4- 1
B40.2302 Class #2
 BM6 chapters 4, 5, 6
 Based on slides created by Matthew Will
 Modified 9/18/2001 by Jeffrey Wurgler
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
The Value of Common Stocks
Slides by
Matthew Will,
Jeffrey Wurgler
Irwin/McGraw Hill
Chapter 4
©The McGraw-Hill Companies, Inc., 2000
4- 3
Topics Covered
 How To Value Common Stock
 Capitalization Rates
 Stock Prices and EPS
 Cash Flows and the Value of a Business
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4- 4
Stocks & Stock Market
Common Stock - Ownership shares in a
publicly held corporation.
Secondary Market - Market in which
previously-issued securities are traded.
Dividend - Periodic cash distribution from the
firm to the shareholders.
P/E Ratio - Price per share divided by earnings
per share.
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Stocks & Stock Market
Book Value - Net worth of the firm according to
the balance sheet.
Liquidation Value - Net proceeds that would be
realized by selling (liquidating) all assets and
paying off all creditors.
Market Value Balance Sheet – Balance sheet
that uses market value of assets and liabilities
(instead of the usual accounting value).
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4- 6
Valuing Common Stocks
Expected Return - The percentage gain that an investor
forecasts from a specific investment over a set
period of time. Sometimes called the market
capitalization rate.
Div1  P1  P0
Expected Return  r 
P0
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4- 7
Valuing Common Stocks
Expected return can be broken into two parts:
Dividend Yield + Capital Appreciation
Div1 P1  P0
Expected Return  r 

P0
P0
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4- 8
Valuing Common Stocks
Dividend Discount Model - Model of today’s stock
price which states that share value equals the present
value of all expected future dividends.
Div1
Div2
Div H  PH
P0 


...

1
2
H
(1  r ) (1  r )
(1  r )
H - Time horizon for your investment.
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4- 9
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay annual cash
dividends of $3, $3.24, and $3.50 per share over the next
three years, respectively. At the end of three years you expect
to sell your share at a market price of $94.48. What should
be the price of a share today with a 12% expected return?
3.00
3.24
3.50  94.48
PV 


1
2
3
(1  .12) (1  .12)
(1  .12)
PV  $75.00  P0
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4- 10
Valuing Common Stocks
No Growth DDM
If we forecast no growth, and plan to hold our stock
indefinitely, then we can value the stock as a
perpetuity.
Div1
EPS1
Perpetuity PV  P0 
or
r
r
Assumes all earnings are
paid to shareholders. So
Div = EPS each year. No
retentions, no growth.
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4- 11
Valuing Common Stocks
Constant Growth DDM - A version of the dividend
growth model in which dividends grow at a constant
rate g.
Div1
P0 
rg
When you use the growing perpetuity formula to
value a stock, you are using the “Gordon Growth
Model.”
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4- 12
Valuing Common Stocks
Example
If a stock is selling for $100 in the stock market,
what might the market be assuming about the growth
rate of dividends?
$3.00
$100 
.12  g
g .09
Irwin/McGraw Hill
Answer
The market is
assuming the dividend
will grow at 9% per
year, indefinitely.
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4- 13
Valuing Common Stocks
Example – continued
Suppose in the same example you knew g was 9%
per year, but didn’t know r. What is the market’s
estimate of r?
$3.00
$100 
r  .09
r  .12
Irwin/McGraw Hill
Answer
The market has set r at
12% per year.
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4- 14
Valuing Common Stocks
 If the board elects to pay a lower dividend, and
reinvest the remainder, the stock price may increase
because future dividends may be higher.
Payout Ratio - Fraction of earnings paid out as
dividends.
Plowback Ratio - Fraction of earnings retained or
“plowed back” into the firm.
Payout Ratio + Plowback Ratio = 1
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4- 15
Valuing Common Stocks
An accounting return measurement
Return on Equity  ROE
EPS
ROE 
Book Equit y Per Share
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Valuing Common Stocks
Instead of asking an analyst, growth can be
derived from applying the return on equity to
the percentage of earnings plowed back into
operations.
g = Plowback Ratio x ROE
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4- 17
Valuing Common Stocks
Example
We forecast a $5.00 dividend next year, which represents 100% of
earnings. This will provide investors with a 12% expected return.
Instead, we decide to plow back 40% of the earnings at the firm’s current
accounting return on equity of 20%. What is the value of the stock before
and after the plowback decision?
No Growth (Div=EPS)
5
P0 
 $41.67
.12
Irwin/McGraw Hill
With Growth (Div<EPS)
g  .40  .20  .08
(1  .40) * 5
P0 
 $75.00
.12  .08
©The McGraw-Hill Companies, Inc., 2000
4- 18
Valuing Common Stocks
Example - continued
With the no growth policy, the stock price is $41.67.
With the plowback / growth policy, the price rose to
$75.00.
The difference between these two numbers (75.0041.67=33.33) is called the Present Value of Growth
Opportunities (PVGO).
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Valuing Common Stocks
Present Value of Growth Opportunities (PVGO)
Net present value of a firm’s future
investments.
Sustainable Growth Rate - Steady rate at which
a firm can grow without new external capital:
ROE x Plowback Ratio.
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4- 20
EPS, P/E, and share price
 Under a no-growth policy, Div=EPS, so:
EPS
P0 
r
 In general, share price = capitalized value of
average earnings under no-growth policy, plus
PVGO:
EPS
P0 
 PVGO
r
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EPS, P/E, and share price
 Rearranging,

