T14.1 Chapter Outline
Chapter 14
Cost of Capital
Chapter Organization
 14.1 The Cost of Capital: Some Preliminaries
 14.2 The Cost of Equity
 14.3 The Costs of Debt and Preferred Stock
 14.4 The Weighted Average Cost of Capital
 14.5 Divisional and Project Costs of Capital
 14.7 Calculating WACC for Bombardier
 14.8 Summary and Conclusions
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Cost of Capital
 The rate of return that compensates investors for the use of the
capital needed to finance the firm/project
 This expected return on the part of the investor in turn
represents the firm’s cost for that capital
 Investors expect higher returns to compensate for higher levels
of risk
 The terms required return, appropriate discount rate and cost of
capital are all used interchangeably - they all essentially mean
the same thing
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Slide 2
Cost of Capital continued
 A key point is the cost of capital depends primarily on the use of
the funds ----not the source


so if we were analyzing a ‘risk free’ investment we should use a
proxy for a risk free return as the cost of capital for the project
as the risk increases - the discount rate should increase because
the required return by investors is increasing to compensate them
for the higher risk
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Slide 3
Financial Policy and Cost of Capital
 A firm’s capital structure ie its mixture of debt and equity is a
function of the firm’s financial policy - it is up to management to
decide the capital structure for the firm

how that structure is decided is for another class!
 A firm’s cost of capital is a mixture of returns needed to
compensate its creditors and shareholders - it reflects both the
cost of debt and equity capital
 A firm’s weighted average cost of capital (WACC) reflects the
respective weighting of the firm’s debt and equity capital in its
capital structure
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Slide 4
The Cost of Equity
 ‘The return that equity investors require on their
investment in the firm’
 This expected return must be estimated - there is no direct
means of observing the return that investors are expecting.
 Two Approaches:
 The Dividend Growth Model Approach
• the return that shareholders require on the stock is seen as
the firm’s cost of equity capital
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Slide 5
Cost of Equity
 The SML or Security Market Line Approach
 The SML essentially tells us the reward (return) for bearing risk in
financial markets – what return is expected for a given level of risk
 required return is a function of 3 things:
• risk free rate
• market risk premium
• systematic risk of the asset relative to the average risk - called
the ‘beta’ coefficient
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Slide 6
T14.3 The Dividend Growth Model Approach
 Estimating the cost of equity: the dividend growth model
approach
According to the constant growth model,
P0 =
D1
RE - g
Rearranging,
RE =
D1
+g
P0
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Slide 7
T14.4 Estimating the Dividend Growth Rate –based on historical growth
Dollar Change
Percentage
Change
Year
Dividend
1990
$4.00
1991
4.40
$0.40
10.00%
1992
4.75
0.35
7.95
1993
5.25
0.50
10.53
1994
5.65
0.40
7.62
-
-
Average Growth Rate
(10.00 + 7.95 + 10.53 + 7.62)/4 = 9.025%
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Slide 8
Estimating the Dividend Model Growth Rate - Earnings Retention Approach
 If we assume the retention ratio remains constant
 Then:
 growth in earnings = growth in dividends
 growth in earnings is a function of both the retained earnings and
the return on the retained earnings
 Using ROE (an historical return) as a proxy for investors expected
return
g = Retention Ratio * ROE
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Slide 9
The Cost of Equity - SML Approach
 Required return is a function of 3 things
 risk free rate
 market risk premium - reflecting the risk associated with the market
as a whole e.g the TSE risk
 systematic risk of the asset relative to the average risk - called the
‘beta’ coefficient - reflecting how the individual stock in question
varies with the market as a whole- so if the stock historically is
much more volatile (risky) than the market then the return should
reflect that incremental risk
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Slide 10
T14.5 Example: The SML Approach
 From the SMl comes the Capital Asset Pricing Model (CAPM)
 According to the CAPM:
RE = Rf + bE  (RM - Rf)
Rf = risk free rate of return
Rm = market risk
Rm-RF = market risk premium
BE = estimate of systematic risk, the risk for an individual security relative
to the market risk as a whole
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Slide 11
SML Approach
Get the risk-free rate (Rf ) from financial press—many use the 1year Treasury bill rate, say 6%.
2. Get estimates of market risk premium and security beta.
a. Historical risk premium — RM - Rf = e.g. 7.1% on
Canadian equities
b. Beta — historical
(1)
Investment information services - e.g., S&P, Value
Line
(2)
Estimate from historical data
3. Suppose the beta is 1.40, then, using the approach:
RE
=
Rf + bE  (RM - Rf)
=
2.5% + 1.40  7.1%
=
12.44%
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Slide 12
Cost of Equity - Summary
 The return that equity investors require on their investment in
the firm
 Investor’s expected returns = company’s cost of equity capital
 2 approaches in estimating this expected return/ cost
 Dividend Growth Model
 SML approach
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Slide 13
The Cost of Debt
1. The cost of debt, RD, is the return the firm’s long term creditors
demand on new borrowing.
• The interest rate on the new borrowing reflects that expected
return and is the cost of that capital to the firm
2. The cost of debt is observable:
a. Yield on currently outstanding debt.
b. Yields on newly-issued similarly-rated bonds.
3. The historic debt cost is irrelevant -- why?
Example: We sold a 20-year, 12% bond 10 years ago at par. It is
currently priced at 120. What is our cost of debt?
The yield to maturity is 8.90%, so this is what we use as the cost of
debt, not 12%.
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Slide 14
Costs of Preferred Stock
1. Preferred stock is a perpetuity, so the cost is
RP = D/P0
2. Notice that cost is simply the dividend yield.
Example: We sold an $8 preferred issue 10 years ago. It
sells for $120/share today.
The dividend yield today is $8.00/120 = 6.67%, so this
is what we use as the cost of preferred.
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Slide 15
The Weighted Average Cost of Capital
 Capital structure weights
1. Let:
E = the market value of the equity.
D = the market value of the debt.
Then:
V = E + D, so E/ V + D/ V = 100%
2. So the firm’s capital structure weights are E/ V and D/ V.

