions

EB545 – Corporate Finance                                                    98
•   Treat all projects as if equity financed.
•   Treat all cash outflows as coming from stockholders and all
cash inflows as going to them.
•   Caculate NPV, then undertake separate analysis of
financing decisions.

5. Depreciation
•   Non-cash expense
•   Important because it reduces taxable income (which are
cash flows).
•   Provides an annual tax shield (product of depreciation and
marginal tax rate)
•   Accelerated depreciation (for IRS) versus straight-line (for
stockholders' income statement).

6. Discounting Inflows and Outflows

EB545 – Corporate Finance                                                       99
•   Proper discount rate depends on the risk of the cash flow -
not whether it is an inflow or an outflow.
•   One person's inflow is another person's outflow - in
equilibrium, all sellers and buyers must agree on asset
values at the margin.
•   Assumes homogeneous expectations or a well functioning
information market.

7. Choice of Discount Rate
•   We are only concerned with rates that are available in the
capital market today.
•   What is the value of \$1 discounted at today's 1-year
interest rate (same for n years).

EB545 – Corporate Finance                                                      100
Other Capital Budgeting Issues
Optimal Timing of Investment

•   The fact that a project has a positive NPV does not mean
that it is best undertaken now.
•   Negative NPV projects today might become a valuable
opportunity at some later date.
•   Examine alternative dates and find the one which adds the
most to the firm's current value.

Net future value as of date t
(1+ r)t

EXAMPLE: Timber cutting (B&M)

EB545 – Corporate Finance                                                    101
Year of Harvest         0        1           2          3          4           5
Net Future Value        50    64.4        77.5        89.4      100          109.4
NPV if harvested in Year 1 = \$64.4/1.10 = \$58.5
Year of Harvest         0        1           2          3         4             5
Net Present Value     50       58.5       64.0       67.2       68.3          67.9
Optimal Point of Investment is Year 4 - where NPV is maximized.

Equipment Utilization and Replacement
Weigh increased costs of utilization against cost of replacement.

EB545 – Corporate Finance                                                            102
Equivalent annual cost: represents an annuity with the same PV
and life as the equipment or machine.
PV of Annuity = PV of Cash outflows for Machine
= annuity payment x t -year annuity factor

EXAMPLE: The president's executive jet is not fully utilized. You
judge that its use by other officers would increase direct operating
costs by only \$20,000 per year and would save \$100,000 a year in
airline bills.A new jet costs \$1.1 million and (at its current low rate
of use) has a life of 6 years. Assume the opportunity cost of capital is
12% and the company pays no taxes. Should you try to persuade the
president to allow other officers to use the plane.

With a 6 year life the equivalent annual cost (at 12%) of a new
jet is \$1,100,000/4.111 = \$267,575. If the jet is replaced at the
end of year 3 rather than 4, the company will incur an

EB545 – Corporate Finance                                                          103
incremental cost of \$267,575 in Year 4. The present value of
this cost is:
\$267,575/1.124 = \$170,049

The present value of the savings is:
3
\$80,000
∑ 112t = \$192,147
.
t =1
So, the president should allow wider use of the present jet
because the PV of the savings is greater than the PV of the
cost.

NOTE: As an aside, although a decision on usage of the new jet can be postponed, it
appears that other officers should continue to use the plane. If the increased usage causes
the plane life to be reduce 25% (i.e. 6 to 4.5 years), the increase in the equivalent annual
cost is \$330,420-267,548 = \$62,872. This is less than the annual saving of \$80,000.

Equipment Replacement
1.     Present Value of Incremental Cash Benefits

EB545 – Corporate Finance                                                                              104
Consider the following:
CF = Cash flow
∆ = New minus Old
S = Sales
C = Operating Costs
D = Depreciation
t = tax rate

∆CF = (∆S - ∆C - ∆D)(1-t) + ∆D

2.   Salvage Value
•   New machine
•   Old machine

3.   Initial Capital Investment
•     Proceeds from sale of old machine

EB545 – Corporate Finance                                    105
•    Tax consequences of sale or disposal of old machine
•    Cost of new machine

EB545 – Corporate Finance                                                   106
Capital Rationing
•   Basic assumption is that capital is limited.
•   Inconsistent with notion of perfect capital
markets.
•   "Soft" rationing vs. "hard" rationing
•    Soft Rationing
•   Provisional and arbitrary limits set by management of the
firm.
•   Not indicative of any real imperfections in capital markets.
•   Means of controlling investment among managers.
•   Means of dealing with biased cash flow forecasts.
•   For projects with significant NPV's, firm is capable of
raising more money and loosening the artificial constraint.

EB545 – Corporate Finance                                                       107
•    Hard Rationing
•   Wealth of firm's shareholders is maximized when the firm
accepts every project that has a positive net present value.
•   Refleccts a barrier between the firm and capital markets -
market imperfections
markets
•   Projects with positive NPV's are passed up
•   Often there are other issues at work, i.e. control of the firm.
•   Must not ignore risk of the project - opportunity cost of
capital takes this into account.

Capital Rationing Models
•   Assume there are capital budget limitations.
•   Must incorporate a method of selecting among the
available opportunities that maximizes NPV of the firm.

EB545 – Corporate Finance                                                          108
1.   PROFITABILITY INDEX

EXAMPLE (B&M): Suppose there is a 10% opportunity cost of
capital, company has total resources of \$10 million and has the
following opportunities:

Cash Flow
Millions \$                  NPV - 10%
Project    Period 0     Period 1      Period 2      \$ Millions      P.I.
A          -10          +30           +5            21              3.1
B          -5           +5            +20           16              4.2
C          -5           +5            +15           12              3.4
•    Firm has sufficient resources to invest in either project A or in
projects B&C.
•    Individually, B&C have lower NPV's - but together they have a
greater NPV than A.
•    Choosing among projects based solely on individual NPV's may

EB545 – Corporate Finance                                                         109
•    Alternative: Select projects that offer the highest ratio of PV to
initial outlay (PI).

Profitability Index = Present Value
Investment

Limitations to PI:
1. May only be applicable to a single period model.
2. When there are other constraints on the choice of projects
3. Unable to utilize when there are project dependencies.

EXAMPLE (B&M):
Cash Flow

EB545 – Corporate Finance                                                         110
Millions \$                 NPV - 10%
Project   Period 0    Period 1      Period 2       \$ Millions      P.I.
A          -10         +30           +5            21              3.1
B          -5          +5            +20           16              4.2
C          -5          +5            +15           12              3.4
D          0           -40           60            13              1.4

•    If we accept B&C, we cannot accept D which is more than
budget limit in Period 1.
•    However, we can select A in Period 0 and have sufficient cash
to take D in Period 1.
•    NOTE: A&D have lower PI's than B&C -but have a higher
NPV.
•    Because constraint applies to two periods, PI index fails us as an
appropriate capital rationing criteria.

2.   Linear Programming Models
•   General optimization procedure.

EB545 – Corporate Finance                                                         111
•       Mathematical model with the folowing properties:
1.   A linear objective function which is to be maximized or minimized.
2.   A set of linear constraints.
3.   Variables which are all restricted to nonnegative values.

