CHAPTER
The Cost of Capital



Sources of capital
Component costs
WACC
9-1
Cost of Capital
The items on the financing side of the balance
sheet are called capital components. The
major capital components are equity,
preference and debt.
Capital like any other factor of production has
a cost.
A company’s cost of capital is the average cost
of the various capital components or securities
employed by it.
Put differently, it is the average rate of return
required by the investors who provide capital
to the company.
9-2
Cost of Capital
Cost of the capital is the central concept in
financial management. It is used for
evaluating investment projects, for
determining the capital structure, for
assessing leasing proposal etc.
9-3
What sources of long-term
capital do firms use?
Long-Term Capital
Long-Term Debt
Preferred Stock
Common Stock
Retained Earnings
New Common Stock
9-4
Concepts of weighted average cost of
capital


A company’s cost of capital is the weighted
average cost of various sources of finance
used by it. For example, Equity, Preference
and Debt.
Suppose that a company uses equity,
preference and Debt in the proportion of 50,
10 and 40. If the component costs of
equity,preference and debt are 16%, 12% &
8% respectively, Calculate WACC.
9-5
Concepts of weighted average cost of
capital
WACC = (proportion of equity)(cost of
equity)+(proportion of preference)(cost of
preference)+(proportion of debt)(cost of debt)
WACC = (.5)(16)+ (.10)(12)+ (.4)(8)
WACC = 12.4%
For the shake of the simplicity, we have ignored
other forms of capital like convertible or callable
preference, convertible or callable debt, bonds with
payment linked to stock market index, bonds that
are puttable or extendable, warrant so on and so
forth.
9-6
Cost of Debts
conceptually the cost of debt instrument is
the yield to maturity of that instrument.
Let us apply this concept to different types of
debt instruments such as Debentures, Bank
Loan and commercial paper.
I+(F - Po)/n
Formula for rd=
0.6 Po+0.4 F
9-7
Cost of Debts
where,
I = annual interest payment
Po = current market price of the debenture
F = Face value
n = remaining period of maturity.
Example,
Face Value
Coupon rate
Remaining period to maturity
Current market price
=
=
=
=
1000
12%
4 years
1040
9-8
Cost of Debts
120+(1000 - 1040)/4
r=
The Yield to maturity or d
0.6 x 1040+0.4 x 1000

The cost of a bank loan is simply the current interest the bank would
charge if the firm were to raise a loan.
For example, Multiplex limited has a Tk. 300 million outstanding bank
loan on which it is paying an interest of 13%.
however, if Multiplex limited were to raise a loan now, the bank would
charge 12%. This then represent the cost of the bank loan.
9-9
Cost of Debts
Commercial paper is a short term debt instrument. Which is
issued at a discount and redeemed at par.
Hence the cost of commercial paper is simply its implicit
interest rate.
For example: Multiplex limited has outstanding commercial
paper that has a balance maturity of 6 months. The face
value of one instrument is Tk. 1,000,000 and it is traded in
the market at Tk. 965,000. The implicit interest rate for 6
months is,
1,000,000
- 1 = 0.0363 or 3.63%.
965,000
Annualized interest rate = (1.0363)2- 1= 0.0739 = 7.39%
9-10
Cost of Debts
When a firm uses different instrument of debt, the average cost of debt has to
be calculated. In our example of Multiplex Limited, the following data on the
debt employed are reviled.
Debt
Instrument
Face value
Market Value Coupon Rate
YTM or
Current rate
NonConvertible
Debenture
Tk. 100 Million
Tk. 104 Million
12%
10.7%
Bank Loan
Tk. 200 Million
Tk. 200 Million
13%
12.0%
Commercial
Paper
Tk. 50 Million
Tk. 48.2
Million
N/A
7.39%
Total Debts Capital employed = 352.25 Million
9-11
Cost of Debts
The average cost of debt is calculated using the market
value proportions and yields/current rate of various debt
instruments.
The Average Cost of Debts of Multiplex Limited = 10.7%
[104/352.25] + 12.0% [200/352.25] + 7.39 [48.25/352.25]
= 10.98%

