Chapter 6 Cost of Capital

CHAPTER FIVE
COST OF CAPITAL
The Cost of Capital
 The Cost of Capital is the required return for a capital
budget.
 It is the opportunity cost of funds tied up in the
project.
 It is the rate of return at which investors are willing to
provide financing for the project today.
 It reflects the risk of the project.
Components of capital
Debt
Preferred equity
Common stock equity:
 Internal- retained earnings
 External- new issues of common stock
N.B. Non interest bearing sources like A/P
and Accruals are not components of
capital.
1. Cost of debt (Kd)
is the after-tax cost today of raising funds through borrowing.
Steps
1st step, Determine the net proceeds per debt(bond) to the firm
issuing the value of the bond (usually 1000 birr) after the cost of
selling the bond to the firm is deducted.
2nd step, Determine the effective before-tax-cost-of-debt (bond)
use the net proceeds from the bond issue as a time zero cash
inflows. i.e, interest rate that equalize NPV=0 (present value of
interest + principal) = Net proceed. Ki=using present value of annuity
Ki = pmt(
3rd, Determine the after-tax-cost-of-debt= K d = Ki(1-T)

Example
Assume that the Ethiopian Government
(National Bank of Ethiopia) sells bond
issues for 20 million Birr that is to mature in
25 years time. Each bond is expected to
have a par value of 1000 Birr and carries a
coupon interest rate of 12 percent. The
income tax rate is assumed to be 40 percent.
The government (NBE) nets for 985 Birr per
bond. Compute the specific (component)
cost of debt (bond) capital to the
The annual interest payment equals 1000x12% = 120 Birr per bond per
year. Thus, the 120 Birr will be paid as an interest per bond for the
coming 25 years. In addition, the principal (face) value of the bond
(i.e. 1000Birr) will be paid at the end of the 25 years at maturity).
Net present value= (Proceed from sale of bond). (Present value of
interest payments annuity)-(present value of principal payment at
maturity)

NPV 12% = 985 – [120 (PVIFA12%,25)] – 1000 (PVlF 12%,25)
=985 – 941.17 – 58.80 = 985 – 1000
= -15
NPV 13% = 985 – [120 (PvlFA 13%,25) – 1000 (PVlF 13%,25)
=985 – 879.60 – 47 = 985 –927
= +58
Hence, the cost of debt before-tax = Kd = 12% + 15/73%
=12% + 0.21% = 12.21%, or
Kd = 13% -58/73%
= 13% - 0.79% = 12.21%
After-tax specific cost of capital of debt=Kd(1-T)
=12.21% (1-0.40)
=7.33%
Therefore, the Ethiopian Government is required to pay an effective
cost-of-capital of debt after-tax of 7.33 percent on the bond it has
issued.
If the Ethiopian Government sells the bonds at a net proceed of
1000Birr per bond which is equal to the principal (par value) of the
bond, the sum of the present values of the series payments and the
present value of the principal payment at maturity of the bond is equal
to the proceed at time zero at the discounting rate that is equal to the
bond’s coupon rate, that is 12 percent.
Net, present value (12%) = 1000 – [120 (PVIFA 12%25)] – 1000 (PVIF
12%,25)
= 1000 – [120(7.8431)] – 1000 (0.0588)
= 1000 – 1000 = 0
After-tax specific cost of debt (bond)of capital = Kd-KdT
= 12% - (12%)(0.40)
The cost of debt tends to be the
least expensive of the other forms
of financing sources for two
reasons:
 Bond holders have greater
security than preferred or
common stockholders
 Interest is tax deductible.
2. Cost o f preferred stock (Kp)
The cost of preferred stock is the today’s cost of using preferred
stock to raise funds.
Kp = Dp/Pn
Eg. 2. Duchess Company is contemplating issuance of a 10%
preferred stock that is expected to sell for its $87 per share par
value. The cost of issuing and selling the stock is expected to be $5
per share. What is the cost of the stock?
Pd=10% * 87 =8.7
Kp= 8.7/82 = 10.61%
No tax adjustments are made when calculating the specific cost
capital of preferred stock (Kps) because preferred dividend unlike
interest expenses on debt, are non-tax deduct able, hence there are
not tax saving associated with use of preferred stock as a source of
capital.
3. The cost of common stock
Two sources:
1. Internal – Retained earnings
2. External - new issues of common stock
Three methods:
A. The discounted cash flow approach