EXAMPLE:
The Ice-Cold Refrigerator Company can invest capital funds in
a variety of company projects which have varying capital
requirements over the next 4 years. Faced with limited capital
resources, the company must select the most profitable projects
and budgets for the capital expenditures. The estimated present
values of the projects, the capital requirements and the available
capital projections are shown below:

Present                    Capital       Require.
Project                    Value         Year 1       Year 2        Year 3         Year4
Plant Expansion            90,000        15,000       20,000        20,000         15,000

EB545 – Corporate Finance                                                                       112
Warehouse Expansion     40,000     10,000    15,000     20,000     5,000
New Machinery           10,000     10,000    0          0          4000
New Product Research    37,000     15,000    10,000     40,000     35,000

Available Capital                  40,000    50,000     40,000     35,000
Funds
The following definitions are chosen for decision variables:
•    x1 = 1 if the plant expansion project is accepted; 0 if rejected.
•    x2 = 1 if the warehouse expansion project is accepted; 0 if rejected.
•    x3 = 1 if the new machinery project is accepted; 0 if rejected.
•    x4 = 1 if the new product research project is accepted; 0 if rejected.

Linear Programming formulation has:
1. Separate constraint for each year's available funds;
2. Separate constraint requiring each variable is less than or equal to 1.

EB545 – Corporate Finance                                                         113
3.   Integer Programming Models
•    Applicable to real-world problems where accept/reject decisions
•    Method avoids fractional values in solution set.
•    Involve 0-1 or binary integer variables.
•    Widely use method in capital budgeting problems.

4.   Multi-Objective Decision Models
•   Utility theory based model - applicable in a world of certainty
or uncertainty.
•   Means of incorporating multiple investment criteria
•   Profitability index, NPV, IRR, Payout, etc.

EB545 – Corporate Finance                                                       114
•    Evaluate firm's relative strength of desirability on each
objective.
•    Evaluate relative importance of each criteria (set of weights).
•    General mathematical form:

EB545 – Corporate Finance                                                      115
Risk and Return
•   "Opportunity cost of capital depends on the risk
of the project"
•   Major topics of interest
Security Risk
Portfolio Risk
Diversification

•   Risk-return relationships in capital market over
the last 60 years
1.   Common stocks - (S&P composite index)
2.   Government bonds
3.   Corporate Bonds
4.   Treasury Bills

EB545 – Corporate Finance                                  116
Average Annual Rate of Return
Nominal     Real            (versus T-Bills)
Treasury Bills       3.6%        0.5%            0
Government Bonds 4.7%            1.7%            1.1%
Corporate Bonds      5.3%        2.4%            1.7%
Common Stocks        12.1%       8.8%            8.4%

(Note: Average inflation - 3.1%)
1. Treasury Bills: short maturity and no risk of default (inflation risk).
2. Government Bonds: longer term asset, sensitive to changes in interest rates
(bond prices fall when interest rates rise and vice versa).
3. Corporate Bonds: similar to government bonds, except risk of default.
4. Common Stocks: direct share in the risk of the enterprise.

•   Evaluating and investment opportunity with
same risk as S&P 500 - or market portfolio.

EB545 – Corporate Finance                                                            117
Hypothesis: Opportunity cost or discount rate should be E(r) on
market portfolio (rm).
Assumption: Future is like the past and we use a 12.1% ROR.
Methodological Shortcoming: Market returns are not stable
over time.
Alternative: Look at the individual components of rm
a. risk-free rate (rf)
where,
rm (1990) = rf (1990) + normal risk premium
= 0.08 + 0.084
= 0.164 (16.4%)

(NOTE: This assumes a normal, stable risk premium)

•   Evaluating and investment opportunity with risk
characteristics different from S&P 500.

EB545 – Corporate Finance                                                      118
•   Measures of Risk and Return
1.   Expected Return: a measure of central tendency.
n
E (r ) = ∑ hri
i
(mean)
i =1
where h = probability of occurrence of return i

2.   Variance: An average deviation meaure of dispersion,
obtained by averaging the squares of deviations of
individual observations from the mean.
n
σ2 (r ) = ∑ hi[ri − E (r )]2
i =1

3.   Standard Deviation: an average deviation measure of
dispersion equal to the positive square root of the variance.
σ2 = σ

4.   Covariance: an absolute measure of the extent to which
two sets of variables move together over time.

EB545 – Corporate Finance                                                         119
n
∑[(rat − ra )(rb − rb )]
Covr r = t =1            t           (sample covariance)
a b          n −1

EXAMPLE:
Month
1        2           3       4          5      Mean
Stock A     0.04     -0.02       0.08    -0.04      0.04   0.02
Stock B     0.02     0.03        0.06    -0.04      0.08   0.03

(0.04-0.02)(0.02-0.03)        = -0.0002
(-0.02-0.02)((0.03-0.03)      = 0.0000
(0.08-0.02)(0.06-0.03)         = 0.0018
(-0.04-0.02)(-0.04-0.03)       = 0.0042
(0.04-0.02)(0.08-0.03)         = 0.0010
-----------

EB545 – Corporate Finance                                                         120
Total       0.0068

Covr r = 0.0068 = 0.0017
a b (5−1)
•   Positive Covariance: when one stock produces a return
above its mean, the other tends to do as well.
•   Note: Covariance number tells us little about the
relationship between returns on the two stocks.

•    Population Covariance
n
Covr r = ∑ hi[ra − E (ra )][rb − E (rb )]
a b
i        i
i =1
5.   Correlation Coefficient: normalized measurement of joint
movement between two variables.
•   Covariance number is unbounded (- to + infinity)
•   Put bounds on covariance by dividing by the σ of the two
investments.
•   Correlation coefficient, ρ, ranges from +1 to -1.

EB545 – Corporate Finance                                                   121
Covr
ρa , b = σ σ ra b

r r
a    b

EB545 – Corporate Finance                       122
Correlation Coefficient
r                                                  r
b                                                  b

r                                             r
a                  Perfect negative             a
Perfect Positive           Correlation
Correlation                  (-1)
(+1)

rb

r
Uncorrelated                  a
Returns
(0)

EB545 – Corporate Finance                                                         123
•    Note that in the case of perfect positive and negative
correlation, if we know the returns on stock b, then we could
predict a.
•    Magnitude of the slope is irrelevant.
•    Coefficient may range from -1 to +1.

Also, it follows that:
Covr r = ρa , bσr σr
a b        a   b

6.   Characteristic Line'
•  Extension of covariance to relationship between individual
stock and market portfolio.

EXAMPLE:
Month 1        Month2          Month 3    Month 4        Month 5
Stock J      0.02           0.03            0.06       -0.04          0.08
Market Port. 0.04           -0.02           0.08       -0.04          0.04

EB545 – Corporate Finance                                                       124
CHARACTERISTIC LINE

0.08

0.06

Slope of Line = Bj
0.04
j's Return

0.02

0
-0.04   -0.02           0            0.02        0.04   0.06   0.08

-0.02

-0.04

Market Return

EB545 – Corporate Finance                                                               125
•    Characteristic Line

1.   Describes the relationship between returns on the
stock and the market portfolio.
2.   Shows the return that you expect the stock to produce,
given a particular market ROR.
3.   The slope of the characteristic line is the stock's beta
factor or βj (refer to the intercept of the characteristic
line as a.)

7.   Beta                               Intercept

EB545 – Corporate Finance                                                          126
Cov(rj ,rm )
Bj =                                 a j = r j − β jrm
σ2r  m

(rm, t − rm )2
n
Variance of market returns:         σ =∑
2
m
t =1    n −1
From preceding Table, market σ2 = 0.0024;
So,
βj = 0.0017/0.0024 = 0.708
aj = 0.03-0.708(0.02) = 0.0158

•    Beta is an indicator or the degree to which a stock responds
to changes in the return produced by the market.
•    If we knew the market was going to be higher by 1% next
month, we would increase our expectation for stock j's
return by 0.708%

Reducing Risk Through Diversification

EB545 – Corporate Finance                                                        127
•   Most stocks are substantially more variable than the market
portfolio - only a few have lower standard deviation of
returns.
•   Why doesn't the market's variability reflect the average
variability of its components?
•   Diversification works to reduce risk because prices of
different stocks do not move exactly together.
•   Even in a 2 stock portfolio, a decline in the value of one stock
in the portfolio can be offset by a rise in the price of the other
stock.
•   Result: Variability of portfolio is less than the average
variability of the two stocks in the portfolio.