we are using market values for the firm’s debt and equity in determining the
‘weights’- if these are fluctuating widely, then book values would be the alternative.
3. Interest payments on debt are tax-deductible, so the after tax cost of
debt is the pretax cost multiplied by (1 - corporate tax rate).
After tax cost of debt = RD  (1 - Tc)
4. Thus the weighted average cost of capital is
WACC = (E/V)  RE + (D/V)  RD  (1 - Tc)
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Slide 16
Example: Eastman Chemical’s WACC
 Eastman Chemical has 78.26 million shares of common stock
outstanding. The book value per share is $22.40 but the stock
sells for $58. The market value of equity is $4.54 billion.
Eastman’s stock beta is .90. T-bills yield 4.5%, and the market
risk premium is assumed to be 9.2%.
 The firm has four debt issues outstanding.
Coupon
Book Value
Market Value
6.375%
$ 499m
$ 501m
6.32%
7.250%
7.635%
7.600%
Total
495m
200m
296m
$1,490m
463m
221m
289m
$1,474m
7.83%
6.76%
7.82%
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Yield-to-Maturity
Slide 17
Example: Eastman Chemical’s WACC (concluded)
 Cost of equity (SML approach):
RE = .045 + .90  (.092) = .045 + .0828 = .1278  12.8%
 Cost of debt:
Multiply the proportion of total debt represented by each issue by its yield to
maturity; the weighted average cost of debt = 7.15%
 Capital structure weights:
Market value of equity = 78.26 million  $58 = $4.539 billion
Market value of debt = $501m + $463m + $221m + $289m = $1.474 billion
V = $4.539 billion + $1.474 billion = $6.013 billion
D/V = $1.474b/$6.013b = .2451  25%
E/V = $4.539b/$6.013b = .7549  75%
 WACC = .75 (12.8) + .25  7.15(1 - .35) = 10.76%
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Slide 18
Summary of Capital Cost Calculations (Table 14.1)
I. The Cost of Equity, RE
A.
Dividend growth model approach
RE = D1 / P0 + g
B.
SML approach
RE = Rf + b E  (RM - Rf)
II. The Cost of Debt, RD
A.
For a firm with publicly held debt, the cost of debt can be
measured as the yield to maturity on the outstanding debt.
B.
If the firm has no publicly traded debt, then the cost of debt
can be measured as the yield to maturity on similarly rated
bonds.
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Slide 19
Summary of Capital Cost Calculations (concluded)
III. The Weighted Average Cost of Capital (WACC)
A.
The WACC is the required return on the firm as a whole. It is the
appropriate discount rate for cash flows similar in risk to the firm.
B.
The WACC is calculated as
WACC = (E/V)  RE + (D/V)  RD  (1 - Tc)
where Tc is the corporate tax rate, E is the market value of the
firm’s equity (common and or preferred, D is the market value of
the firm’s debt, and
V = E + D. Note that E/V is the percentage of the firm’s
financing (in market value terms) that is equity, and D/V is
the percentage that is debt. Notice E could be common equity or
common and preferred equity
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Slide 20
Divisional and Project Costs of Capital
 When is the WACC the appropriate discount rate?
When the project is about the same risk as the firm.
 The WACC is not appropriate when a company has more
than one line of business e.g. Two divisions, and each has
a distinctive risk profile. Today’s telecommunications
companies with regulated telephone business alongside
higher risk e-business ventures
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Slide 21
Divisional and Project Costs of Capital
 Other approaches to estimating a discount rate:

