Valuation of Cash Flow Streams:
Company Valuation
Global Financial Management
Campbell R. Harvey
Fuqua School of Business
Duke University
charvey@mail.duke.edu
http://www.duke.edu/~charvey
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Overview
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Stocks and stock markets
Valuation:
» Use present value formula
Dividend growth models
» Applications
» Extensions
Financial ratios
» Dividend yields
» P/E multiples
Discounted cash flow models (DCF)
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Common Stock
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Stockholders are owners of the firm.
Stockholders are residual claimants.
Stockholders have the right to:
» vote at company meetings
» dividends and other distributions
» sell their shares
Stockholders benefit in two ways:
» dividends
» capital gains
Stock is issued by public corporations to finance investments.
Stock is initially issued in the primary market (IPOs and
secondary offerings).
Stock is traded in the secondary market on organized
exchanges.
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World Stock Markets
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New York
Tokyo
London
Frankfurt
Paris
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Mexico
Canada
Brussels
Hong Kong
Singapore
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Johannesburg
Sydney
Stockholm
Amsterdam
Switzerland
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International Stock Market Indices
UKX
CAC
DAX
IBEX
MIB30
BEL20
AEX
SMI
NKY
HSI
AS30
STI
TS300
MEXBOL
Value
Net Chg Pct Chg
FT-SE 100 Index
4207.70
10.20
0.24
CAC 40 INDEX
2425.10
17.33
0.71
DAX INDEX
3001.37
8.05
0.26
IBEX 35 INDEX
5470.23
85.41
1.58
MILAN MIB30 INDEX
18485.00
344.00
1.89
BEL20 INDEX
2006.79
8.22
0.41
AMSTERDAM EXCHANGES INDX
670.08
0.53
0.07
SWISS MARKET INDEX
4019.89
12.79
0.31
NIKKEI 225 INDEX
18090.03
-54.30
-0.29
HANG SENG STOCK INDEX
13856.40
25.72
0.18
ASX ALL ORDINARIES INDX
2435.50
-0.80
-0.03
SING: STRAITS TIMES INDU
2244.21
23.84
1.07
TSE 300 Index
6136.39
32.73
0.53
MEXICO BOLSA INDEX
3741.87
40.04
1.08
Value on January 17, 1997, Change relative to previous day
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U. S. Stock Markets
Major U. S. Stock Exchanges
New York Stock Exchange (NYSE)
American Stock Exchange (AMEX)
Over-The-Counter (OTC)
» National Association of Securities Dealers (NASDAQ)
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U. S. Stock Market
INDU
SPX
CCMP
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DOW JONES INDUS. AVG
S&P 500 INDEX
NASDAQ COMB COMPOSITE IX
Other Indices
NYSE Composite
Russell 2000
Wilshire 5000
Value Line
Value
Net Chg Pct Chg
6795.37
30.00
0.44
773.68
3.92
0.50
1349.49
9.02
0.67
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Transactions Involving Stocks
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Buy
 Savings motive
 Expect stock to
appreciate in value
 Long position
Sell
 Liquidity needs
 Expect stock to decline
in value
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Short Sell
 Sell stock without first owning it.
 Borrow stock from your broker
with the promise to repay it at
some later date.
 Sell the borrowed stock.
 Repurchase it at a later date to
repay your broker.
 Responsible for all dividends and
other distributions while short the
stock.
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Stock Valuation
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The price an investor is willing to pay for a share of stock
depends upon:
» Magnitude and timing of expected future dividends.
» Risk of the stock.
The stock’s discount rate, re, is the rate of return investors can
expect to earn on securities with similar risk.
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Why short-termists are long-termists
Shareholders require a rate of return re for buying a share. They buy for
P0 and sell after one year for P1 and receive dividends D1:
D P
P0  1 1
1  re
The next buyer also sells after one year:
P1 
D2  P2
D
D  P2
 P0  1  2
1  re
1  re 1  re 2
The same holds for P2. Continuing gives:
P0 
D1
D2
D3