EB545 – Corporate Finance                                                             128
Portfolio
Standard
Deviation

1        5          10          15          Number of
Securities

Systematic versus Unsystematic (unique) Risk
1.       Unsystematic Risk (unique)
•   Risk that can be potentially eliminated by diversification.
•   Firm or industry specific.
•   Management Risk
•   Financial or operating leverage
•   Able to diversify away.

EB545 – Corporate Finance                                                              129
2.       Systematic Risk
•   Stems from economy wide perils which affect all
•   Interest rate risk
•   Stock market risk
•   Unable to completely diversify away.
•   For a reasonably diverisfied portfolio, this is the only risk
that matters.

EB545 – Corporate Finance                                                             130
Portfolio Analysis
•   Expected Return: weighted average of the expected returns
on the individual stocks contained in the portfolio.
E (rp ) = ∑ x j E (r j )
n

j =1

where, xj is the percent of investment in stock j

•   Variance: function of the variance of each stock included in the
portfolio as well as the covariance between stocks' returns.
σ2 = xi2σi2 + x2σ2j + 2 xi x jρi , jσi σ j
p             j

where,
xi = % of portfolio invested in asset i
σi2 = variance of returns on asset i
ρij = correlation coefficient between assets i & j
where -1 ≤ ρij ≤ 1

EB545 – Corporate Finance                                                         131
Example of Portfolio Effect:
Return & Probabilities for investments 1 and 2
State of Economy     Probability      1's Return     2's Return
Recession            0.20             5%             20%
Slow Growth          0.30             7%             8%
Moderate Growth      0.30             13%            8%
Strong Economy       0.20             15%            6%
Expected Value = E(r1) = ∑ r1 p1 = 10.0%

Expected Value = E(r2) = ∑ r2 p2 = 10.0%

Standard Deviation = σ1 = ∑ (r1 − r1)2 p1 = 15.4% = 3.9%
Standard Deviation = σ2 = ∑ (r2 − r2 )2 p2 = 25.6% = 51%
.    PORTFOLIO
EFFECT:
E (rp ) = ∑ x j E (r j )
n

j =1

E(rp) = 10%

EB545 – Corporate Finance                                                   132
(%)
Possible Outcomes
(j)
20%

15%
(i,j)

10%

(i)
5%

Recession      Slow          Semi-    Strong
Growth        Strong   Growth
PORTFOLIO STANDARD DEVIATION:
σ2 = xi2σi2 + x2σ2j + 2 xi x jρi , jσi σ j
p             j

where,   x1 = 0.50, σ1 = 3.9
x2 = 0.50, σ2 = 5.1
ρ1,2 = -0.70
σp = 1.8%

EB545 – Corporate Finance                                              133
•   Portfolio standard deviation is less than the standard deviation of
either investment (3.9% or 5.1%).
•   Any time two investments have a correlation coefficient less than
+1, some risk reduction will be possible by combining the assets
in a portfolio.
•   The extent that we can still get risk reduction from positively
correlated items gives extra meaning to portfolio management.

Impact of various assumed correlation coefficients for
Investments 1 and 2:

Correlation Coefficient Portfolio Stand. Dev.
+1.0                     4.5%
+0.5                     3.9%
0.0                     3.2%
-0.5                     2.3%
-0.7                     1.8%
-1.0                     0.0%

EB545 – Corporate Finance                                                       134
EXAMPLES OF PERFECT POSITIVE AND NEGATIVE
CORRELATION
State Probability RA   RB
1     0.25        0.06 0.12
2     0.25        0.08 0.10
3     0.25        0.10 0.08
4     0.25        0.12 0.06

E(RA) = 0.09                          Var(RA) = 0.0005
E(RB) = 0.09                          Var(RB) = 0.0005
Cov(RA,RB) = ∑ Pi[ RA − E ( RA )][ RB − E ( RB )] = −0.0005
n

i =1

Correlation Coefficient =
ρ A, B =
COV ( RA RB )
=       −0.0005      = −1
σ Aσ B        ( 0.0005)( 0.0005)
Portfolio with 50% in A and 50% in B:
E(Rp) = 0.09         Var(Rp) = 0

EB545 – Corporate Finance                                           135
•   In this portfolio the expected return is a certain return. No
matter which state occurs, the return is 0.09.
•   If there is a perfect negative correlation between two assets, then
the Var(Rp) equals 0. This means it is a risk-free portfolio.

Alternatively, if perfect positive correlation exists between two
assets, the portfolio standard deviation is a weighted average of
the assets' standard deviation.
EXAMPLE:
Asset A: E(R) = 0.10          σ = 0.05       xA = 0.50
Asset B: E(R) = 0.12          σ = 0.08       xA = 0.50

Assuming ρA,B = 1.0, then σp = 0.065

•   INDIVIDUAL SECURITIES AFFECT ON PORTFOLIO RISK

EB545 – Corporate Finance                                                       136
1. Risk of a well-diversified portfolio depends on the market risk of
the securities included in the portfolio.
2. In other words, how sensitive are each of the stocks in the
portfolio to market movements, both individually and
collectively?
3. Stocks with β greater than 1.0 tend to amplify overall movements
in the market - both upward and downward.

•   LIMITS TO DIVERSIFICATION

EB545 – Corporate Finance                                                         137
1. The variabilityof a portfolio reflects mainly the covariance.
2. When there are just two securities in a portfolio, there are an
equal number of variance and covariance boxes.
3. As the number of stocks, n, increases in the portfolio, you
4. If average covariance were zero, it would be possible to
eliminate all risk; however, covariances are almost always
positive.
5. No matter how many stocks you include, there are limits to the
benefits of diversification.

EB545 – Corporate Finance                                                       138
Maximizing Return Given Risk
The Minimum Variance and Efficient Sets
(Markowitz Model)
1. Given the level of risk, or standard deviation, we prefer
portfolio positions with higher expected rates of return.
2. Given the level of expected return, we prefer portfolio
positions with lower risk.
3. Given the characteristics of the available population of stocks,
the investment opportunity set has a perimeter that is
represented by a bullet-shaped curve.
4. This perimeter is referred to as the minimum variance set.

EB545 – Corporate Finance                                                          139
Expected
Return (%)

20

15

10

5

5   10   15   Standard
Deviation (%)

EB545 – Corporate Finance                                   140
THE MIMIMUM VARIANCE SET:
• Each point on the minimum variance set represents a portfolio,

with portfolio weights allocated to each of the stocks in the
population.
• Given a particular expected rate of return, the portfolio on the

MV set has the lowest possible standard deviation achievable
with the available population of stocks.
• The terms minimum variance set and minimum standard

deviation set can be used interchangeabley.
• The minimum variance set can be divided into two halves, a top

and bottom - separated at the minimum variance point (MVP).
The MVP represents the single portfolio with the lowest possible
standard deviation, the global minimum variance portfolio.
• The most desirable portfolios for us to hold are those in the top

half of the bullet.
• Top half of the bullet is call the efficient set - Given a

particular level of standard deviation, the portfolios in the
efficient set have the highest attainable expected rate of return.

