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1. 9/20/2022 1
HFT 4464
Chapter 8
Cost of Capital

2. 8-2
Chapter 8
Introduction
 A firm’s long-term success depends upon the
firm’s investments earning a sufficient rate of
return. This sufficient or minimum rate of
return necessary for a firm to succeed is
called the cost of capital.
 The cost of capital can also be viewed as the
minimum rate of return required to keep
investors satisfied.

3. 8-3
Organization of Chapter 8
 Measure the cost of capital on a marginal,
after-tax basis.
 Estimating the cost of capital components
 Debt
 Preferred stock
 Common equity
 Internal— new retained earnings
 External—new issues of common stock

4. 8-4
Organization of Chapter 8
 Estimating the weighted average cost of
capital
 Separating the finance decision from the
investment decision

5. 8-5
The Weighted Average
Cost of Capital
 The weighted average cost of capital is:
 The firm’s minimum required rate of return on
investments
 Measured as a percentage rate (%)
 An average cost of the various sources of capital
employed by a firm
 Debt
 Preferred stock
 Retained earnings
 Common stock

6. 8-6
The Weighted Average
Cost of Capital
 Also, the weighted average cost of capital is:
 The cost of long-term sources of funds; long-
term sources of funds are relevant because
these are the funds used to make long-term
investments.
 Measured on an after-tax basis.
 Measured as a marginal cost of capital. We
want to measure the cost of new capital used to
finance new investments.

7. 8-7
The Weighted Average
Cost of Capital
 The weights used are determined by a firm’s
target capital structure. A target capital
structure is the % of various capital components
a firm plans to use to fund investments.
 An example is a firm may plan to raise 70% of
capital from long-term debt and 30% from
equity. Another firm may plan to raise 40% of
capital from long-term debt, 10% from preferred
stock, and 50% from equity.

8. 8-8
The Weighted Average
Cost of Capital
 The basic weighted average cost of capital (ka) equation
is:
 ka = ( wd * kd ) + ( wp * kp ) + ( we * ke )
 Cost of Capital = (%Debt * Cost of Debt) + (% P.S. *
Cost of P.S.) + (%C.S. * Cost of C.S.)
 Where the w’s represent the firm’s target capital
structure and must add up to 100%.
 And the k’s represent the cost of each capital
component—debt, preferred stock, and common equity.

9. 8-9
Estimating the Cost
of Capital Components
 Components of a firm’s capital structure may
include:
 Long-term debt
 Preferred stock
 New retained earnings
 Common stock

10. 8-10
Estimating the Cost
of Capital Components
 A component’s cost of capital is a reflection of
the investor-required rate of return.
 A business loan at a 10% interest rate provides
a 10% return to the investor (lender) and a 10%
cost to the business plus any transaction costs
the company may pay to process the loan.

11. 8-11
Estimating the Cost
of Capital Components
 A component’s cost of capital is just the
investor-required return plus an adjustment for
transaction costs.
 These transaction costs are called issuance or
flotation costs and consist of fees paid to
investment bankers and lawyers for assisting a
firm in the issuance of securities.

12. 8-12
Seniority Risk and the Cost of Capital
 Debt securities have the least seniority risk and
common stock the most seniority risk of the 3
basic security types a corporation may issue.
 Therefore investors demand the lowest returns
on debt securities and the highest returns on
common stock.

13. 8-13
Seniority Risk and the Cost of Capital
 There is a clear ranking of cost for a firm’s
funds raised by different security types.
 The cost of debt securities is lowest due to their
relatively low risk.
 The cost of common stocks is the highest due to
its relatively high risk to investors.
 The cost of preferred stocks falls between the
above two.

14. 8-14
The Cost of Debt
 The interest cost of debt is a tax-deductible
cost. We take this into account by multiplying a
firm’s before-tax cost of debt by one minus the
firm’s marginal tax rate:
 kd = kdbt x (1 – t)
 With a 10% before-tax cost and a 40% marginal tax
rate the relevant after-tax cost of debt is:
 kd = 10% x (1 – 40%) = 6%

15. 8-15
The Cost of Debt
 The before-tax interest cost on bonds can be computed
with the same method used to compute the yield to
maturity on bonds in Chapter 6.
 Net Proceeds = (Coupon * PVA) + (Face Value * PVLS)
 Where Vnet is the net proceeds from the bond issuance
after issuance costs are paid.
 
 n
dbt
dbt
n
dbt
net
k
1
$1,000
k
k
1
1
-
1
x
C
V

















16. 8-16
The Cost of Debt
 Suppose a firm is considering the issuance of a 20-year
bond at a $1,000 price with a 9% coupon rate and
issuance costs of $10 for each bond.
 Kdbt = 9.11% and the after-tax cost of debt assuming a
40% tax rate is:
 kd = 9.11% x (1 - 40%) = 5.47%
 
 20
dbt
dbt
20
dbt
k
1
$1,000
k
k
1
1
-
1
x
$90
$990

















17. 8-17
The Cost of Preferred Stock
 Preferred stock is sometimes considered a
perpetuity, but many issues have a call feature
or a sinking fund as described in Chapter 6.
 We will show how to compute the cost of funds
raised with preferred stock assuming the
preferred stock is a perpetuity and also
assuming there is a stated ending date for the
preferred stock.

