PROJECT APPRAISAL PLANNING AND CONTROL

1. CHAPTER 10
THE COST OF CAPITAL

2. OUTLINE
. Some preliminaries
· Cost of debt and preference
· Cost of equity: the CAPM approach
· Cost of equity: other approaches
. Determining the proportions
· Weighted average cost of capital
· Weighted marginal cost of capital
· Determining the optimal capital budget
· Floatation costs and the cost of capital
· Factors affecting the weighted average cost of capital
· Misconceptions surrounding cost of capital
· How institutions calculate cost of capital

3. Company Cost of Capital and
Project Cost of Capital
 The company cost of capital is the rate of return expected by the
existing capital providers.
 The project cost of capital is the rate of return expected by capital
providers for a new project the company proposes to undertake.
 The company cost of capital (WACC) is the right discount rate for
an investment which is a carbon copy of the existing firm.

4. Cost of Debt
n I F
P0 =  +
t = 1 (1 + rD)t (1 + rD)n
P0 = current price of the debenture
I = annual interest payment
n = number of years left to maturity
F = maturity value
rD is computed through trial-and-error. A very close
approximation is:
rD = I + (F – P0)/n
0.6P0 + 0.4F

5. Illustration
Face value = 1,000
Coupon rate = 12 percent
Period to maturity = 4 years
Current market price = Rs.1040
The approximate yield to maturity of this debenture is :
120 + (1000 – 1040) / 4
rD = = 10.7 percent
0.6 x 1040 + 0.4 x 1000

6. Cost of Preference
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.

7. Illustration
Face value : Rs.100
Dividend rate : 11 percent
Maturity period : 5 years
Market price : Rs.95
Approximate yield :
11 + (100 – 95) / 5
= 12.37 percent
0.6 x 95 + 0.4 x 100

8. Cost of Equity
 Equity finance comes by way of (a) retention of earnings and (b)
issue of additional equity capital.
 Irrespective of whether a firm raises equity finance by retaining
earnings or issuing additional equity shares, the cost of equity is
the same. The only difference is in floatation cost.
 Floatation costs will be discussed separately.

9. Approaches to Estimate Cost of Equity
• CAPM Approach
• Dividend Yield Plus Risk Premium Approach
• Dividend Discount Model Approach
• Earnings-price Approach

10. CAPM Approach
 It is useful to decompose the total risk associated with a security
into two components:
Total risk = Unique risk + Market risk
 Since the unique risk of a security can be diversified away,
whereas the market (or systematic) risk cannot be diversified
away, the CAPM suggests that investors are compensated only for
learning the systematic risk.

11. CAPM
The CAPM is reflected in the following equation that relates the
expected return on an investment to its systematic risk.
E(Ri) = Rf + [ E(RM) – Rf] βi
where: E(Ri) = expected return on security i
Rf = risk-free rate
E (RM) = expected return on the market portfolio
βi = the systematic risk of the security

12. Inputs Required for Applying CAPM
 Risk-free Rate
 Rate on a short-term government security (Treasury bill)
 Rate on a long-term government security that has a maturity of
10 years and more.
 Market Risk Premium
 Historical risk premium
 Forward looking risk premium
 Beta
 Beta of a security is the slope of the following regression
relationship
Rit = i + βiRMt + eit

13. Calculation of Beta
Rit = i + i RMt + eit
iM
i =
M
2

14. Period
Return on
stock A, RA
Return on
market
portfolio, RM
Deviation of
return on stock A
from its mean
(RA - RA)
Deviation of
return on market
portfolio from its
mean (RM - RM)
Product of the
deviation,
(RA - RA)
(RM - RM)
Square of the
deviation of
return on market
portfolio from its
mean
(RM - RM)2
1 10 12 0 3 0 9
2 15 14 5 5 25 25
3 18 13 8 4 32 16
4 14 10 4 1 4 1
5 16 9 6 0 0 0
6 16 13 6 4 24 16
7 18 14 8 5 40 25
8 4 7 -6 -2 12 4
9 - 9 1 -19 -8 152 64
10 14 12 4 3 12 9
11 15 -11 5 -20 -100 400
12 14 16 4 7 28 49
13 6 8 -4 -1 4 1
14 7 7 -3 -2 6 4
15 - 8 10 -18 1 -18 1
RA = 150 RM = 135 (RA - RA) (RM - RM) 2
RA =10 RM = 9 (RM - RM) = 221 = 624
Calculation of Beta