EB545 – Corporate Finance                                                       141
Finding the Minimum Variance Portfolio
Consider an example where we build portfolios from three
available stocks with the following expected returns:
A, Acme Steel:                5%
B, Brown Drug:                10%
C, Consolidated Electric:     15%
The covariance matrix for the stocks is given by:
A        B        C
A         0.25 0.15         0.17
B         0.15 0.21         0.09
C         0.17 0.09         0.28
By taking the square root of the variances going down the diagonal
of the matrix, we can compute the standard deviations of the stocks as
follows:
A, Acme Steel σ(rA):               0.50
B, Brown Drug σ(rB):               0.46
C, Consolidated Electric σ(rC):    0.53

EB545 – Corporate Finance                                                      142
Expected
Return (%)

MINIMUM VARIANCE SET FOR
CONSOLIDATED, BROWN & ACME
30

20
MVP         Consolidated

Brown
10
Acme

10 20 30 40 50 60    Standard
Deviation (%)

EB545 – Corporate Finance                                       143
Portfolio Weight
in Stock B xB

R
1.0

Q

L
U

S                  T
xA
-1.0          0
1.0       Portfolio Weight
in Stock A

-1.0

EB545 – Corporate Finance                                          144
•   Acme Steel (A) and Brown Drug (B) portfolio weights are
plotted.
•   Consolidated Electric's portfolio weight is implied by the value
for xA and xB
•   For example, if we are at Point U, portfolio weight in Brown is
equal to 0.30 and portfolio weight in Acme is 0.0. Since there
are only three stocks, portfolio weight in Consolidated is equal
to 1- xA - xB = 0.70.
•   Each point represents a portfolio with particular weights
assigned to each stock.

DEF. "Selling Short": When you sell short, you borrow shares of
stock from someone (usually through your broker). You are
obligated to return to this person, after a certain period of time,
the same number of shares you borrowed. When short-selling a
stock as part of your portfolio, the weight assigned to the stock
is negative.

EB545 – Corporate Finance                                                         145
Now consider the triangle area bounded by points R,S & T.:
1. All points in the triangle represent portfolios where we have
invested positive amounts in each of the three stocks.
2. Consider Point L, where we invest 50% in Acme, 45% in Brown
and 5% in Consolidated.
3. For portfolios on the perimeter, we invest a combined total of
100% of our money in two stocks and 0 position in the third.
4. At point Q, we invest 60% in Brown, 40% in Conslolidated and
nothing in Acme. Conversely, on perimeter RT we are taking no
position in Consolidated.
5. If we are outside the triangle, at any point to the northeast of the
line Y'X, we are selling Consolidated short.
6. If we are positioned to the west of the figure's vertical axis, we
are selling Acme short.
7. If we are anywhere to the south of the horizontal axis, we are
selling Brown short.
8. At point Y', we are selling Acme short and adding the proceeds
to our equity to invest in Brown.

EB545 – Corporate Finance                                                          146
Iso-expected Return Lines: Line, drawn on a mapping of
portfolio weights, which shows the combinations of weihts all of
which provide for a particular portfolio rate of return.
•   In general, the slope and relative position of the iso-expected return lines are
dependent on the relative expected returns of the stocks considered.
•   If we want to see combinations of weights that are consistent with a different value
for portfolio return, then we must look at different iso-expected return lines.
Iso-variance ellipse: Ellipse, drawn on a mapping of portfolio
weights, which shows the combinations of weights all of which
provide for a particular portfolio variance.
•   Ellipses are all concentric about the point MVP.
•   Similar to lines denoting points of equal altitude on a topographic map.
•   Iso-variance ellipses represent points of constant variance.
Critical Line: A line tracing out, in portfolio weight space, the
portfolio weights in the minimum variance set.
•   Critical line can be found by tracing out points of tangency between iso-expected
return lines and iso-variance ellipses.
•   Finding the minimum variance set is tantamount to finding the location of the critical
line.

EB545 – Corporate Finance                                                                                 147
Portfolio Weight
in Stock B     x
B
1.0

Q

L

xA
-1.0                 0                               1.0
Portfolio Weight
in Stock A

12%   10%
-1.0            16%
18%

EB545 – Corporate Finance                                                                  148
Portfolio Theory with Borrowing and Lending
•   Suppose that you can lend and borrow money at some risk-
free interest rate, rf.
•   For example: Invest some of your money in T-Billls and
some in common stock portfolio M.
E(r)

Borrowing

M

Lending

rf

EB545 – Corporate Finance                                                   149
Since borrowing is negative lending, you can borrow at rf
and invest more in stock portfolio M.

NOTE: What we see is that regardless of the level of risk
preferred, you get the highest expected rate of return by a
mixture of portfolio M and borrowing or lending.
Meaning:
1. The best portfolio of stocks must be selected and that is
the portfolio where the capital market line is tangent to
the efficient frontier.
2. Blend this portfolio with borrowing and lending to match
individual risk preferences.

EB545 – Corporate Finance                                                   150
Capital Asset Pricing Model
ASSUMPTIONS:
1. All investors seek to invest in Markowitz efficient portfolios.
2. Unlimited borrowing and lending at the risk-free rate.
3. All investors have homogeneous expectations.
4. No taxes and no transaction costs.
5. Capital markets are in equilibrium.

Central Message: In a competitive market, the expected
risk premium varies in direct proportion to beta.

EB545 – Corporate Finance                                                         151
SECURITY MARKET LINE
E(r)
B

M
rm

A                         Market Portfolio
r
f

0.5        1.0              2.0Beta
Expected Risk Premium on investment = (Beta) x (Expected Risk Premium on Market)
ri - rf = βi(rm-rf)
So, the expected risk premium on portfolio A is 1/2 the risk premium on the market, and
portfolio B has twice the expected risk premium.

EB545 – Corporate Finance                                                           152
CAPM
In terms of Beta:
E (ri ) = rf + βi[ E (rm − r f )]
and
Cov(ri ,rm )
βi =
σ2 (rm )

So, for capital budgeting purposes, where the risk
characteristics of the project are consistent with the risk of
firm i, the the opportunity cost of capital for further
investment is E(ri).

EB545 – Corporate Finance                                                     153
Four Basic Principles of Portfolio Selection:
1. Investors like high expected returns and low standard
deviation; stock portfolios that offer highest E(r) for a given σ
are efficient portfolios.
2. To know the marginal impact of a stock on a portfolio, you
must look at its contribution to portfolio risk; contribution
depends on the stock's sensitivity to changes in the value of
the portfolio.
3. Stock's sensitivity to changes in the value of market portfolio
is Beta (β) - measures marginal contribution of a stock to risk
of the market portfolio.
4. If investors can borrow and lend at the risk-free rate of
interest, then they should always hold a mixture of the rf
investment and one particular common stock portfolio.

EB545 – Corporate Finance                                                           154
WHAT WOULD HAPPEN IF A STOCK DID NOT
LIE ON THE SECURITY MARKET LINE?
E(r)

SML
M           B
r
m
Market Portfolio

rf         A

Beta
0.5    1.0             2.0

EB545 – Corporate Finance                                         155
WHAT WOULD HAPPEN IF A STOCK DID
NOT LIE ON THE SECURITY MARKET
LINE (SML)?
1. Would you buy stock A? If you wanted an investment with a
Beta of 0.50, NO! If every rational investor shares your view,
then the price of A drops and E(r) goes up.
2. What about stock B? Again, one can achieve higher return
(with equivalent risk) by investing in a stock or portfolio on
the SML. Again, price of B must fall until E(r) is equivalent.