Divisional cost of capital - each division’s cost of capital is
calculated separately

Pure play approach - look externally and find companies
that focus on as exclusively as possible the type of project
in which we are considering investing. (could be used in
estimating the cost of capital for the division

Subjective approach - subjective adjustments to the overall
WACC
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Slide 22
Comments on Bombardier WACC
 Short-term versus long-term financing in estimating WACC
 Market versus Book Value
WACC = (E/V)  RE + (D/V)  RD  (1 - Tc)
 YTM on bonds, and the cost of debt: RD
 The cost of preferred stock in the WACC calculation
V = E+P+D
WACC = (E/V)  RE + (P/V)  RP+(D/V)  RD  (1 - Tc)
…..many factors have now changed for Bombardier!!!!
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Slide 23
Solution to Problem 14.16
 Elway Mining Corporation has 8 million shares of common
stock outstanding, 1 million shares of 6 percent preferred
outstanding, and 100,000 9 percent semiannual coupon bonds
outstanding, par value $1,000 each. The common stock
currently sells for $35 per share and has a beta of 1.0, the
preferred stock currently sells for $60 per share, and the bonds
have 15 years to maturity and sell for 89 percent of par. The
market risk premium is 8 percent, T-bills are yielding 5 percent,
and the firm’s tax rate is 34 percent.
a. What is the firm’s market value capital structure?
b. If the firm is evaluating a new investment project that has
the same risk as the firm’s typical project, what rate should the
firm use to discount the project’s cash flows?
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Slide 24
Solution to Problem 14.16 (continued)
a. MVD =
100,000 ($1,000) (.89) = $89M
MVE =
8M($35) = $280M
MVp =
1M($60) = $60M
V
89M + 280M + 60M = $429M
=
D/V =
89M/429M = .207,
E/V =
280M/429M = .653, and
P/V =
60M/429M = .140.
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Slide 25
Solution to Problem 14.16 (concluded)
b. For projects as risky as the firm itself, the WACC is the appropriate
discount rate. So:
RE = .05 + 1.0(.08) = .13 = 13%
B0 = $890 = $45(PVIFARD,30) + $1,000(PVIFRD,30)
RD = 10.474%, and RD (1 - Tc) = (.10474)(1 - .34) = .0691 = 6.91%
RP = $6/$60 = .10 = 10%
WACC = .653 (13) + .207 (6.91) + .14 (10)
= 11.32%
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Slide 26
Solution to Problem 14.20
 True North, Inc. is considering a project that will result in initial
aftertax cash savings of $6 million at the end of the first year,
and these savings will grow at a rate of 5 percent per year
indefinitely. The firm has a target debt/equity ratio of .5, a cost of
equity of 18 percent, and an aftertax cost of debt of 6 percent.
The cost-saving proposal is somewhat riskier than the usual
project the firm undertakes; management uses the subjective
approach and applies an adjustment factor of +2 percent to the
cost of capital for such risky projects. Under what circumstances
should True North take on the project?
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Slide 27
Solution to Problem 14.20 (concluded)
WACC = (.3333)(.06) + (.6666)(.18) = .14
Project discount rate = .14 + .02 = .16
NPV = - cost + PV cash flows
PV cash flows = [$6M/(.16 - .05)] = $54.55M
So the project should only be undertaken if its cost is less than
$54.55M.
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Slide 28