Tax Adjustment
Post-Tax Cost of Debt = Pre-tax Cost of Debt (1 – Tax rate)
9-12
Cost of Preference
Preference capital carries a fixed rate of dividend and is redeemable in nature.
Given the fixed nature of preference dividend and principal repayment commitment
and the absence of tax deductibility, the cost of preference is simply equal to its
yield.
Problem: Consider the preference stock of Multiplex Limited for which the following
data are given,
Face value
: Tk. 100
Dividend rate
: 11 %
Maturity Period : 5 years
Market Price
: Tk. 95
11 + (100 - 95)/5
The Yield to maturity =
0.6 x 95+0.4 x100
= 12.37%
9-13
Cost of Equity
Equity Finance may be obtained in two ways
(1) Retention of earnings
(2) Issue of additional equity
The cost of equity or the return required by the equity shareholder is the same in
both the cases.
Cost of Equity : The SML Approach
According to SML Approach, the required return on a company’s equity is,
rE= Rf+ β (RM - Rf )
Where,
Rf = Risk free rate
β = beta of the equity of the company
RM = Expected return on the market portfolio.
To use the SML Approach, the following inputs are required Rf = the risk free rate
β = the beta of the equity stock, (RM - Rf ) = the market risk premium.
9-14
Cost of Equity
The Dividend Growth Model Approach
Financial analyst who do not have faith in the SML approach often prefer
Dividend Growth Model to estimate the cost of equity.
D1
D2
P0 =
+
+ …………………….
(1+rE)1
(1+rE)2
Where,
P0 = current price of the stock
Dt=dividend expected to be paid at the end of year t
rE = Equity shareholders required rate of return
If dividend are expected to grow at a constant rate of “g” percent per
year, then Equation becomes,
9-15
Cost of Equity
D1
D1(1+g)
+
(1+rE)2
P0 =
+
(1+rE)1
This simplifies to,
D1
P0 =
rE – g
Solving the above equations for rE we get,
D1
rE=
+g
P0
D0(1+g)
+g
=
P0
D1(1+g)2
+ …………….
(1+rE)3
9-16
Calculating the weighted
average cost of capital
WACC = wErE+ wprp + wdrd(1-T)
Where,
wE = Proportion of Equity
rE = Cost of Equity
Wp = Proportion of Preference
rp = Cost of Preference
Wd = Proportion of Debt
rd = Cost of Debt
9-17
Calculating the weighted
average cost of capital
The cost of specific sources of capital for
“X” company limited are:
rE = 16%
wE = 0.60
rp = 14%
Wp = 0.05
rd = 12%
Wd = 0.35
The Tax Rate for “X” company limited is 30%
Required: Calculate the WACC
9-18
Calculating the weighted
average cost of capital
Source of
Capital
Debt
Proportion
Cost
.60
16%
Weighted
Cost (1)x(2)
9.60%
Preference
.05
14%
0.70%
Equity
.35
12(1-.30)
2.94%
= 8.4%
WACC = 13.24%
9-19
Calculating the weighted Marginal cost of
capital
The relationship between additional financing
and WACC can be estimated by the WMCC.
The procedure for determining WMCC involves

Estimate the cost of each source of financing for
various level of its use.

Identify the level of total new financing at which
the cost of new components would change.
These level is called breaking points, can be
established using the following relationship
TFj
BPj =
Wj
9-20
Calculating the weighted Marginal cost of
capital
BPj = breaking point on account of financing
source j
TFj = Total new financing from source j at
the breaking point
Wj = proportion of financing source j in the
capital structure