B. The CAPM= Ks = KRF + β(Km –KRF)
C. The bond-yield-plus-premium approach
Ks = Co.’s own bond yield + Risk Premium on
common stock over Co. bonds
Comparison:
CAPM: helps to directly incorporate risk in the cost of capital.
DCF: helps to incorporate floatation costs
The specific (component) cost of capital of common stock
is the minimum rate of return that the business firm must
earn for its common shareholders in order to maintain the
market value of the firm’s equity.
When the firm sells its common stock issue and nets for
Pn Birr amount per share, it can set the net proceeds equal
to the stocks’ intrinsic value because investors have been
willing to acquire the security at the price that nets the
firm an amount of Pn Birr. The intrinsic value of common
stock is estimate by using an equation:
V = Do (1+g) Where Do = Current dividend per
share
 K-g g = Compound dividend
growth rate
This equation is used to compute the intrinsic value of the share
of common stock that returns an indefinite dividend stream.
In addition, dividends on common shares are assumed to
grow at a given growth compound rate each year.
Then the market interest (discount) rate (k) is a measure of
specific (component) cost of capital of common stock is given by
the symbol Ke.
To determine the value of Ke, we equate Pn and v; Pn=V
Pn = Do (1+g) because V = Do (1+g)

K-g Ke = D (1+9) + 9
o K- g
P
Substituting Ke K in the above equation, you get;
n
Pn = Do (1+g)
Ke-g
Solving for specific cost of capital of common stock (ke)
from the above equation, you arrive at:

Pn (Ke – g) = Do (1+g)
Ke = Do (1+g) + g
Ke –g =Do (1+ g)
Pn
Pn
Example
Assume that Nib international Bank (NIB) sells
an issue of common stock to potential investors in
the country. The selling price per the common
share of the bank is 20 Birr. The bank incurs a
selling (flotation) cost of 2.50 Birr per share. The
current dividend of the bank’s common share is
2.00 Birr per share and expected to grow a 5
percent annual compound rate.
Compute the specific cost of capital of common
stock of Nib International Bank.
 The net proceeds per share = Pn = Selling price – Flotation cost
 = 20-2.50 = 17.50 Birr per share
 = 0.12 + 0.05 = 0.17 or 17%
4. Specific Cost of Retained Earnings
There are two difficulties with computing the specific
(component) cost of capital of retained earnings.
Both of these difficulties arise from the nature of the
retained earnings.
Retained earnings are an internal, as opposed to external
source of funds.
First, retained earnings are not securities, like that of stocks and
bonds. Thus, they do not have market values/prices that can be
used to compute their specific cost of capital.
Second, since retained earnings do not represent funds provided
directly by common stock holders (investors), there may be a
tendency to equate the specific cost of capital of retained earnings
with zero.
The approach that is used to measure the specific cost of capital of
retained earnings is to realize that retained earnings represent profits
earned during the current year and available to common shareholders
that the business firm decides to reinvest in itself rather than payout as
dividends.
Thus, the shareholders are made to reinvest part of their earnings in the
firm. In return, the shareholders expect the firm to earn a rate of return
on these retained fund which is at least equal to the rate earned on the
outstanding common stock.
Both the outstanding common stock and the retained earnings belong
to the common stockholder’s equity and the shareholders expect
similar returns on both capital sources. Therefore, the specific cost of
capital of retained earnings is estimated on the bases on the specific
cost of capital of common stock.
The other logic behind attaching the specific cost of capital of retained
earnings to that of common stock is that the market price of common
stock is the reflection of the performance of the business firm which is,
to the same extent, measured by the amount of net profit after tax that
Therefore, it is reasonable to estimate the
specific cost of capital of retained earnings based
on the market value of common share (Po),
current dividend per common share (Do), and
compound dividend growth rate per year (g) but
ignoring the selling (flotation) costs since
retained earnings are not marketable securities.
Hence, Specific cost of capital of retained
earnings = Kr = Do (1+g)
+g
Po
Where, Do = Current dividend per common share
G = Compound dividend growth rate
WEIGHTED AVERAGE COST OF
CAPITAL
It reflects, on the average, the firm’s cost

of long-term financing.
WACC= (Wd x Kd) + (Wp x Kp) + (WRE x
KRE)+(WE x KE)
Weights may be based on:
target capital structure
 market value or
 book value.
Example 4: The following relates to XY Company.
Source of Finance
Cost (after tax) Book Value Market value
Debt 5.6% 100,000 100,000
Preferred stock 10.6% 75,000 100,000
Retained Earnings 13% 125,000 300,000
Common Stock 14% 100,000
Required: Determine the WACC for XY Co.

assuming that weights are based on:
a)Book value
b)Market value

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CHAPTER FIVE

3rd, Determine the after-tax-cost-of-debt= K d = Ki(1-T)

A. The discounted cash flow approach

It reflects, on the average, the firm’s cost

Debt 5.6% 100,000 100,000

Preferred stock 10.6% 75,000 100,000

Retained Earnings 13% 125,000 300,000

Common Stock 14% 100,000

Required: Determine the WACC for XY Co.

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