EPS
PVGO 

 r 1 
P0
P0 

 EPS/P ratio underestimates r if PVGO > 0
 “Growth stocks” sell at high P/E ratios
because PVGO is high.
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4- 22
FCF and PV
 Free Cash Flows (FCF) are the theoretical
basis for all PV calculations.
 FCF is more relevant than EPS.
 FCFt = cash inflowst – cash outflowst
 PV(firm) = PV(FCF)
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FCF and PV
Valuing a Business
The value of a business is often computed as the
present value of FCF out to a valuation horizon (H).
 The value at H is sometimes called the terminal value
or horizon value
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
H
(1  r ) (1  r )
(1  r )
(1  r )
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4- 24
FCF and PV
Example
Given the cash flows for Concatenator Manufacturing
Division, calculate the PV of near term cash flows, PV
(horizon value), and the total value of the firm. r=10% and
g= 6%
Year
1
2
3
4
5
6
Asset Value
10.00 12.00 14.40 17.28 20.74 23.43
Earnings
1.20 1.44 1.73 2.07 2.49 2.81
Investment
2.00 2.40 2.88 3.46 2.69 3.04
Free Cash Flow
- .80 - .96 - 1.15 - 1.39 - .20 - .23
.EPS growth (%) 20
20
20
20
20
13
Irwin/McGraw Hill
7
8
9
10
26.47 28.05 29.73 31.51
3.18 3.36 3.57 3.78
1.59 1.68 1.78 1.89
1.59 1.68 1.79 1.89
13
6
6
6
©The McGraw-Hill Companies, Inc., 2000
4- 25
FCF and PV
Example - continued
.
PV(near te rm FCF)
.80 .96
1.15 1.39
.20
.23





 3.6
2
3
4
5
6
1.1 1.1 1.1 1.1 1.1 1.1
1  1.59 
PV(horizon value) 
  22.4
6 
1.1  .10  .06 
PV(busines s)  -3.6  22.4  18.8
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Why Net Present Value Leads to
Better Investment Decisions than
Other Criteria
Slides by
Matthew Will,
Jeffrey Wurgler
Irwin/McGraw Hill
Chapter 5
©The McGraw-Hill Companies, Inc., 2000
4- 27
Topics Covered
 NPV and its Competitors
The Payback Period
 The Book Rate of Return
 Internal Rate of Return

 Capital Rationing – what to do?
Profitability Index
 Linear Programming

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NPV and Cash Transfers
 Evaluating projects requires understanding
the flows of cash.
Cash
Investment
opportunities
Firm
Shareholder
(real assets)
Invest…
Irwin/McGraw Hill
… or pay
dividend …
Investment
opportunities
(financial assets)
… so shareholders invest
for themselves
©The McGraw-Hill Companies, Inc., 2000
4- 29
Payback
 The payback period of a project is the time it
takes before the cumulative forecasted cash
inflow equals the initial outflow.
 The payback rule says only accept projects
that “payback” within some set time frame.
 This rule is common but very flawed.
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4- 30
Payback
Example
Examine the three projects and note the mistake we
would make if we insisted on only taking projects
with a payback period of 2 years or less.
Project
A
B
C
Irwin/McGraw Hill
Payback
C0
C1
C2
C3
Period
- 2000 500 500 5000
3
- 2000 500 1800
0
2
- 2000 1800 500
0
2
NPV@ 10%
 2,624
- 58
 50
©The McGraw-Hill Companies, Inc., 2000
4- 31
Book Rate of Return
Book Rate of Return – An accounting measure of
profitability. Also called accounting rate of return.
book income
Book rate of return 
book assets
Note the components reflect tax and accounting
figures, not market values or cash flows.
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Internal Rate of Return
 The Internal Rate of Return is the discount rate that makes
the project’s NPV = 0.
 IRR rule is to accept a project if the IRR>cost of capital.
Example
You can purchase a machine for $4,000. The investment will
generate $2,000 and $4,000 in cash flows in the next two
years. What is the IRR on this investment?
2,000
4,000
NPV  4,000 