Calculate the WACC

Prepare the WMCC schedule
9-21
Calculating the weighted Marginal cost of
capital
Assume “Y” Company Limited plans to use equity and Debt in
the following proportion
Equity : 40
Debt : 60
“Y” Company Limited estimates the cost of its sources of
finance for various levels of usage as follows,
Source of Finance Range of New Financing
Cost
(Taka in Million)
Equity
0 - 30
18%
More than 30
20%
Debt
0 – 50
10%
More than 50
11%9-22
Calculating the weighted Marginal cost of
capital: Determination of Breaking Point
Source of
Capital
Cost
(1)
Range of
new
Financing
(2)
Breaking
point
(Tk. In
Million)
(3)
Range of total new
financing
(Tk. In Million)
(4)
18%
0-30
30/.40 =
75
0 – 75
20%
Above 30
-
Above 75
10%
0-50
50/.60 =
83.3
0 – 83.3
11%
Above 50
-
Above 83.3
Equity
Debt
Firm’s weighted average cost of capital will change at Tk. 75 million and Tk.
83.3 Million.
9-23
Calculating the WACC for various ranges of
Total financing for “Y” Company Limited.
Range of
total new
financing
0-75
Source of
Capital
(1)
Proportion
(2)
Cost %
(3)
Weighted Cost %
(2)x(3)=(4)
Equity
0.4
0.18
0.072
Debt
0.6
0.10
0.060
WACC = .132
75-83.3
Equity
0.4
.20
.080
Debt
0.6
.10
.060
WACC = .140
9-24
Calculating the WACC for various ranges of
Total financing for “Y” Company Limited.
Range of
total new
financing
Source of
Capital
(1)
Above 83.3 Equity
Debt
Proportion
(2)
Cost %
(3)
Weighted Cost %
(2)x(3)=(4)
0.4
.20
0.080
0.6
.11
0.066
WACC = .146
9-25
Calculating the WMCC
Range of Total Financing
(Tk. In Million)
0 – 75
Weighted Marginal Cost
of Capital (%)
75 – 83.3
14.0
Above 83.3
14.6
13.20
9-26
Calculating the weighted Marginal cost of
capital
Assume “Z” Company Limited plans to use equity,preference
and Debt in the following proportion
Equity : 0.45, Preference: 0.05, Debt : 0.50
“Z” Company Limited estimates the cost of its sources of finance for
various levels of usage as follows,
Source of Finance
Range of New Financing
Cost
(Taka in Million)
Equity
0 - 10
15%
10 – 30
16.50%
More than 30
18.00%
Preference
0–1
14.50%
More than 1
15.00%
Debt
0 – 15
7.50%
15 – 40
8.00%
More than 40
8.40%
9-27
Problem
Assume “Z” Company Limited plans to use
equity, preference and Debt in the following
proportion
Equity : 0.45, Preference: 0.05, Debt : 0.50
“Z” Company Limited estimates the cost of its
sources of finance for various levels of usage
as follows,
9-28
Problem
Source of Finance
Equity
Preference
Debt
Range of
New Financing
0 - 10
10 – 30
More than 30
0–1
More than 1
0 – 15
15 – 40
More than 40
Cost
15%
16.50%
18.00%
14.50%
15.00%
7.50%
8.00%
8.40%
9-29
Step 1:
Determining the Breaking points and the
Resulting ranges of Total new financing
Source of Capital
Equity
Preference
Cost
(1)
Range of new
Financing
(2)
Breaking point
(Tk. In Million)
(3)
Range of total new
financing
(Tk. In Million)
(4)
15.00
0 – 10
10/0.45
= 22.22
0 – 22.22
16.50
10 – 30
30/0.45
= 66.67
22.22 – 66.67
18.00
30 and Above
-
66.67 – Above
14.50
0–1
1 / 0.05
= 20.00
-
0 – 20.00
1 and Above
20.00 and above
7.50
0 – 15
15 / 0.50
= 30.00
0 – 30.00
8.00
15 – 40
40 / .50
= 80.00
30.00 – 80.00
8.40
40 and Above
-
80.00 and Above
Debt
9-30
Step 2:
WACC for various range of total new financing
Range of Total
Cost(%)
New Financing
(Tk. In Million)
Source of
Proportion
Cost
Capital
[1]
[2]
0 – 20.00
Equity
Preference
Debt
WACC
0.45
0.05
0.50
15.00
14.50
7.50
6.750
0.725
3.750
11.225
20.00-22.22
Equity
Preference
Debt
WACC
0.45
0.05
0.50
15.00
15.00
7.50
6.750
0.750
3.750
11.250
22.22 – 30.00
Equity
Preference
Debt
WACC
0.45
0.05
0.50
16.50
15.00
7.50
7.425
0.750
3.750
11.925
30.00-66.67
Equity
Preference
Debt
WACC
0.45
0.05
0.50
16.50
15.00
8.00
7.425
0.750
4.000
12.175
[3]
Weighted
[(2) x (3)]
9-31
Step 2:
WACC for various range of total new financing
Range of Total
Cost(%)
New Financing
(Tk. In Million)
Source of
Proportion
Cost
Capital
[1]
[2]
66.67 – 80.00
Equity
Preference
Debt
WACC
0.45
0.05
0.50
18.00
15.00
8.00
8.100
0.750
4.000
12.850
Above 80.00
Equity
Preference
Debt
WACC
0.45
0.05
0.50
18.00
15.00
8.40
8.100
0.750
4.200
13.050
[3]
Weighted
[(2) x (3)]
9-32
Step 3:
Weighted Marginal Cost of Capital Schedule
Range of Total Financing
(Tk. In Million)
0 – 20.00
20.00-22.22
22.22 – 30.00
30.00-66.67
66.67 – 80.00
Above 80.00
Weighted Marginal Cost of Capital
(%)
11.225
11.250
11.925
12.175
12.850
13.050
9-33
Finding a divisional cost of capital:
Using similar stand-alone firms to
estimate a project’s cost of capital

Comparison firms have the following
characteristics:






Target capital structure consists of 40%
debt and 60% equity.
kd = 12%
kRF = 7%
RPM = 6%
βDIV = 1.7
Tax rate = 40%
9-34
Calculating a divisional cost of capital

Division’s required return on equity


Division’s weighted average cost of capital


ks = kRF + (kM – kRF)β
= 7% + (6%)1.7 = 17.2%
WACC = wd kd ( 1 – T ) + wc ks
= 0.4 (12%)(0.6) + 0.6 (17.2%) =13.2%
Typical projects in this division are
acceptable if their returns exceed 13.2%.
9-35