EXAMPLE:
1. Assume initially, that stock A's expected dividend and
expected market price are \$5.00 and \$100 respectively. The
beginning market price is \$100 and consequently, the
expected rate of return is equal to:

E (rA ) = E (dividend + ending market price) −1
beginning market price

EB545 – Corporate Finance                                                        156
E (rA ) = E (\$5.00 + \$100) −1 = 0.05 (or 5%)
\$100

2. Now suppose an item of good news is received by the market place
and the information does nothing to change the market's assessment
of the risk characteristics of the stock; however, it does change its
assessment of the dividend and ending price.

3. The new expected dividend is \$7.00 and the new expected ending
price is \$105.00. If there is no change in the beginning price, the new
expected rate of return is:
E (rA ) = E (\$7.00 + \$105) −1 = 0.12
\$100

4. It is now in everyone's interest to increase their investment in stock
A. The buying pressure on the stock will force its price up and its
expected rate of return down, until it resumes its equilibrium
position. The market price at that point will be:

EB545 – Corporate Finance                                                          157
0.05 = E (\$7.00 + \$105) −1
\$106.67
•   NOTE: This same kind of market pressure holds each stock in its
equilibrium position. Should anything disturb the stock from its
position, opportunities will arise to earn superior returns by
immediately forces the stock back to its equilibrium price.

CONCLUSIONS:
1. In equilibrium, all stocks must lie on the security market
line.
2. An investor can always obtain an expected risk premium of
β(rm-rf) by holding a mixture of the market portfolio and the
risk-free investment.
3. Stocks on average lie on the security market line; so, if none
lie on the line then none can lie above the line.
Validity and Role of CAPM

EB545 – Corporate Finance                                                     158
•   While the capital asset pricing model is not perfect, it does seem to
capture important elements of risk.
•   There is an important role in this theory of the market portfolio. For any
efficient portfolio, the expected risk premium on each stock (ri-rf) must be
proportional to its beta measured relative to that efficient portfolio.
•   If the market portfolio is efficient, then (ri-rf) will be proportional to beta
measured relative to the market portfolio.
•   The market portfolio should in principle include all assets; the available
market indexes clearly fall short of that ideal.
•   If a particular index is, ex post, part of the efficient set, then returns and
beta will plot along a straight line; the problem is how close is close
enough in terms of fitting a line.
•   Beta is, however, a valuable measure of risk: simple, objective, plausible
and consistent with theory - it correctly excludes diversifiable risk.
•   Regard CAPM as a useful rule of thumb - not as the final word on
how the world works.

Arbitrage Pricing Theory (APT)

EB545 – Corporate Finance                                                               159
• Fundamental assumption is that security returns are generated
by a process identical to a single index (CAPM) or multi-
index (Markowitz) model.
• APT suggests that the covariances that exist between security

returns can be attibuted to the fact that securities respond, to
one degree or another, to the pull of one or more factors.
• Basic assumption is that each stock's return depends partly on

macroeconomic influences and partly on firm-specific factors.
• Factors may include oil prices, interest rates, level of

industrial activity, inflation rate, etc.
• Assume that the relationship between security returns and

factors is linear.
rj = aj + β1,jI1,j + β2,jI2,j +. . .+ βn,jIn,j
where,     I = value of any one of the indices which affects the
rate of return of the security.
β = individual beta for each index (may be positive or
negative)

EB545 – Corporate Finance                                                         160
•   The portfolio's Beta with respect to any one of the factors is a
simple weighted average of the betas of the securities in the
portfolio:
β1, P = ∑ x jβ1, j
M

j =1

•   As in the CAPM, diversification does eliminate unique or
business risk and diversified investors can ignore it when
deciding to buy or sell a stock.
•   APT states that the expected risk premium on a stock should
depend on the expected risk premium associated with each
factor and the stock's sensitivity to each factor.

EB545 – Corporate Finance                                                           161
Arbitrage?
•  If we assume that Beta for each index is 0, then the expected
risk premium is equal to 0; the portfolio is essentially risk-
free and should offer a return equal to the risk-free rate.
• If the portfolio offered a higher return, investors could make a

risk-free (or "arbitrage") profit by borrowing to buy the
portfolio.
• If the portfolio offered a lower return, investors could sell the

portfolio and invest the funds in U.S. Treasury Bills.
If the arbitrage pricing relationship holds for diversified
portfolios, it must generally hold for the individual stocks.

EB545 – Corporate Finance                                                          162
APT vs. CAPM
•   Similar in that both theories stress that E(r) depends on risk
stemming from economy-wide influences and is not affected
by unique risk.
•   If each of APT's factors is proportional and cumulative to
CAPM's market portfolio beta, then result is equivalent.
•   Identifying the factors of importance in APT is difficult.
•   APT must have (1) reasonably short list of macroeconomic
factors; (2) risk premium measures associated with each of
these factors; and (3) measurement of stock sensitivity to each
factor.

EB545 – Corporate Finance                                                          163
Capital Budgeting Under Uncertainty
Company Cost of Capital
•   Rate of return required by investors;
•   Opportunity cost of capital for firm's existing assets.

Project Beta
•   Measure of risk for a specific project or investment
opportunity.
•   Relate risk of project to market risk.
•   Difficult to assess.

EB545 – Corporate Finance                                                  164
E(r)
SML

Company
Cost of Capital
15%

r f (7%)

1.0 1.30
Project Beta

Average Beta of Firm's Assets = 1.30
Note: True cost of capital depends on the use to which the
capital is put.

EB545 – Corporate Finance                                                 165
• Accept any project that more than compensates for
project beta.
• Emphasis is on project beta - not firm beta!

• Note Difference between company cost of capital rule and

project beta rule:
1. Company cost of capital rule say accept any project with
E(r) greater than 15% (above horizontal line).
2. Project Beta rule would exclude certain projects above the
company cost of capital line.
•   Project Beta:
E(project return) = rf + (project Beta)(rm - rf)
Example:
State     Prob. rm           r1       r2
1         0.10      -0.15 -0.30       -0.09
2         0.30      0.05     0.10     0.01
3         0.40      0.15     0.30     0.05
4         0.20      0.20     0.40     0.08

Assume

EB545 – Corporate Finance                                                        166
Risk-free rate = 0.05              E(r1) = 0.20      E(r2) = 0.03
E(rmarket) = 0.10                  σmarket = 0.10

Capital Structure and Company Cost of Capital
•   Cost of capital is a hurdle rate that depends on business risk
of firm's investment opportunity.
•   But, shareholders also bear financial risk to the extent that the
firm issues debt.
•   The more a firm relies on debt financing, the riskier its
common stock.
•   Borrowing creates financial leverage.
Pushes up risk of common stock.

EB545 – Corporate Finance                                                            167
Weighted Average Cost of Capital (WACC)
Definition: Expected return on a portfolio of all the firm's
securities. Used as a hurdle rate for capital investment.
WACC = (Aftertax cost of debt x % of debt in capital structure)
+ (Cost of Preferred x % of Preferred in Capital Structure) +
(Cost of common x % of common in capital structure)

EXAMPLE:Consider you own 100% of firm A's debt and
equity. What is your E(r) on this portfolio?
Company Cost of Capital = rassets = rportfolio
=       debt      rdebt + equity requity
debt + equity         debt + equity

Asset Value = \$100       Debt Value = \$40
Equity Value = \$60
---------------------    --------------------
Asset Value = \$100 Firm Value = \$100
rassets = debt rdebt + equity requity
value       value

EB545 – Corporate Finance                                                      168
If you demand 8% return on debt and 15% return on equity,
ACC = 40 (0.08) + 60 (0.15) = 0.122 or 12.2%
100         100
Effect of Changes in Capital Structure
Assume the firm issues an additional \$10 of equity and uses it to
payoff debt.
Balance sheet changes to the following:
Asset Value = \$100 Debt Value = \$30
Equity Value = \$70
--------------------- --------------------
Asset Value = \$100 Firm Value = \$100
NOTE: Change in financial structure does not affect the amount
or risk of the cash flows on the total package of debt and equity.
WACC is 12.2% both before and after the change.
However,
• Change does affect the required rate of return on individual securities.