...
2
1  re 1  r e 
1  re  3
Share price = PV of dividends
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The “Constant Growth” Formula
Assumption: Dividends grow at a constant rate g for ever:
D2  D1 (1  g ), Dt  Dt 1 (1  g ) ...  D1 (1  g ) t 1  D0 (1  g ) t
Then:
D1 1  g
D1
D1 (1  g)
P0 

...
2
1  re (1  re )
1  re  t
t 1
D1
... 
re  g
Prospective Dividend per Share
Share Price 
Required return - growth rate
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Issues:
» constant growth
» g < re.
» Is this a real or a nominal calculation?
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Simplifying the Dividend Discount
Model
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Constant Dividends
g  0  D1  D2 ...  D
Then the pricing relation simplifies to:
P0 
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D
D
 re 
re
P0
» Stock similar to perpetual bond
If dividends are constant, then we have that:
Required return on equity = Dividend yield
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Constant Dividends: An Example
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Consider a company that pays a dividend of:
$3 per share
in bad years (Probability = 50%)
$15 per share
in good years (Probability = 50%)
» Required rate of return is 18%
» What is the share price?
E( Div)  0.5 * $3  0.5 * $15  $9
P0 
$9
 $50
0.18
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Constant Dividends:
RJR Nabisco Preferred Stock
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RJR Nabisco has a preferred stock outstanding
» annual dividend of $2.50 per share.
» Securities with similar risk are expected to return 9.6%
– what is the price of the preferred stock?
P0 
D $2.50

 $26.04
re 0.096
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Constant Growth:
Duke Power Common Stock
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Duke Power currently pays a dividend of $2.04 per share.
» Demand for electric power is growing at 4% per year,
» Inflation averages 3% per year,
» Duke Power expects its profits and dividends to grow at about
7% per year.
» Stockholders require a 12% rate of return
– what is the market price of Duke Power’s common stock?
P0  1  g 
P0 
D0
re  g
2.04(1.07)
 $43.66
0.12  0.07
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Valuation with Growing Dividends
An Example: Valuation of GM
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Generally, companies have growing dividends on stocks, hence
apply general formula:
D1
P0 
re  g
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Consider data for GM:
» Number of shares:
855,820
» Market capitalization
$42.051bn
» Historic dividend
$1.50 per share
» Your forecast:
$1.60
– What valuation do you obtain for GM, depending on g
and r?
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Valuation of GM
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Alternative valuations:
Return/Growth
7%
8%
9%
10%
11%
12%
3%
34.23
27.39
22.82
19.56
17.12
15.21
4%
45.64
34.23
27.39
22.82
19.56
17.12
4.50%
54.77
39.12
30.43
24.90
21.07
18.26
5%
68.47
45.64
34.23
27.39
22.82
19.56
6%
136.93
68.47
45.64
34.23
27.39
22.82
7%
136.93
68.47
45.64
34.23
27.39
Example:
855,820,000*$1.60=$1.37bn
MCAPGM
D1997
$1.37bn


$34.23bn
rGM  gGM 0.09  0.05
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Valuing a Business
A Hybrid Approach
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Sometimes equity analysts have knowledge about the
immediate, but not the distant future
» Dividend forecasts for immediate future (2-5 years)
» Assume constant growth for distant future (>5 years)
» How do you change the model?
Dividends
Value
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Modify the Growth Model
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The formula for a T-year horizon can be written as:
t T
Dt
PT
P0  t 1

1  re t 1  re T
Apply the growth model to the price in T:
D
PT  T 1
re  g
Then the current value of the share is:
P0  t 1
t T
Dt