18. 8-18
The Cost of Preferred Stock
 Computing the cost of funds raised with preferred stock
is similar to computing the investor’s rate of return as in
Chapter 6. If the preferred stock is perpetual:
 Cost of P.S. = P.S. Dividend / P.S. Net Proceeds
 Where Vnet is the net proceeds from the preferred stock
issuance after issuance costs are paid.
net
p
p
V
d
k 

19. 8-19
The Cost of Preferred Stock
 Suppose a firm is considering the issuance of
preferred stock at $100 market price, with a
10% dividend rate and issuance costs of $3 per
share. The par value is also $100 per share.
What is the cost of raising funds with preferred
stock in this case?
%
31
.
10
$97
$10
3
-
$100
$100
x
10%
kp 



20. 8-20
The Cost of Preferred Stock
 Let’s consider the same example with one change.
What will be the cost of raising funds with preferred
stock if all the preferred stock will be called at a $100
par value in 10 years? The computation is similar to the
bond computation but without the tax impact!
 Kp = 10.50%
 
 10
p
p
10
p
k
1
$100
k
k
1
1
-
1
x
$10
$97

















21. 8-21
Common Equity
 Funds provided from a firm’s common equity
have 2 possible sources:
 Funds provided by reinvestment of a firm’s
profits are called new retained earnings. We call
this internal equity because these funds come
from the firm itself.
 Funds provided by the sale of new common
stock we call external equity.

22. 8-22
The Cost of Internal Equity
 The source of internal equity are profits not paid out as
dividends. Profits belong to the common stockholders.
The stockholders could have used this money to make
further investments of their own. Thus profits should
only be reinvested if the firm can earn as much as
stockholders could earn on their own. How much is
this?
 We will estimate this by the rate of return stockholders
can expect when they buy the firm’s common stock at its
current price. We will use this rate as the cost of funds
raised from internal equity!

23. 8-23
The Cost of Internal Equity
 How do we measure the rate of return investors
expect when they buy a firm’s common stock?
We will present 3 different methods for
estimating this rate of return and thus the cost
of using funds from internal equity:
 The dividend valuation model
 The capital asset pricing model
 The bond yield plus risk premium method

24. 8-24
The Cost of Internal Equity
 The constant growth dividend valuation model
was presented in chapter 7:
 We need to algebraically rearrange the terms to
solve for investor rate of return:
 
g
k
d
P
e
1
0


g
P
d
k
0
1
e 


25. 8-25
The Cost of Internal Equity
 Suppose a firm’s common stock is selling for
$40 per share, pays a current dividend of $3.50
per share and earnings and dividends are
expected to grow at a 4% rate into the
foreseeable future. The cost of internal equity
estimate is:
%
10
.
13
4%
$40
4%)
(1
x
$3.50
ke 




26. 8-26
The Cost of Internal Equity
 The capital asset pricing model (CAPM) was presented
in Chapter 4. The CAPM estimates investor-required
rate of return on common stock as a function of the
firm’s systematic risk as measured by beta.
 investor-required rate of return = Risk Free Rate +
{ ( Market Rate – Risk Free Rate) * beta }
j
f
m
f
j x
)
R
R
(
R
k 




27. 8-27
The Cost of Internal Equity
 Suppose a firm’s beta is estimated at 1.20, the
expected risk-free rate of return is 5%, and the
expected market return is 12%. The CAPM can
be used to estimate the firm’s internal cost of
equity:
13.4%
x
5%)
12%
(
5%
ke 






28. 8-28
The Cost of Internal Equity
 The bond yield plus risk premium method of
estimating the cost of internal equity:
 Begins with an estimate of the firm’s before-tax
bond yield.
 A risk premium is added to the bond yield to
estimate the cost of internal equity.
 The difficulty is in estimating the appropriate
risk premium. This risk premium may vary over
time and across different firms.

29. 8-29
The Cost of Internal Equity
 Suppose a firm has bonds trading at an 8.5%
yield. The typical risk premium over bond yield
for an average company is 4%. But we believe
our firm to have above-average risk so we think
5% is a better estimate of its risk premium over
bond yield. The cost of internal equity using the
bond yield plus risk premium is:
 ke = 8.5% + 5% = 13.5%
 Cost of Internal Equity = Bond Yield + Risk Premium

30. 8-30
The Cost of External Equity
 If retained earnings growth is not sufficient to
meet a firm’s need for equity funding, then new
shares of common stock may be sold to raise
capital. We call this external equity since the
funds come from outside the firm.
 The cost of external equity should be the same
as the cost of internal equity plus additional
issuance costs. Of course issuance costs are
not relevant to internal equity.

