Investor’s required rate of return is not the same as the firm’s cost of capital 1.. Each type of capital used by the firm debt, preferred stock, and common stock should be incorporated
Trang 1
CHAPTER 12 Cost of Capital
CHAPTER ORIENTATION
In Chapters 7 and 8 we considered the valuation of debt and equity instruments Theconcepts advanced there serve as a foundation for determining the required rate of returnfor the firm and for specific investment projects The objective in this chapter is todetermine the required rate of return to be used in evaluating investment projects
CHAPTER OUTLINE
I The concept of the cost of capital
A Defining the cost of capital:
1 The rate that must be earned in order to satisfy the required rate of
return
2 The rate of return on investments at which the price of a firm's
common stock will remain unchanged
B Investor’s required rate of return is not the same as the firm’s cost of capital
1 Each type of capital used by the firm (debt, preferred stock, and
common stock) should be incorporated into the cost of capital, withthe relative importance of a particular source being based on thepercentage of the financing provided by each source of capital
2 Using the cost of a single source of capital as the hurdle rate is
tempting to management, particularly when an investment isfinanced entirely by debt However, doing so is a mistake in logicand can cause problems
II Computing the weighted cost of capital A firm's weighted cost of capital is a
function of (l) the individual costs of capital, (2) the capital structure mix, and (3)the level of financing necessary to make the investment
A Determining individual costs of capital
Trang 21 The before-tax cost of debt is found by trial-and-error by solving for
kd in
d t n
1
t (1 k )
$I
d)k(1
$M
where NPd = the market price of the debt, less flotation
costs,
$It = the dollar interest paid to the investor each
period,
$M = the maturity value of the debt
kd = before-tax cost of the debt (before-tax
required rate of return on debt)
n = the number of periods to maturity
The after-tax cost of debt equals: kd (1 - T)
where T = corporate tax rate
2 Cost of preferred stock (required rate of return on preferred stock),
kps, equals the dividend yield based upon the net price (market priceless flotation costs), or
kps = dividendnet price =
ps
NPD
3 Cost of Common Stock There are two measurement techniques to
obtain the required rate of return on common stock
a dividend-growth model
b capital asset pricing model
4 Dividend growth model
a Cost of internally generated common equity, kcs
kcs = dividendmarket in priceyear1 +
in
growthannual
kcs =
cs
1
PD+ g
Trang 3b Cost of new common stock, kncs
where NPcs = the market price of the common stock less
flotation costs incurred in issuing new shares
5 Capital asset pricing model
kc = krf + (km - krf)where kc = the cost of common stock
krf = the risk-free rate
= beta, measure of the stock's systematic risk
km = the expected rate of return on the market
6 It is important to notice that the major difference between the
equations presented here and the equations from Chapters 7 and 8 isthat the firm must recognize the flotation costs incurred in issuingthe security
B Selection of weights The individual costs of capital will be different for
each source of capital in the firm's capital structure To use the cost ofcapital in investment analyses, we must compute a weighted, or overall, cost
of capital
1 It will be assumed that the company's current financial mix resulting
from the financing of previous investments is relatively stable andthat these weights will closely approximate future financing patterns
2 In computing weights, we could use either the current market values
of the firm's securities or the book values as shown in the balancesheet Since we will be issuing new securities at their current marketvalue, and not at book (historical) values, we should use the marketvalue of the securities in calculating our weights
III PepsiCo approach to weighted average cost of capital
A PepsiCo calculates the divisional cost of capital for its snack, beverage and
restaurant organizations by first finding peer-group firms for each division and using their average betas, after adjusting for differences in financial leverage, to compute the division's cost of equity They also use accounting betas in estimating the cost of equity They then compute the cost of debt foreach division Finally, they calculate a weighted cost of capital for each division
Trang 4B PepsiCo's WACC basic computation
E+ kd[1-T]
where:
kwacc = the weighted average cost of capitalkcs = the cost of equity capital
kd = the before-tax cost of debt capital
T = the marginal tax rateE/(D+E)= percentage of financing from equityD/(D+E)= percentage of financing from debt
C Calculating the Cost of Equity
Based on capital asset pricing model:
kcs = krf + (km - krf)where:
kcs = the cost of common stockkrf = the risk-free rate
= beta, measure of the stock's systematic risk