1 g
1  re t 1  re T
DT
re  g
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Valuing a Business
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Consider a company with cash flows from operations of $1
million for the most recent year.
The company’s cash flows are expected to grow at a rate of
10% for the next 5 years and at a constant rate of 5% thereafter.
To generate this increase in cash flows, the company is required
to reinvest 50% of its cash flows for the first 5 years and 25% of
its cash flows thereafter.
Given the risk of the business, the required rate of return is 15%.
What is the value of the business?
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Valuing a Business (cont.)
Year 1 Year 2 Year 3 Year 4 Year 5
1.10
1.21
1.33
1.46
1.61
Operating
Cash Flows
New Capital -0.55
Investment
Net Cash
0.55
Flow (Div)
Present
0.48
Value
-0.61
-0.67
-0.73
-0.81
0.60
0.66
0.73
0.80
0.45
0.43
0.42
0.40
Present value= CF(1)+...+CF(5)=0.48+0.45+0.43+0.42+0.40=2.18
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Valuing a Business
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Value of dividends over the first 5 years is $2.18.
Value of business at the end of the 5th year:
P5 
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161
. 1  0.25105
.
D6

 $12.68
re  g
015
.  0.05
Value of the Business:
$12.68
P0  $2.18 
 $8.48
5
115
.
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Another Application:
Estimating the required return on equity
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Holders of stock receive returns in two forms:
» Dividend payouts
» Capital gains (stock appreciation P1-P0)
re 
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D1 P1  P0

P0
P0
Note:
» The required rate of return is not equal to the dividend yield
» The expression is in terms of the prospective yield, not the historic
yield
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Required Returns and the Growth
Model
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Use the growth model formula to solve for the required rate of
return to give:
D
re  1  g
P0
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Hence, the required rate of return is equal to the prospective
dividend yield plus the growth rate.
Note that you can synthesize the previous results:
P  P0
g 1
P0
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If dividends grow at a constant rate, then:
» share prices grow at the same rate
» yield stay constant
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Another view: P/E-ratios
Next year’s EPS:
Payout ratio:
P/E-ratio:
Earnings yield:
E1

D1
E1
P0/E1
E1/P0
The we obtain the following results: D1  E1
re 

P0


E1 re  g
E1
*  g
P0
» Which assumptions do you have to make in order to argue that
stocks with a low P/E multiple are undervalued?
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P/E Ratios and Growth
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You can use the expression for the historic yield to infer the
growth rate:
re  D0 P0 Required return  Yield
g