• Risk is the same but shifted from one security holder to another.

• Stockholders and bondholders required rates of return will change.

EB545 – Corporate Finance                                                            169
EXAMPLE:
Since firm carries less debt load, let's assume bondholder
require less return - suppose it decreases from 8% to 7.3%.
Then,
rassets = debt rdebt + equity requity
value        value
rassets = 30 (0.073) + 70 (requity ) = 0.122
100           100
So, requity = 14.3%

NOTE: Lower leverage makes equity safer and reduces
shareholder required rate of return.
If we take this to the limit, where debt is equal to 0, then
requity = 12.2%

EB545 – Corporate Finance                                                     170
WACC and Taxes
EXAMPLE: Tax rate (t) = 50%

Market Value    Market Yield   % of Cap. Struc.
Debt         \$400            0.08           40%
Preferred    \$100            0.10           10%
Common       \$500            0.12           50%
Total        \$1000                          100%

After Tax Cost of Debt = 0.08 x (1-t) = 0.08 x 0.5 = 0.04
(Because interest is deductible)

WACC = (0.40 x 0.04) + (0.10 x 0.10) + (0.50 x 0.12) = 0.087

Caution: WACC does not consider risk of project - while
appropriately applied, CAPM does!

EB545 – Corporate Finance                                          171
Financial Leverage - Effect on Beta
• Stockholders and debtholders receive cash flow and share risk.
• Debtholders bear much less risk than shareholders; for

example, debt betas are near 0 for blue-chip stocks.
• Firm's asset beta is equal to beta of firm's debt and equity

(weighted average)
βassets = βportfolio = D/V(βdebt) + E/V(βequity)
Consider Prior WACC Example where:
Asset Value = \$100 Debt Value = \$40
Equity Value = \$60
---------------------     --------------------
Asset Value = \$100 Firm Value = \$100
Assume that the βdebt = 0.2 and the βequity = 1.2
then,      βassets = (0.4 x 0.2) + (0.6 x 1.2) = 0.80
What happens after refinancing? Suppose βdebt falls to 0.1
βassets = 0.80 = (0.3 x 0.1) + (0.7 x βequity)
So, βequity = 1.1

EB545 – Corporate Finance                                                       172
Asset Betas:
Example: Morgan Company
Beta = 2.0      rf = 0.10        E(rm) = 0.20
Cost of Capital:
E(ri) = rf + βi(E(rm) - rf) = 0.30
Suppose Year 1 payoff for asset i = \$130
then
Value of firm, PV0 = \$130/1.30 = \$100
Now suppose the firm raises \$100 to invest in the risk-free asset,
which will have a payoff of \$110:
PV0       C1         β      Req. ROR
Co. Before Inv. \$100        \$130       2.0    0.30
New Investment \$100         \$110       0      0.10
Co. After Inv.    \$200      \$240       1.0    0.20
NOTE: Beta for company after investment can be computed
by weighted average.

EB545 – Corporate Finance                                                        173
E(r)
SML

30%                   Company Befo

Company After

r f (10%)

1.0      2.0
Beta

Operating Leverage

EB545 – Corporate Finance                            174
•   Fixed operating costs, so called because they accentuate
variations in profits.
•   Just as commitment to fixed debt increases financial leverage,
commitment to fixed production charges adds to the beta of a
capital project.
•   Cash flows generated by any productive asset are made up of
revenues, fixed costs and variable costs.
•   Variable Costs: raw materials, sales commissions, some labor.
•   Fixed costs: wages of workers under contract, property taxes.
•   Fixed costs are cash outflows, whether asset is idle or not.
•   Other things being equal, projects with higher ratio of fixed
costs to project value have higher project betas.
Operating Leverage =        % ∆EBIT
% ∆Sales

EXAMPLE:
Selling Price per unit:       \$20 (p)
Variable Costs per Unit:      \$12 (v)
Fixed Operating Costs:        \$60,000 (Fo)

EB545 – Corporate Finance                                                         175
Interest Expense:            \$25,000 (Ff)

Degree of Operating Leverage at 15,000 units (x):
DOL = % ∆ EBIT = x( p − v) =             15, 000(20 − 12)     = 2.0
% ∆ Sales     x( p − v) − FO 15, 000(20 − 12) − 60,000
So, for each 1% change in sales( up or down), EBIT will
change by two times that. Note that this is at a single point in
time.

Degree of Financial Leverage at 15,000 units (x):
DFL = % ∆Net Earnings
% ∆EBIT
x( p − v) − FO        15, 000(20 − 12) − 60, 000
DFL =                     =                                     = 1.71
x( p − v) − FO − Ff 15, 000(20 − 12) − 60, 000 − 25, 000
•   For each 1% change in EBIT, net earnings will change by
1.71 times that.
•   The more fixed financial costs, the higher the degree of
finanical leverage (DFL).

EB545 – Corporate Finance                                                           176
Degree of Combined Leverage at 15,000 units:

DCL =           x( p − v)        =     15, 000(20 − 12)      = 3.4
x( p − v) − ( Fo + F f ) 15, 000(20 − 12) − 85, 000
or
DCL = DOL x DFL
= 2.0 x 1.7
= 3.4

•   The more leverage you have, the riskier you are.
•   Relationship between DOL and DFL is positively related.
•   Higher DOL or DFL will generate a higher beta for the
firm.

EB545 – Corporate Finance                                                       177
•   Financial leverage could include lease payments, preferred
dividends, interest payments and some types of taxes.
•   Different companies use different definitions for fixed item
in DFL.
•   Empirical tests confirm that companies with high operating
leverage actually do have high betas.

EB545 – Corporate Finance                                                     178
Risk Analysis Techniques for Capital
Budgeting
Sensitivity Analysis
•   Pro forma cash flows are evaluated with specific variables in
the analysis forecasted at various levels, one at a time.
•   For example, commodity price levels may be forecasted
under pessimistic, most likely and optimistic scenarios and
resulting NPV's calculated.
•   Simple and useful method for ranking the relative impact on
project value from various variables.
•   Useful in terms of establishing a floor value or worst case
scenario.
•   Major drawback is that only one variable's probability spread
can be evaluated at a time.
•   NOTE: Underlying variables may be interrelated.

EB545 – Corporate Finance                                                        179
Simulation
•  Primary Objective is to define the distribution of profit (or
NPV) which could be anticipated for the project.
• Unlike sensitivity analysis, simulation considers the impact of

changes on all variables simultaneously.
• Accommodates for both independent and dependent random

variables.
EXAMPLE: Consider an investment which ultimate net profit is a
function of three separate, independent variables x, y & z. Suppose
the relationship is defined as:
Pr ofit = 3.4 x − [( 1 + 17.9)(0.4 z 2 )]
14 y
where Profit is the dependent variable.

Using an oil exploration example, x, y & z may be net pay thickness,
recovery factors, productive area, drilling costs, crude price,
operating expense, etc.
Now suppose we know the exact values which x, y , z take on.

EB545 – Corporate Finance                                                        180
DO WE KNOW THE RESULTING PROFIT?
Yes, this is a deterministic computation; no uncertainty with
regard to the variables of interest.

a. Given we live in an uncertain world, though, suppose all we
know are ranges of outcomes for x, y, & z - which value do we
use?
b. Simulation allows us to model all the values in a range, for each
random variable and compute a distribution of profit.