0
1
2
(1  IRR ) (1  IRR )
IRR  28.08%
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Internal Rate of Return
2500
2000
IRR=28%
1000
500
0
10
90
80
70
60
50
40
30
-500
20
0
10
NPV (,000s)
1500
-1000
-1500
-2000
Discount rate (%)
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4- 34
Internal Rate of Return
Pitfall 1 - Strange cash flow patterns
 With some cash flows the NPV of the project increases as the
discount rate increases.
 This is contrary to the normal relationship.
NPV
Discount
Rate
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Internal Rate of Return
Pitfall 1 – Strange cash flow patterns
 Example where IRR gets it wrong for this reason:
 1,000  3,600  4,320  1,728  20%
C0
Irwin/McGraw Hill
C1
C2
C3
IRR
 .75
NPV @ 10%
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4- 36
Internal Rate of Return
Pitfall 2 - Multiple Rates of Return (even stranger CF patterns)
 Some cash flow patterns can generate NPV=0 at two different IRRs!
 The following cash flow generates NPV=0 at both (-50%) and 15.2%.
NPV
1000
IRR=15.2%
500
Discount
Rate
0
-500
IRR=-50%
-1000
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Internal Rate of Return
Pitfall 2 - Multiple Rates of Return
 Example where IRR gets it wrong for this reason:
 1,000  800  150  150  150  150  150
C0
Irwin/McGraw Hill
C1
C2
C3
C4
C5
C6
©The McGraw-Hill Companies, Inc., 2000
4- 38
Internal Rate of Return
Pitfall 3 - Mutually Exclusive Projects
 IRR ignores the scale of the project.
F
E
Project
Irwin/McGraw Hill
 20,000  35,000 75
 10,000  20,000 100
C0
Ct
IRR
 11,818
 8.182
NPV @ 10%
©The McGraw-Hill Companies, Inc., 2000
4- 39
Internal Rate of Return
Pitfall 4 – Flat Term Structure Assumption
 IRR has problems when the term structure isn’t flat.
 In this case, we’d need to compare the project IRR
with the expected IRR (yield to maturity) offered by
a traded security that
Has equivalent risk
 Has same time-pattern of cash flows

 At this point easier to calculate NPV!
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4- 40
Internal Rate of Return
Even calculating IRR can be hard. Financial calculators
can perform this function easily, though. In the previous
example,
HP-10B
EL-733A
BAII Plus
-350,000
CFj
-350,000
CFi
CF
16,000
CFj
16,000
CFfi
2nd
16,000
CFj
16,000
CFi
-350,000 ENTER
466,000
CFj
466,000
CFi
16,000
ENTER
16,000
ENTER
{IRR/YR}
IRR
{CLR Work}
466,000 ENTER
All produce IRR=12.96
Irwin/McGraw Hill
IRR
CPT
©The McGraw-Hill Companies, Inc., 2000
4- 41
Profitability Index
 When resources are limited (capital is
“constrained” or “rationed”) the profitability
index (PI) provides a tool for selecting among
various project combinations and alternatives.
 The highest weighted-average PI can indicate
the right plan in these circumstances.
Irwin/McGraw Hill
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4- 42
Profitability Index
NPV
Profitabil ity Index 
Investment
Example
We only have $300,000 to invest. Which do we select?
Proj
A
B
C
Irwin/McGraw Hill
NPV
230,000
141,250
194,250
Investment
200,000
125,000
175,000
PI
1.15
1.13
1.11
©The McGraw-Hill Companies, Inc., 2000
4- 43
Linear Programming
 Maximize Cash flows or NPV
 Minimize costs
Example
Max NPV = 21Xa + 16 Xb + 12 Xc + 13 Xd
subject to
10Xa0 + 5Xb0 + 5Xc0 + 0Xd0 <= 10
-30Xa1 - 5Xb1 - 5Xc1 + 40Xd1 <= 12
Irwin/McGraw Hill
©The McGraw-Hill Companies, Inc., 2000
Principles of Corporate Finance
Brealey and Myers

Sixth Edition
Making Investment Decisions with
the Net Present Value Rule
Slides by
Matthew Will,
Jeffrey Wurgler
Irwin/McGraw Hill
Chapter 6
©The McGraw-Hill Companies, Inc., 2000
4- 45
Topics Covered
 What To Discount
 IM&C Project
 Project Interaction
Timing
 Equivalent Annual Cost
 Replacement
 Cost of Excess Capacity
 Fluctuating Load Factors