km = the expected rate of return on the marketBetas for each division are estimated by calculating an average unleveredbeta from a group of divisional peers
The average beta for each division's peer group is unlevered and then levered using that division's target debt-to-equity ratio
re-D Calculating the Cost of Debt
The after-tax cost of debt is equal to:
kd (1 - T)where:
kd = before-tax cost of debt
T = marginal tax rate
Trang 5IV Required rate of return for individual projects
A Using the weighted cost of capital Investments with an internal rate of
return exceeding the weighted cost of capital should be accepted Doing so,
we must assume that the project has similar business risk as existing assets.Otherwise, the weighted cost of capital does not apply
B The weighted cost of capital, kwacc does not allow for varying levels of
project risk We need to specify the appropriate required rates of return forinvestments having different amounts of risk
C Risk also results from the decisions made within the company This risk is
generally divided into two classes:
1 Business risk is the variability in returns on assets and is affected by
the company’s investment decisions
2 Financial risk is the increased variability in returns to the common
stockholder as a result of using debt and preferred stock
ANSWERS TO END-OF-CHAPTER QUESTIONS
12-1 The cost of capital is the rate that must be earned on investments in order to satisfy
the required rate of return of the firm's investors This rate is a function of theinvestors' required rate of return, the corporation's tax rate, and the flotation costsincurred in issuing new securities Therefore, the cost of capital determines the rate
of return that must be achieved on the company's investments, so as to earn thetarget return of the firm's investors Stated differently, the cost of capital is the rate
of return that will leave the price of the common stock unchanged
12-2 Two objectives may be given for determining a company's weighted average cost of
capital:
(1) The weighted average cost of capital is used as the minimum acceptable rate
of return for capital investments The value of the firm should bemaximized by accepting all projects where the net present value is positivewhen discounted at the firm's weighted average cost of capital
(2) The weighted average cost of capital is also used in evaluating a firm’s
historical performance That is, to create shareholder value a firm must notonly earn a profit in the traditional accounting sense, but it must earn areturn on its invested capital that is acceptable to the investors who providethe firm’s financing This “acceptable return” is the firm’s weighted averagecost of capital
12-3 All types of capital, including debt, preferred stock, and common stock, should be
incorporated into the cost of capital computation, with the relative importance of aparticular source being based upon the percentage of financing to be provided.12-4 The effect of taxes on the firm's cost of capital is observed in computing the cost of
debt Since interest is a tax deductible expense, the use of debt indirectly decreases
Trang 6the firm's taxes Therefore, since we have computed the internal rate of return on
an after-tax basis, we also compute the cost of debt on an after-tax basis Incompleting a security offering, investment bankers and other involved individualsreceive a commission for their services As a result, the amount of capital net ofthese flotation costs is less than the funds invested by the individual purchasing thesecurity Consequently, the firm must earn more than the investors' required rate ofreturn to compensate for this leakage of capital
12-5 a Equity capital can be raised by either retaining profits within the firm or by
issuing new common stock Either route represents funds invested by thecommon stockholder The first avenue simply indicates that the commonstockholder permits management to retain capital that could be remitted tothese investors
b Even though a new stock issue does not result from retaining internal
common equity, these funds should not be reinvested unless managementcan reasonably expect to satisfy the investors' required rate of return Inessence, even though no explicit out-of-pocket cost results from retainingthe capital, the cost in measuring a firm's cost of capital is actually theopportunity cost associated with these funds for the investor
c The two popular methods for computing the cost of equity capital include
(1) the dividend-growth model, and (2) the capital asset pricing model Thefirst approach finds the rate of return that equates the present value of futuredividends, assuming a constant growth rate, with the current market price ofthe security The CAPM finds the appropriate required rate of return, giventhe firm's systematic risk
12-6 In general, the relative costs of various sources of capital reflect the riskness of the