1  D0 P0
1  Yield
Consider auto industry:
MCAP
No. of shares ('000)
Share Price
Dividend p. share
Dividend Yield
EPS
P/E ratio
Chrysler Ford
GM
24.671
38.152
42.051
713500 1186000
855820
34.58
32.17
49.14
1.3
1.43
1.5
3.76%
4.45%
3.05%
2.78
3.58
7.28
6.78
10.1
7.8
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Growth rate in the Auto Industry
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Infer growth rate in the auto industry
Returns
9%
10%
11%
12%
13%
14%
15%
Implied growth rates
Chrysler Ford
GM
5.05%
4.36%
5.77%
6.01%
5.32%
6.74%
6.98%
6.28%
7.71%
7.94%
7.23%
8.68%
8.91%
8.19%
9.65%
9.87%
9.15%
10.62%
10.83%
10.11%
11.59%
Example:
g Ford  Re turn  12% 
0.12  0.0445
 0.0723  7.23%
1.0445
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Summary
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Stocks and equity securities can be valued by using present
value techniques
» The discounting horizon does not depend on the investment
horizon of individual investors in the stock market
Investors are compensated through cash dividends and through
capital gains
» Required returns on equity are generally not equal to the
dividend yield, but to the dividend yield plus the growth rate
P/E-ratios should be used with caution:
» Depends on simplifying assumptions
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Issues in Capital Budgeting:
Investment
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How should capital be allocated?
» Do I invest / launch a product / buy a building / scrap /
outsource...
» Should I acquire / sell / accept offer for company or division?
» How should the capital budgeting process be organized?
Which choices should I make?
» make or buy
» which distribution channel
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Issues in Capital Budgeting:
Financing
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Choose between financing alternatives
» How should I finance this deal?
» Should I change my capital structure?
» Lease or buy?
Risk Management
» Hedging
» Taking a view
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Discounted Cash Flows
A Tool For Rational Decision Making
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What can be an object of capital budgeting procedures?
» There must be a choice - choose a base case and an
alternative. (Do nothing/status quo)
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Identify incremental cash flows from project
» Treat as incremental cash flows to shareholder
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Calculate the value of the project.
» Taking into account timing and risk
» Aggregate cash flows into one single number
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Show that doing all and only projects which have positive net
present value maximizes the value of the firm.
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Estimating Relevant Cash Flows
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The relevant cash flows for evaluating a new investment project
are the incremental cash flows contributed by the project.
Incremental
Cash Flows
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=
Firm’s CFs
-
with Project
Firm’s CFs
without Project
Only Incremental Cash Flows are Relevant.
»
»
»
»
Include all incidental effects, including project interactions.
Don’t forget to include investment in working capital.
Forget about sunk costs.
Include all opportunity costs (e.g., land used to construct a
new plant).
» Beware of allocated overhead expenses.
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Estimating Relevant Cash Flows:
Basic Principles
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Discount Cash Flows, Not Accounting Profits.
» For capital budgeting purposes, the point of recognition is when
the money is actually received or spent.
» Don’t forget the effect of taxes.
Separate Investment and Financing Decisions
» Ignore all financing costs, even if the project is partially financed
with debt.
» Treat the project as if it were all-equity financed.
» Financing side effects will be considered later.
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Depreciation
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Depreciation is a non-cash expense that only affects cash flows
through its tax effect.
Assets are depreciated down to their estimated salvage values.
Any removal costs associated with old equipment are expensed
immediately.
Sales tax, delivery costs, and installation are regarded as part of the
cost of the new asset for depreciation purposes.
Removal costs of the old asset are not regarded as part of the cost
of the new asset and are expensed immediately.
If an asset is later sold for an amount above (below) its book value,
the excess is taxable (deductible).
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Example: Estimating Cash Flows
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A new machine costs $60,000
» installation costs of $2,000.
» generates revenues of $155,000 and
» expenses of $100,000 annually.
» depreciated to its estimated salvage value over of $6,000
over its seven year life.
– What are the relevant cash flows?
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Compute Cash Flows
Step 1: Compute Tax cash flows
Year
Revenues
Expenses
Depreciation
Taxable Income
Tax
0
1
155,000
-100,000
-8,000
47,000
15,980
...
...
...
...
...
...
7
155,000
-100,000
-8,000
47,000
15,980
Step 2: Compute Cash Flows
Year
Revenues
Expenses
Tax
Cost of Machine
Salvage
Net Cash Flow
0
1
155,000
-100,000
-15,980
...
...
...
...
6
155,000
-100,000
-15,980
7
155,000
-100,000
-15,980
39,020
6,000
45,020
-62,000
-62,000
39,020
...
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Cash Flow and Accounting Numbers:
How to Value a Company
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The value of the firm is the present discounted value of all net
cash flows accruing to all security holders (debt and equity).
Define:
The capital cash flow of period t CCF(t) is the net cash flow
received by all security holders of the firm combined:
CCF
= EBIT
- (EBIT - Interest)*T
- Depreciation & Amortization
- Change in working capital
- Capital Expenditure
+ Asset Sales
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Capital Cash Flows
Since Net Income = (1 - T)*(EBIT - Interest) we have the alternative
definition:
CCF
=
Net Income
+ Interest
- Depreciation & Amortization
- Change in working capital
- Capital Expenditure
+ Asset Sales
Then we can value a company as:
 CCF ( t )
V (0)  t 1
(1  r ) t
where r is the company’s cost of capital.
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Summary and Preview
Most investment and financing problems can be analyzed as capital
budgeting problems
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Focus is on cash flows, not accounting numbers
» Use accounting numbers, remove non-cash flow charges like
depreciation
– However, depreciation has tax consequences
– Taxes are cash flows
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Capital budgeting always focuses on decisions, hence
» Include all cash flow consequences affected by a decision
On the agenda:
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Take into account the time value of money
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Use single criterion to evaluate project
» NPV, compare with IRR, payback
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Account for risk, inflation, and taxes
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