31. 8-31
The Cost of External Equity
 The same general approach to handling
issuance costs with bonds and preferred stock
is used to in the cost estimation for external
equity. The market price of the security is
reduced by the amount of the issuance costs.
The dividend valuation model uses market price
to estimate the cost of equity:
g
P
d
k
net
1
ne 


32. 8-32
The Cost of External Equity
 Let’s use the same example as before. A firm’s
common stock is selling for $40 per share, expects to
pay a dividend of $3.64 in 1 year, and growth rate is
4%. If the issuance costs are $6 per share, the cost is:
 Remember, the cost of internal equity for this firm was
13.10% using the dividend valuation model.
%
71
.
14
%
4
$34
$3.64
4%
6
-
$40
$3.64
kne 





33. 8-33
The Cost of External Equity
 We just have this 1 model for estimating the cost of
external equity, but we have 3 models for estimating the
cost of internal equity! We should just estimate the cost
adjustment for external equity (14.71%–13.10%) of
1.61% and add this to whatever estimate we use for
internal equity.
 For example, if you use the 13.4% estimate of cost of
internal equity from the CAPM, then add 1.61% to this
to estimate a cost of external equity of 15.01%!

34. 8-34
The Weighted Average
Cost of Capital
 Now that we know how to compute the
components’ cost of capital we are ready to
complete the weighted average cost of capital
estimation. Previously we presented the
equation for this computation:
 ka = wd x kd + wp x kp + we x ke
 We also need to know a firm’s target capital
structure so we can estimate the wi’s.

35. 8-35
The Weighted Average
Cost of Capital
 Suppose our firm has a target capital structure
of 40% long-term debt (wd), 10% preferred
stock (wp), and 50% common equity (we).
 Assume the firm has sufficient retained
earnings growth to need no funds from a new
common stock issuance.
 Let’s use our previously computed 5.44% cost
of long-term debt and 10.31% cost of funds
from preferred stock.

36. 8-36
The Weighted Average
Cost of Capital
 For the cost of internal equity let’s use an
average of our 3 estimates:
%
33
.
13
3
13.5%
13.4%
13.1%
ke 




37. 8-37
The Weighted Average
Cost of Capital
 Now we have all the inputs we need to estimate the
weighted average cost of capital:
 ka = 0.4 x 5.47% + 0.1 x 10.31% + 0.5 x 13.33%
 ka = 9.88%
 Therefore, this firm should use 9.88% as the minimum
required rate of return when evaluating investments.
 An average return of 9.88% is required to pay off the
firm’s contractual obligations on bonds and preferred
stock and still have enough left over to satisfy common
shareholders with a sufficient return!

38. 8-38
The Weighted Average
Cost of Capital
 Let’s now consider how this computation will change if
external equity becomes part of the equation.
 Suppose the firm is considering investing up to $100
million in new projects. According to the target capital
structure the following funds will be needed:
 Long-term debt funding = 0.4 x $100 million = $40 million
 Preferred stock funding = 0.1 x $100 million = $10 million
 Common equity funding = 0.5 x $100 million = $50 million

39. 8-39
The Weighted Average
Cost of Capital
 What if the firm expects to have only $20 million of new
retained earnings to help finance this growth when up to
$50 million of equity funding may be required?
 The other $30 million of equity funding could be provided
by a new issue of common stock—external common
equity!
 The cost adjustment for external equity we obtained was
1.61%. When added to our cost of internal equity, we
obtain:
 Ke = 13.33% + 1.61% = 14.94%

40. 8-40
The Weighted Average
Cost of Capital
 The new estimate for the weighted average cost of
capital is:
 ka = .4x5.47% + 0.1x10.31% + 0.2x13.33%
+ .3x14.94% = 10.37%
 We have broken up the weight for equity into 2
components:
 20% for internal equity ($20/$50)
 30% for external equity ($30/$50)
 Therefore, this firm should use 10.37% as the minimum
required rate of return when evaluating investments.

41. 8-41
Using The Weighted Average
Cost of Capital
 A weighted average cost of capital should
always be used to evaluate an investment
project even if all the capital components are
not used to finance the project.
 Thus, even if a project is financed with only
debt, the project should still return at a minimum
the weighted average cost of capital computed
using the firm’s marginal cost of capital and its
target capital structure.

42. 8-42
Summary of Chapter 8 Topics
 Cost of capital measured as an average,
marginal, after-tax cost of long-term sources of
funds
 The weights used to compute a firm’s weighted
average cost of capital reflect the firm’s target
capital structure.

43. 8-43
Summary of Chapter 8 Topics
 The components’ cost of capitals are reflections
of investor-required rates of return. Show how
to compute the cost of funds from:
 Debt
 Preferred stock
 Common equity
 Internal—new retained earnings
 External—new issues of common stock

44. 8-44
Summary of Chapter 8 Topics
 Estimate the weighted average cost of capital.
 The finance decision should be separate from
the investing decision.

45. 8-45
9/20/2022 45
Homework
 Problems:
 1,3,4,6 & Handout