source to the investor For example, for a given firm, we would expect debtsecurities to be less risky than preferred stock which is less risky than commonstock Consequently, debt would demand a lower required return than the firm’spreferred stock, which is lower than the required rate of return for common stock
Trang 7SOLUTIONS TO END-OF-CHAPTER PROBLEMS
The following notations are used in this group of problems:
kps = the cost of preferred stock
kcs = the cost of internally generated common funds
kncs = the cost of new common stock
g = the growth rate
kd = the before-tax cost of debt
T = the marginal tax rate
Dt = dollar dividend per share, where Do is the most recently paid
dividend and D1 is the forthcoming dividend
P = the value (present value) of a security
NP = the value of a security less any flotation costs incurred in issuing the
security12-1A
a Net price after flotation costs = $1,125 (1 - 05)
=
)05.1(50.27
$
)07.1(80.1
+ 07
Trang 843
$
50.3+ 07
$
150
$09
)09.01(25
$
)05.01(05.1
$1,000
Rate Value Value
Trang 9For: 11% $1,079.56 $1,079.56
kd% 1,035.0012% 1,000 00
$
56.44
$ 0.01 = 1156 = 11.56%
debtofcost After tax = kd (1 - T)
debtofcost After tax = 11.56% (1 - 0.34) = 7.63%
d kps =
ps
NPD
kcs =
38
$
3+ 0.04 = 11.90%
kncs = $127.45(1(100.06.06))+ 0.06 = 1206 = 12.06%
Trang 1012-4A $958 (1 - 0.11) = $852.62 = the net price (value less flotation
costs)
d
15 1
t (1 k )
$70
d)k(1
$1,000
Rate Value Value For: 8% $914.20 $914.13
kd% 852.629% 839 27
$
58.61
$
50.2
= 7.69%
12-6A NPd = t
d t n
1
t (1 k )
$I
d)k(1
t (1 k )
$120
d)k(1
$
00.55
$ 01 = 1285 = 12.85%
debtofcost After tax = kd(1 - T) = 12.85%(1 - 34) = 8.48%
Trang 1112-7A Cost of preferred stock (kps)
kps =
PriceNet
Dividend
=
ps
NPD
=
$98
$100
x 14%
= 98
=
50.21
$
)15.01(70
0
+ 0.15
= 1874 = 18.74%
12-9A.If the firm pays out 50 percent of its earnings in dividends, its recent earnings must
have been $8 ($4 dividend divided by 5)
Thus, earnings increased from $5 to $8 in five years Using Appendix C andlooking for a table value of 625 ($5/$8), the annual growth rate is approximatelyten percent
a Cost of internal common stock (kcs):
=
58
$
)10.1(
=
)08.01(58
$
40.4
+ 10
=
36.53
$
40.4 + 10
Trang 12
+ 10
)09.01(
000,1
000,500
t (1 k )
$140
+ 10
d)k(1
$ 64 43 $ 69 84
kd = 0.10 + (0.01)
84.69
$
43.64
)09.01(
000,1
= $100 (6.418) + $1,000 (.422)
= $1,063.80
Trang 132 NPd = $1,063.80 (1 - 0.105)
= $952.10
3 Number of Bonds =
10.952
$
000,500
t (1 k )
$100
+ 10
d)k(1
$1,000
Rate Value ValueFor: 10% $1,000.00 $1,000.00
kd% 952.1011% 940 .90
$ 47 90 $ 59 10
kd = 0.10 + (0.01)
10.59
$
90.47
b There is a very slight decrease in the cost of debt because the flotation costs
associated with the higher coupon bond are higher ($138.65 in flotationcosts for the 14 percent coupon bond versus $111.70 for the 10 percentcoupon bond)
12-12A
Source Capital Structure After-tax cost of capital Weighted costCommon Stock 40% 18% 7.2%Preferred Stock 10% 10% 1.0%Debt 50% 8% x (1-.35) 2.6%
kwacc = 10.8%
Trang 14Net price after flotation costs = $975 - $15
= $960.00Cost of debt:
$1,000
Rate Value ValueFor: 6% $1,000.00 $1,000.00
kd% 960.007% 908 .48
$ 40 00 $ 91 52
kd = 0.06 + (0.01)
52.91
$
00.40
Cost of common stock, kncs
=
)05.01(30
$
25.2
Trang 1512-14A
Net price after flotation costs = $1,050 (1-.04)
= $1,008.00Cost of debt:
$1,000
Rate Value ValueFor: 6% $1,096.84 $1,096.84
kd% 1,008.007% 1,000 00
$ 88 84 $ 96 84
kd = 0.06 + (0.01)
84.96
$
84.88
Cost of preferred stock (kps)
kps =
PriceNet
Dividend
=
ps
NPD
=
325
$
00.2
=
22
$2
$
)10.1(3
+ 10
= 166 = 16.6%
Source Market Value Weight After-tax cost of capital Weighted CostBonds $4,000,000 33 4.8% 1.6%Preferred
Stock 2,000,000 .17 9.1% 1.5%Common Stock 6,000,000 50 16.6% 8.3%
12,000,000 1.00 kwacc = 11.4%
Trang 17SOLUTION TO INTEGRATIVE PROBLEM
Nealon, Inc - Weighted Cost of Capital
t (1 k )
$80
$1,000
Rate Value ValueFor: 9% $917.04 $917.04
kd% 879.7510% 843 .92
$ 37 29 $ 73 12
kd = 0.09 + x (0.01)
12.73
$
29.37
Cost of Preferred Stock:
50.1
=
35
$
)06.01(50
2
+ 0.06
= 1357 = 13.57%
Weighted Cost of Capital (kwacc) is calculated as follows:
Weights Costs Weighted Costs
Preferred Stock 15 8.83% 1.32%Common Stock 47 13.57% 6 38%
1.00 kwacc = 10.09%
Trang 18Solutions for Problem Set B
The following notations are used in this group of problems:
kps = the cost of preferred stock
kcs = the cost of internally generated common funds
kncs = the cost of new common stock
g = the growth rate
kd = the before-tax cost of debt
T = the marginal tax rate
Dt = dollar dividend per share, where Do is the most recently paid
dividend and D1 is the forthcoming dividend
P = the value (present value) of a security
NP = the value of a security less any flotation costs incurred in issuing the
security12-1B
a Net price after flotation costs = $1,125 (1 - 06)
= $1,057.50
$1,057.50 = t
d
10 1
t (1 k )
$120
d)k(1
$1,000
Rate Value ValueFor: 11% $1,058.68 $1,058.68
kd% 1,057.5012% 1,000 00
$
18
1 01 = 1102 = 11.02%
debtofcost After tax = kd(1 - T)
debtofcost After tax = 11.02%(1 - 34) = 7.27%