1. CHAPTER The Cost of Capital
Sources of capital
Component costs
WACC

2. 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.

3. 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.

4. What sources of long-term capital do firms use?

5. 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.

6. 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.

7. 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

8. 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 = 1000
Coupon rate = 12%
Remaining period to maturity = 4 years
Current market price = 1040

9. Cost of Debts
120+( )/4
The Yield to maturity or rd=
0.6 x 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.

10. 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 = or 3.63%.
965,000
Annualized interest rate = (1.0363)2- 1= = 7.39%

11. 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
Non-Convertible Debenture
Tk. 100 Million
Tk. 104 Million
12%
10.7%
Bank Loan
Tk. 200 Million
13%
12.0%
Commercial Paper
Tk. 50 Million
Tk Million
N/A
7.39%
Total Debts Capital employed = Million

12. 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] % [200/352.25] [48.25/352.25]
= 10.98%
Tax Adjustment
Post-Tax Cost of Debt = Pre-tax Cost of Debt (1 – Tax rate)

13. Cost of Preference 11 + (100 - 95)/5
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 + ( )/5
The Yield to maturity =
0.6 x x100
= 12.37%

14. 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.

15. 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,

16. Cost of Equity D1 D1(1+g) D1(1+g)2 P0 = + + + …………….
(1+rE)1 (1+rE)2 (1+rE)3
This simplifies to, D1
P0 =
rE – g
Solving the above equations for rE we get,
rE= + g P0
D0(1+g)
= g

17. 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

18. 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

19. Calculating the weighted average cost of capital
Source of Capital
Proportion
Cost
Weighted Cost (1)x(2)
Debt
.60
16%
9.60%
Preference
.05
14%
0.70%
Equity
.35
12(1-.30)
= 8.4%
2.94%
WACC = 13.24%

20. 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

21. 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

22. 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 %
More than %
Debt 0 – %
More than %

23. Range of total new financing
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
(4)
Equity
18%
0-30
30/.40 = 75
0 – 75
20%
Above 30 -
Above 75
Debt
10%
0-50
50/.60 = 83.3
0 – 83.3
11%
Above 50
Above 83.3
Firm’s weighted average cost of capital will change at Tk. 75 million and Tk Million.

24. Range of total new financing
Calculating the WACC for various ranges of Total financing for “Y” Company Limited.
Range of total new financing
Source of Capital
(1)
Proportion
(2)
Cost %
(3)
Weighted Cost %
(2)x(3)=(4)
0-75
Equity
0.4
0.18
0.072
Debt
0.6
0.10
0.060
WACC = .132
.20
.080
.10
.060
WACC = .140

25. Range of total new financing
Calculating the WACC for various ranges of Total financing for “Y” Company Limited.
Range of total new financing
Source of Capital
(1)
Proportion
(2)
Cost %
(3)
Weighted Cost %
(2)x(3)=(4)
Above 83.3
Equity
0.4
.20
0.080
Debt
0.6
.11
0.066
WACC = .146

26. Calculating the WMCC Range of Total Financing (Tk. In Million)
Weighted Marginal Cost of Capital (%)
0 – 75
13.20
75 – 83.3
14.0
Above 83.3
14.6

27. 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 %
10 – %
More than %
Preference 0 – %
More than %
Debt 0 – %
15 – %
More than %

28. 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,

29. Problem Source of Finance Range of Cost New Financing
Equity %
10 – %
More than %
Preference 0 – %
More than %
Debt – %
15 – %
More than %

30. Range of total new financing
Step 1: Determining the Breaking points and the Resulting ranges of Total new financing
Source of Capital
Cost
(1)
Range of new Financing
(2)
Breaking point
(Tk. In Million)
(3)
Range of total new financing
(4)
Equity
15.00
0 – 10
10/ = 22.22
0 – 22.22
16.50
10 – 30
30/ = 66.67
22.22 – 66.67
18.00
30 and Above -
66.67 – Above
Preference
14.50
0 – 1
1 and Above
1 / 0.05
= 20.00
0 – 20.00
20.00 and above
Debt
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

31. Step 2: WACC for various range of total new financing
Range of Total Source of Proportion Cost Weighted Cost(%)
New Financing Capital
(Tk. In Million) [1] [2] [3] [(2) x (3)]
0 – Equity
Preference
Debt
WACC
Equity
Preference
WACC
22.22 – Equity
WACC
Equity
Debt
WACC

32. Step 2: WACC for various range of total new financing
Range of Total Source of Proportion Cost Weighted Cost(%)
New Financing Capital
(Tk. In Million) [1] [2] [3] [(2) x (3)]
66.67 – Equity
Preference
Debt
WACC
Above Equity
Debt
WACC

33. Step 3: Weighted Marginal Cost of Capital Schedule
Range of Total Financing Weighted Marginal Cost of Capital
(Tk. In Million) (%)
0 –
22.22 –
66.67 –
Above

34. Comparison firms have the following characteristics:
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%

35. Calculating a divisional cost of capital
Division’s required return on equity
ks = kRF + (kM – kRF)β
= 7% + (6%)1.7 = 17.2%
Division’s weighted average cost of capital
WACC = wd kd ( 1 – T ) + wc ks
= 0.4 (12%)(0.6) (17.2%) =13.2%
Typical projects in this division are acceptable if their returns exceed 13.2%.