15. Estimation Issues
 Estimation period
 A longer estimation period provides more data but the risk profile .. firm
may change
 5 Years
 Return Interval
 Daily, Weekly, Monthly
 Market Index
 Standard Practice
Adjusting Historical Beta
 Historical Alignment … Chance factor
 A Company’s Beta May Change over time
Merill Lynch … 0.66 … Historical Beta
0.34 … Market Beta

16. Application of CAPM in Practice
In a survey of companies that use CAPM for estimating the cost of equity, Manoj
Anand found that the risk-free rate of return, beta, and market risk premium are
estimated as follows:
Risk-free Rate
% of companies
• 91 days GOI treasury bill rate 15.91
• 3-7 years GOI treasury bond rate 18.18
• 10 years GOI treasury bond rate 65.91
Beta
% of companies
• Published source 20.45
• CFO’s estimate 15.91
• Industry average 52.27
• Self-calculated 18.18

17. Bond Yield Plus Risk Premium Approach
Yield on the
long-term bonds
of the firm
Should the risk premium be 2 percent, 4 percent, or n percent? There
seems to be no objective way of determining it.
Cost of =
equity
+ Risk premium

18. Dividend Growth Model Approach
If the dividend per share grows at a constant rate of g percent.
D1
P0 =
rE – g
D1
So, rE = + g
P0
Thus, the expected return of equity shareholders, which in equilibrium
is also the required return, is equal to the dividend yield plus the
expected growth rate

19. Earnings – Price Ratio Approach
According to this approach, the cost of equity is equal to :
E1 / P0
where E1 = expected earnings per share for the next year
P0 = current market price per share
E1 may be estimated as : (Current earnings per share) x (1+ growth rate of
earnings per share).
This approach provides an accurate measure of the rate of return required by equity
investors in the following two cases:
 When the earnings per share are expected to remain constant and the dividend
payout ratio is 100 per cent.
 When retained earnings are expected to earn a rate of return equal to the rate of
return required by equity investors.
The first case is rarely encountered in real life and the second case is also somewhat
unrealistic. Hence, the earnings price ratio should not be used indiscriminately as
the measure of the cost of equity capital.

20. How Companies Estimate the Cost of Equity
A survey of corporate finance practices in India by Manoj Anand revealed
that the following methods (in the order of decreasing importance) are
followed by companies in India to estimate the cost of equity.
% companies
considering as very
important or important
• Capital asset pricing model 54.3
• Gordon’s dividend discount model 52.1
• Earnings – yield (Earnings per share/ 34.2
Market price per share,
• Dividend – yield 26.2
• Multifactor model 7.0
Source: Manoj Anand, “Corporate Finance Practices in India: A Survey,” Vikalpa, October – December 2002,

21. Determining the proportions or weights
 The appropriate weights are the target capital structure weights
stated in market value terms.
 The primary reason for using the target capital structure is that the
current capital structure may not reflect the capital structure
expected in future.
 Market values are superior to book values because in order to justify
its valuation the firm must earn competitive returns for shareholders
and debtholders on the current (market) value of their investments.