Pr ofit = 3.4 x − [( 1 + 17.9)(0.4 z 2 )]
14 y

EB545 – Corporate Finance                                                         181
f(z)
f(x)                   f(y)

x                          y          z

RESULTS OF SIMULATION:

(-)     0             (+)

NOTE: Consider full range and distribution of outcomes on
each random variable - not just average or most likely
outcome.

EB545 – Corporate Finance                                              182
c. Actual state of nature: Variables x, y , z will have one specific
value; howwever, before the decision or action we do not know
what that value is.
d. Do not use only mean or most likely case of each random
variable to solve for "mean" or "most likely" profit; this
approach ignores the uncertainty as defined by each distribution.
e. There are a few special situations when the analytic approach
(as opposed to simulation) is possible. For example, if we can
find the PDF associated with each distribution, then insert into
profit equation and solve.

EB545 – Corporate Finance                                                         183
PROCESS OF SIMULATION:
1. Define the distributions for each of the independent variables.
2. Make a series of repetitive calculations for our profit expression.
3. Each value is computed using a value of x, y & z selected from
their respecitive distributions and represents one possible state
of nature.
4. Each repitition of the dependent variable calculation is called a
"simulation pass".
5. Values of the independent variables used for each pass are
obtained through a random number sampling procedure which
honors the shape and range of each variable's distribution.
6. Passes are made until a sufficient number is made to define the
profit distribution (i.e. at least 100, and as many as thousands.)

NOTE: It is inappropriate to use same (single) random number to
sample all distributions on a pass. Using same number implies
fixed values for all variables.

EB545 – Corporate Finance                                                           184
1. Capability to define uncertainty as a range and distribution of
possible outcomes for each unknown factor.
2. May be applied to any type of non-deterministic calculation.
3. No limit to the number of variables that may be modeled.
4. Distributions of random variables can be of any type.
5. Different individuals can describe uncertainty about different
variables.
6. Lends itself well to sensitivity analysis.
7. Provides valuable inputs to decision tree modeling (by
converting continuous to discrete distributios.)

Independent versus Dependent Variables.

EB545 – Corporate Finance                                                       185
EXAMPLE: Compare distributions of net pay thickness and initial
production rates.
ERROR: If the value of thickness sampled was high (which
implies large reserves) and in the same pass, the IP sampled was
very low then the resulting field life would be unrealistic,
• Suppose that we are concerned about whether variables x and y

are related to one another.
Make a cross-plot of x versus y.

EB545 – Corporate Finance                                                       186
CASE OF INDEPENDENCE

r.v. y

r.v. x

Sample each r.v. separately in the simulation pass.

EB545 – Corporate Finance                                        187
CASE OF COMPLETE DEPENDENCY

r.v. y

y = f(x)

r.v. x

If we know x, then we know y (or vice versa); therefore, we
only need specify one distribution in the simulation.

EB545 – Corporate Finance                                                188
CASE OF PARTIAL DEPENDENCY

r.v. y

r.v. x
1. x-y relationship not clearly independent or explicitly
dependent.
2. Variable y has a substantial range of values, given x - so we
need to sample from y on each pass.
3. Also, range of variation of ychanges as x increases.
4. Therefore, the distribution of y changes as x changes and we
must accommodate that change in the simulation.

EB545 – Corporate Finance                                                     189
ACCOUNTING FOR PARTIAL DEPENDENCIES:
1. Prepare a cross-plot.
2. Draw a boundary or envelope around the observed x-y data
point. This boundary defines the limits within which x and y
can vary.
3. Any combination of x-y values outside the boundary have a
zero probability of occurrence.
4. Determine the variation of y within the boundary as a
function of x and define a normalized distribution of y
(0 to 1) which represents the observed variation.
5. In this normalized distribution, 0 corresponds to the
minimum value of y for a given value of x and 1.0
corresponds to the maximum. Such that,
y − ymin
ynorm =
ymax − ymin
where y = ymin, then 0 and y = ymax, then 1.0

6. Inputs to the simulation model are:

EB545 – Corporate Finance                                                  190
a. x distribution cumulative frequency;
b. cumulative frequency of the normalized y distribution;
c. value of y for each pass:

y = ymin + ( ymaxx − ymin x )( ynorm)
x

where,
yminx =   minimum value of y, given a sampled x
ymaxx =   maximum value of y, given a sampled x
ynorm =   value of the dimensionless, normalized y distribution
y     =   computed value of r.v. y to use for each pass.

EB545 – Corporate Finance                                                      191
Securities Markets
•   Primary functions are resource allocation and
exchange of assets.
•   Role of Different Segments of Security Markets
•   Mechanics of Securities Markets
1.   Brokers and Brokerage Firms
2.   Type of Accounts
3.   Types of Orders

•   Role of Regulation

EB545 – Corporate Finance                                192
Types of Security Markets
1.   Primary or "New Issue" Market
•   Involves only new stock or bond issues.
•   Ex.: New sale of Texaco stock or Treasury bills.
•   Major component of primary market is the bond
market.
About 3/4's of all new corporate issues are bonds.
ncluding government issues makes this percentage even higher.
•   Investment banker or underwriter
Middleman in the primary markets.
Ex.: Merrill Lynch or Salomon Bros.
For well-known issues, new issue is boughts by investment banker and then
resold to investors.
•   Underwriting a new issue
Gurantee of a successful issuance.
Underwriter syndicate utilized to share risk, purchase cost and geographical
allocation.

EB545 – Corporate Finance                                                                           193
•   How is new issue price set?
Negotiated
Privately agreed upon
Auctioned competitively (i.e., state and local bond issues)
Prevailing prices for comparable issues
Current market conditions dictate an issue's price.

2.   Secondary or "Used Issue" Market
•   Provides a means for trading existing securities among
investors.
•   Ex.: NYSE, OTC market, etc.
•   "Market-makers" - professionals who hold an
inventory of a stock.
Provides marketability
Allows for easy transfer from sellers to buyers.
"Specialists" on organized exchanges and "delaers" in the OTC.

EB545 – Corporate Finance                                                                    194
•    "Organized exchanges" provide a fixed location where
•    "OTC" market is not physically located in one place;
it is a communications network.
•    Pricing Securities in an "Auction" market.
Prices determined by bidding of market participants called brokers.
Occurs in organized exchanges
•    Pricing securities in a "Negotiated" market
Involves a dealer network
Dealers do have a vested interest because they buy (sell) securities from (to)
you.
Dealer's profit comes from the difference in their "bid-ask spread" - the
Ex.: OTC market for stocks and government securities.

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•    New York Stock Exchange (NYSE)
Largest and most prominent secondary market for stocks.
Over 200 issues are traded here.
Represents over 75% of the dolar volue traded in the U.S. ("Big Board")
1400 members - partners or directors of brokerage firms.
25% of members are specialists - assigned specific stocks and one of the 89
trading posts on the exchange's floor.
•    American Stock Exchange (AMEX)
Organization and trading procedures similar to NYSE.
Smaller nationally organized exchange.
Fewer seats (650) and stocks listed (1000)
Listing requirements are also less strict.
Smaller (especially energy and natural resource companies) dominate the
types of firms listed/
•    Regional Exchanges
Listing requirements are more lenient.
Specialize in smaller companies with limited geographical interest.
"Dual listings - chief attraction is lower commissions.
Ex.: Boston , Cincinnati, Midwest, Pacific Coast Stock Exchanges

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•    Over-the-Counter (OTC) Market
Smaller firms tend to be found in the OTC market (over 10,000)
Trades take place by telephone or other telecommunication devices.
NASD (National Association of Securities Dealers)
Markets exist for stocks, bonds, federal securities, municipal bonds,
negotiable CD's, mutual funds, etc.
Three levels: "national market", "regular market" and "additional OTC"
NASDAQ - The NASD Automated Quotation System - computerized
system that provides quotations on up to 3500 stocks.
•    Listed Options
Offer trading in standardized call and put option contracts.
Listed call-put options are traded on the Chicago Board Options Exchange
(CBOE), AMEX, NYSE, etc.