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What To Discount
Only Cash Flow is Relevant
Irwin/McGraw Hill
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4- 47
What To Discount
Points to watch out for:
Do not confuse average with incremental.
Treat inflation consistently.
Include all incidental effects.
Do not forget working capital requirements.
Forget sunk costs.
Include opportunity costs.
Beware of allocated overhead costs.
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IM&C’s Guano Project
Revised projections ($000s) reflecting inflation
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4- 49
IM&C’s Guano Project
Cash flow analysis ($1000s)
Irwin/McGraw Hill
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4- 50
IM&C’s Guano Project
 NPV (using nominal cash flows)
1,630 2,381 6,205 10,685 10,136
NPV  12,600 




2
3
4
1.20 1.20 1.20 1.20 1.205
6,110
3,444


 3,519 or $3,519,000
6
7
1.20 1.20
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IM&C’s Guano Project
Tax depreciation allowed under the modified accelerated cost
recovery system (MACRS) - (Figures in percent of
depreciable investment).
Irwin/McGraw Hill
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4- 52
Optimal timing
 Even projects with positive NPV may be
more valuable if deferred.
 The relevant NPV is then the current value of
some future value of the deferred project.
Net future value as of date t
Current NPV 
t
(1  r )
Irwin/McGraw Hill
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4- 53
Optimal timing
Example
You may harvest a set of trees at anytime over the next 5
years. Given the FV of delaying the harvest, which harvest
date maximizes current NPV?
FV ($1000s)
Current NPV
0
50
50
1
64.4
58.5
Harvest
2
77.5
64.0
Year
3
89.4
67.2
4
5
100 109.4
68.3 67.9
 Harvesting in year 4 is optimal. And relevant NPV is 68.3.
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4- 54
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
present value of costs
Equivalent annual cost =
annuity factor
Irwin/McGraw Hill
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4- 55
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital, select the lower-cost machine
using equivalent annual cost method.
Costs by year
Machine
A
B
Irwin/McGraw Hill
0
15
10
1
5
6
2
5
6
3
5
PV@6%
28.37
21.00
EAC
10.61
11.45
©The McGraw-Hill Companies, Inc., 2000
4- 56
Machinery Replacement
Annual operating cost of old machine = 8
Cost of new machine
Year:
0
15
1
5
2
5
3
5
NPV @ 10%
27.4
Equivalent annual cost of new machine =
27.4/(3-year annuity factor at, say, 10%) = 27.4/2.5 = 11
Do not replace until operating cost
of old machine exceeds 11.
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Cost of Excess Capacity (?)
A project requires warehouse space and this causes a need for a new
one to be built in Year 5 rather than Year 10. A warehouse costs 100 &
lasts 20 years.
Equivalent annual cost @ 10% = 100/8.5 = 11.7
0 . . . 5
With project 0
0
6 . . . 10
11.7
11.7
11 . . .
11.7
Without project
0
0
0
0
11.7
Difference
0
0
11.7
11.7
0
PV extra cost = 11.7 6 + 11.77 + . . . + 11.7 10 = 27.6
(1.1) (1.1)
(1.1)
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Fluctuating Load Factors
• You operate in a seasonal business. Your two old machines
have a capacity of 1,000 units/year. Half the year, you
operate at 50% capacity. The other half, at 100% capacity.
• The operating expenses of your old machines is $2/unit.
• Discount rate is 10%.
Annual output per machine
Operating cost per machine
PV operating cost per machine
PV operating cost of two machines
Irwin/McGraw Hill
Two Old Machines
750 units
2  750  $1,500
1,500/.10  $15,000
2  15,000  $30,000
©The McGraw-Hill Companies, Inc., 2000
4- 59
Fluctuating Load Factors
• Could replace with two new machines which have $1/unit cost
Annual output per machine
Capital cost per machine
Operating cost per machine
PV operating cost per machine
PV operating cost of two machines
Irwin/McGraw Hill
Two New Machin es
750 units
$6,000
1  750  $750
6,000  750/.10  $13,500
2  13,500  $27,000
©The McGraw-Hill Companies, Inc., 2000
4- 60
Fluctuating Load Factors
Third (better) option: Replace just one machine. New machine
has low operating cost, so operate it all year. Keep old machine
for peak demands.
Annual output per machine
Capital cost pe machine
Operating cost per machine
PV operating cost per pachine
PV operating cost of two machines
Irwin/McGraw Hill
One Old Machine
500 units
0
2  500  $1,000
1,000/.10  $10,000
................................$26,000
One New Machin e
1,000 units
$6,000
1  1,000  $1,000
6,000  1,000 / .10  $16,000
©The McGraw-Hill Companies, Inc., 2000