22. Weighted Average Cost of Capital (WACC)
WACC = wErE + wprp + wDrD (1 – tc)
wE = proportion of equity
rE = cost of equity
wp = proportion of preference
rp = cost of preference
wD = proportion of debt
rD = pre-tax cost of debt
tc = corporate tax rate

23. WACC
Source of Capital Proportion Cost Weighted Cost
(1) (2) [(1) x (2)]
Debt 0.60 16.0% 9.60%
Preference 0.05 14.0% 0.70%
Equity 0.35 8.4% 2.94%
WACC = 13.24%

24. Some Problem Areas in Cost of Capital
• Privately owned firms
• Measurement problems
• Derivative securities
• Capital structure weights

25. Determining the Optimal Capital Budget
10 20 30 40 50 60 70 80 90 100 110 120 130 140
10
11
12
13
14
15
16
17
18
A
B
C
D
E
Marginal Cost of Capital Curve
Optimal Capital Budget
Amount (in million rupees)
14.6%
14.0%
13.2%
Return,
Cost (%)
Investment Opportunity Curve

26. Floatation Cost
 Floatation or issue costs consist of items like underwriting costs,
brokerage expenses, fees of merchant bankers, underpricing cost, and
so on.
 One approach to deal with floatation costs is to adjust the WACC to
reflect the floatation costs:
WACC
Revised WACC =
1 – Floatation costs
 A better approach is to leave the WACC unchanged but to consider
floatation costs as part of the project cost.

27. Factors Affecting the Weighted Average Cost of Capital
• Factors Outside a Firm’s Control
• The level of interest rates
• Market risk premium
• Tax rates
• Factors within a Firm’s Control
• Investment policy
• Capital structure policy
• Dividend policy

28. Misconceptions Surrounding Cost of Capital
 The concept of cost of capital is too academic or impractical.
 Current liabilities (accounts payable and provisions) are considered as capital
components.
 The coupon rate on the firm’s existing debt is used as the pre-tax cost of debt.
 When estimating the market risk premium in the CAPM method, the historical
average rate of return is used along with the current risk-free rate.
 The cost of equity is equal to the dividend rate or return on equity.
 Retained earnings are either cost free or cost significantly less than external
equity.
 Depreciation has no cost.
 Book value weights may be used to calculate the WACC.
 The cost of capital for a project is calculated on the basis of the specific
sources of finance used for it.
 The project cost of capital is the same as the firm’s WACC.

29. How Financial Institutions Calculate Cost of Capital
Financial institutions calculate cost of capital as post-tax weighted
average cost of the mix of funds employed for the project.
The cost for different sources of funds are taken as follows:
 Equity share capital : 15%
 Cash accruals/Retained earnings : 15%
 Preference share capital : Preference dividend rate
 Subsidy/Incentive loans : Zero cost
 Debt : Post-tax rate of interest
(Long-term loans, non-convertible
debentures, deferred credits, bank
borrowings for working capital,
unsecured loans from public)
 Convertible debenture : Convertible portion at 15%
Non-convertible portion at
post-tax interest rate

30. Means of Amount Cost of Total Cost
Financing (Rs. in million) Funds (post-tax)
(A) (B) (C) (D)= C x B
1. Equity and cash accruals 900 15% 135
2. Preference share capital 100 10% 10
3. Rupee term loans (@14%) 800 10.5% 84
4. Non-convertible debentures 400 9% 36
(@12%)
5. Convertible portion of 100 15% 15
convertible debentures
6. Non-convertible portion of 100 7.5% 7.5
convertible debentures (@10%)
7. Bank borrowing for 200 11.25% 22.5
working capital (@15%)
2600 310
The average cost of capital (post-tax) is : 310 / 2600 = 11.92%
Cost of Capital Calculation

31. SUMMARY
 Capital, like any other factor of production, has a cost. A company’s cost of capital
is the weighted average cost of the various sources of finance used by it, viz.,
equity, preference, long-term debt, and short-term debt.
 Note that many companies leave out the cost of short-term debt while calculating
the weighted average cost of capital (WACC). In principle, this is not correct.
Investors who provide short-term debt also have a claim on the operating earnings
of the firm. So, if a company ignores this claim, it will misstate the rate of return
required by its investors.
 WACC is a central concept in financial management. It is used for evaluating
investment projects, for determining the capital structure, for setting the rates that
regulated organisations like electric utilities can charge to their customers, so on
and so forth.
 In general, if a firm uses n different sources of capital its WACC is :
 piri