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3.   Participating in the Market
•  Cash Account
Cash transactions only
"Type 1" account
•   Margin Account
Buy securities with a combination of cash and borrowed funds.
"Type 2" account
By using securities as collateral, you may borrow a certain percentage of the
purchase price, called margin.
Margin call - requirment to put up more collateral when doolar amount of
collateral falls below a certain level.
Note: Using margins can increase or decrease your potential investment
returns - "leveraged" investment.
Because margin magnifies both gains and losses, using a margin account is
a much riskier type of investing.
Ex.: Assume:
1. You buy 200 Exxon shares at \$50 per share.
2. Margin requirement = 50%
3. Broker loan rate = 8%

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•   Asset Management Account
Combines checking, credit card, money market and margin accounts.
Funds are moved among accounts to minimize your interest expense and
maximize short-term yields.
Simplifies cash management problems.
•   "Street-Name" Account
Securities are left with a broker
Offers safe storage and makes trading easier.
Alternative to taking delivery.

•   Long Position
Involves initially purchasing a position in the hope that the security's price
will increase.
Objective in being long is to buy low and sell high.
Entitles you to any dividends or interest paid plus the capital gains.
Strategy when you are "bullish" about a security's future prospects.

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•   Short Position
Involves initially selling a security in the hope that the security will decline
in price.
Objective is still to buy low and sell high - however, you reverse the order
of the transaction.
"Bearish" strategy.
Mechanics:
1.    Your broker borrows the security or shares from the account of
another customer (or brokerage firm).
2.     He then sells the security to you.
3.     Sale proceeds are held in escrow until you liquidate your
position by buying back the (replacing the borrowed) security.
4.    If the security is purchased at a lower price in the future, then
you realize a capital gain and vice versa.

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5.   Types of Orders
•  Market Order - Buy or sell ASAP at the best price
available.
•  Limit Order - Restricts the order to a specified price.
•  Stop-Loss (Stop) Order - An order to buy (sell) a
security when its market price trades at or above
(below) a specified level.

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Regulation of Securities Markets
Securities Act of 1933
•    Major Objective - Full disclosure in order to protect
investors from fraud and to provide them with a basis
for informed judgments.
•    Applies to all interstate offerings to the public over a
certain amount (\$1.5 million). Note: Does not apply to
government and regulated industry offerings.
•    Securities must be registered at least 20 days before
offering.
•    Company must issue a prospectus.

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Securities Act of 1934
•    Major Objective - Applies full disclosure principle to
secondary securities markets.
•    Creation of the Securities and Exchange Commission
•    SEC's purpose is to regulate the organized securities
markets.
•    Requires registration and regulation of national
security exchanges.
•    Watches for price manipulation.
•    Gives SEC power over proxy machinery and
practices.
•    Gives Federal Reserve Board the power to set margin
requirements.

Blue-Sky Laws

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•    State laws which govern securities issues and matters
in individual states.
•    Company must be registered or "blue-skyed" in state
to issue shares there.
•    Individual states have tougher rules and regulations on
the sale of securities than does the SEC.

Industry Self-Regulation
•    National Association of Security Dealers (NASD)
•    Individual exchanges
•    Control trading practices among their members.

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Financing vs. Investment Decisions
•   Financing decisions involve the firm directly in
capital markets.
•   Capital Markets: Any activity which serves to
allocate resources to their most productive
activity.
•   Capital markets generally work well with
respect to the efficient allocation of resources.

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Differences between Investment and
Financing Decisions
1. Not the same degree of finality; financing
decisions are easier to reverse, i.e. higher
abandonment value.
2. More difficult to generate rents or positive
NPV's with financing decisions - more
competitive market.
•   All firms compete in financial market.
•   Investment market is differentiated in terms of competition.

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Efficient Capital Markets
(Informationally)
•   Def.: An efficient capital market is one in which
market prices fully reflect all information
available at that time ("well functioning").
•   If capital markets are efficient, then purchase or
sale of any security at the prevailing market
price is never a positive NPV transaction.
•   Implication is that information is widely and
cheaply available to investors and that all
relevant and ascertainable information is

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1. Abnormal Returns - An abnormal return of firm
i at time t is the deviation between its realized
return and the expected return as per CAPM
model.
2. "Beating the Market" (risk-adjusted basis) -
Must take risk into consideration before
deciding if you "beat the market".
3. Ex ante vs. ex post market efficiency - The key
here is that if the information had been available
to you ex ante could you have earned abnormal
returns.
4. Consistency - Are abnormal returns luck or
consistent behavior?

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Three Forms of Market Efficiency
1. Weak Form - Def.: Prices reflect all information
contained in the record of past prices.
•    "Random-walk" model
a.   Prices changes are random.
b.   Given a price, the size or direction of next change is
unknown.

•    "Technical Rules"
a.   Used by investors to exploit "patterns" they claim to see in
stock prices.
b.   Weak form would suggest these are inappropriate rules
because there is no useful information in the sequence of
past changes in stock prices.

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•    Tests of Random-Walk Model
a.   Is there statistical evidence that the "random-walk" model
does not hold?
b.   Is there economic significance?
•    Serial correlation studies: Is today's price significantly related to yesterday's price?
•    Result: There is slight statistical significance but not economic significance.
•    Runs Test: Are there more positive or negative price changes over a given period
than at random? (Looking at a string of price changes.)
•    Results: No difference than at random.

•    Implications of Random Walk or Weak Form
a.   If prices always reflect all relevant information, then they
will change only when new information arrives.
b.   However, new information by definition cannot be
c.   If stock prices already reflect all that is predictable, then
stock price changes must reflect only the unpredictable.
d.   Therefore, the series of changes must be random.

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•    Two Important Notes Concerning Random
Walk Model:
1.   Randomness is often confused with irrationality;
however, randomness is the predicated result of
rational valuation.
2.   Random Walk Hypothesis does not say actual
prices are random but that price changes are
random (size and direction).

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2. Semi-Strong Form - Def.: Prices reflect not only
past prices, but all other published or publicly
available information.
•    Empirical Tests:
a.   Reaction to earnings announcements.
b.   Reaction to stock splits and dividend announcments.
c.   Effects of secondary distributions
Large blocks sold outside of market hours generates
"combination effect"
Liquidity effect drives price down because it is a large block (temporary
phenomenon).
Information effect drives price down but does not come up.
Combination effect is that price drops and comes back partially,

NOTE: Key here is that most of this information was rapidly and
accurately impounded in the price of the stock.

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a.   P/E Effect - Low P/E stocks have positive abnormal
returns; high P/E stocks have negative abnormal returns.
b.   Size Effect - Small firms on average have earned positive
abnormal returns; large firms, on average, earn negative
abnormal returns.
NOTE: Both a & b could be caused by the fact that there is more information risk in
small firms.
c.   January effect - Firms tend to do better in January
(generate higher returns).
d.   Day of the Week Effect - Monday's tend to have lower
returns than other days of the week.
e.   Value Line Investment Survey - Abnormal returns could be
earned if you could trade the instant Value-Line was
available.
NOTE: Semi-strong form is most commonly accepted