32.  Two basic conditions should be satisfied for using the company’s WACC for
evaluating new investments: (a) The risk of new investments is the same as the average
risk of existing investments. (b) The capital structure of the firm will not be affected by
the new investments. Thus strictly speaking, WACC is the right discount rate for a
project that is a carbon copy of the firm’s existing business. However, in practice
WACC is used as a benchmark hurdle rate that is adjusted for variations in risk and
financing patterns.
 Since debt and preference stock entail more or less fixed payments, estimating the cost
of debt and preference is relatively easy.
 A company raises debt finance through a variety of instruments like debentures, bank
loans, and commercial paper. The cost of debt is the weighted average rate of different
kinds of debt employed by it.
 The weighted average rate of debt is calculated using the market values and yields to
maturity of various debt instruments. Note that we use the yields to maturity or the
current rates as they reflect the rates at which the firm can raise new debt. Since
interest on debt is a tax-deductible expense, the pre-tax cost of debt has to be adjusted
for the tax factor to arrive at the post- tax cost of debt.
 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 deductability, the cost of preference is simply equal to its yield.

33.  Equity earnings may be obtained in two ways: (i) retention of earnings and (ii) issue
of additional equity. The cost of equity or the return required by equity shareholders is
the same in both the cases. Remember that when a firm decides to retain earnings, an
opportunity cost is involved.
 A popular approach to estimating the cost of equity is the security market line (SML)
relationship. According to the SML, the required return on a company’s equity is:
Rf + bi ( E(RM ) - Rf)
Analysts who do not have faith in the SML approach often resort to a subjective
procedure to estimate the cost of equity. They add a judgmental risk premium to the
observed yield on the long-term bonds of the firm to get the cost of equity.
 According to the dividend growth model approach, the cost of equity is equal to:
Dividend yield + Expected growth rate in dividends
 For calculating the WACC we multiply the cost of each source of capital by the
proportion applicable to it. These proportions may be based on book values or target
capital structure or market values. Market value proportions are generally
recommended unless market values are not available or are highly unreliable or
distorted.

34.  WACC tends to rise as the firm seeks more and more capital. This happens
because the supply schedule of capital is typically upward sloping – as suppliers
provide more capital, the rate of return required by them tends to increase.
 A Schedule or graph showing the relationship between additional financing and
WACC is called the weighted marginal cost of capital schedule.
 When projects have risks that are substantially different from those of the overall
firm, applying WACC can potentially lead to poor decisions. In such cases, the
expected return must be compared with the risk-adjusted required return.
 To determine the optimal capital budget, you have to compare the expected return
on proposed capital expenditure projects with the marginal cost of capital
schedule.
 When a firm raises finance by issuing equity and debt, it almost invariably incurs
floatation or issue costs, comprising of items like underwriting costs, brokerage
expenses, fees of merchant bankers, under-pricing costs, so o`n and so forth.
 There are two ways of handling floatation costs. One approach is to adjust the
WACC to reflect the floatation costs. A better approach is to leave the WACC
unchanged but to consider floatation costs as part of the project cost.

35.  The cost of capital is affected by several factors, some beyond the control of the
firm and others depending on the investment and financing policies of the firm.
 Despite the importance of cost of capital in financial management, we find that
several misconceptions characterise its application in practice. The more serious
ones are : (i) The cost of capital is too academic or impractical, (ii) The cost of
equity is equal to the dividend rate or return on equity, (iii) Retained earnings are
either cost free or cost significantly less than external equity, (iv) Depreciation has
no cost, (v) The cost of capital can be defined in terms of an accounting-based
measure, (vi) If a project is financed heavily by debt, its WACC is low.