Appendix B - Cost of Capital

8/9/2019 Appendix B - Cost of Capital

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J B GUPTA CLASSES98184931932, [email protected],

www.jbguptaclasses.com

Copyright: Dr JB Gupta

Appendix B

COST OF CAPITALCOST OF CAPITALCOST OF CAPITALCOST OF CAPITAL

THE cost of capital of a firm is the minimum rate of return which the firm must

earn on its investments in order to satisfy the expectations of investors who

provide funds to the firm. It is the weighted average of the cost of various

sources of finance used by it. The method of computing the cost of capital is to

compute the cost of each type of capital and then find the weighted average of all

types of costs of capital. In other words, two steps are involved in determination

of cost of capital of a firm: (i) computation of cost of different sources of capital,

and (ii) determining overall cost of capital of the firm. For example, a companys

capital structure is as follows:

14 per cent debentures of Rs. 10,00,000, 12 per cent Preference share capital

Rs. 5,00,000, Equity share capital Rs. 5,00,000. It is assumed that equity

shareholders of such companies expect 14 per cent dividend. Total capital Rs.

20,00,000. Income tax rate 30%. CDT 15%

Total cost = {(98,000 debenture interest taking tax saving at the rate of 30%) +

(69,000 preference dividend and corporate dividend tax) +( 80500 equity

dividend and corporate dividend tax)} = 2,47,500

2,47,500

Cost of capital = 100 = 12.375 %

20,00,000

This company should earn a minimum rate of return of 12.375 per cent on its

investments in various projects in order to satisfy the expectation of investors

who have provided funds to it. (Surcharge and education cess ignored)

Q .Q .Q .Q .No. 1No. 1No. 1No. 1:::: In considering the most desirable capital structure for a company, the

following estimates of cost of debt and equity capital (after tax) have been made

at various levels of debt-equity mix :

Debt as % of total Cost of Debt Cost of Equity

Capital Employed (%) (%)


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0 5.0 12.0

10 5.0 12.0

20 5.0 12.5

30 5.5 13.0

40 6.0 14.0

50 6.5 16.0

60 7.0 20.0

You are required to determine the optimal debt equity mix by calculating

composite cost of capital. Ignore corporate dividend tax.

AnswerAnswerAnswerAnswer

Debt as % of total CE Overall cost of capital ( Ko) (%)

0 12.00

10 0.10(5.00) + 0.90(12.00) = 11.30

20 0.20(5.00) + 0.80(12.50) =11.00

30 0.30(5.50) + 0.70(13.00) = 10.75

40 0.40(6.00) + 0.60(14.00) = 10.80

50 0.50(6.50) + 0.50(16.00) = 11.25

60 0.60(7.00) + 0.40(20.00) = 12.20

RECOMMENDATION : DEBT : 30%

COMPUTATION OF COSTCOMPUTATION OF COSTCOMPUTATION OF COSTCOMPUTATION OF COST OF DIFFERENT SOURCESOF DIFFERENT SOURCESOF DIFFERENT SOURCESOF DIFFERENT SOURCES OF CAPITALOF CAPITALOF CAPITALOF CAPITAL

Cost of DebtCost of DebtCost of DebtCost of Debt

Cost of debt is that discounting rate at which present value of all future net cash

flows is equal to net cash inflow at the time of raising the debt.

EXAMPLEEXAMPLEEXAMPLEEXAMPLE AAAA

A company raised a debt of Rs.1,00,000 on 1.1.2001, issue expenses Rs.10,000,

interest rate 20 per cent, debt repayable in five equal installments with interest

issue expenses allowed out of taxable income of first year, interest allowed as

deduction out of taxable income of relevant year. Tax rate 50 per cent. Cash

flows are as follows:

01.01.2001 Rs.90,000 Inflow (Received Rs.1,00,000 as loan minusIssue

expenses Rs.10,000).

31.12.2001 Rs.25,000 Outflow (Repayment Rs.20,000 plus interest

Rs.20,000 minus tax saving on issued expenses Rs.5,000

minustax savings on interest Rs.10,000).


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31.12.2002 Rs.28,000 Outflow (Repayment Rs.20,000 plus interest

Rs.16,000 minustax savings on interest Rs.8,000).

1.12.2003 Rs.26,000 Outflow (Repayment plus interest minus tax

savings on it).

31.12.2004 Rs.24,000 Outflow do

31.12.2005 Rs.22,000 Outflow do

Here cost of capital is that discount rate at which present value of all future cash

outflows (Rs.25,000 of 31.12.2001, Rs.28,000 of 31.12.2002, Rs.26,000 of

31.12.2003, Rs.24,000 of 31.12.2004 and Rs.22,000 of 31.12.2005) would beequal to Rs.90,000. Finding of this rate involves following steps:

(i) Find fake pay back period on the basis of average cash outflows. Average

cash flow = (25,000 + 28,000 + 26,000 + 24,000 + 22,000) divided by 5 =

Rs. 25,000. Fake pay back period =

90,000/25000 = 3.60

(ii) Locate the figure of fake pay back period in annuity table against loan

repayment period which is 5 years in this example. The corresponding rate

is 12 per cent.

(iii) Discount future cash flows at the rate locate under (ii). If the present valueof future cash flows is more than net cash inflow at the time of raising the

loan (i.e., Rs. 90,000 in this example), discount future cash flows at higher

rate than the rate located under (ii). If the present value of future cash

flows is less than net cash inflow at the time of raising the loan, discount

the future cash flows at a rate lower than the rate located under (ii) above.

Present value of future cash flows at 12 per cent.

25,000 .893

28,000 .797

26,000 .71224,000 .636

22,000 .567

90,891

As present value of future net cash outflows is more than net cash flow at the time of

raising the loan, we shall go for a higher rate. Let the rate be 17 per cent.


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25,000 .855

28,000 .731

26,000 .624

24,000 .534

22,000 .456

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(iv) Cost of Debt

Lower rate NPV

= Lower rate + Diff. in rates

Lower rate NPV Higher rate NPV

891

= 12 + 5 = 12.45 per cent

891 9085

There are three different situations regarding computation of cost of debt. (1)

Irredeemable debts, (2) Debts redeemable after certain period in lump sum, (3)

Debts redeemable in installments. The above explained method of calculation of

cost of debt is quite lengthy and complicated. It is unavoidable in third situation,

i.e., debts redeemable in installments. In first two situations, almost similar

results can be obtained by simple formula given below:

Irredeemable debt:

Annual interest (1 - Tax rate)

Cost of debt =------ 100

Net proceeds of debt

Debt redeemable after certain period:

(RV NP)

Annual Int. (I T) +

N

Kd= 100

NP+ RV

2

Kd = Cost of debt T = Tax rate

RV = Redeemable value of debt

NP = Net proceeds of debt issue


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N = Term of debt, i.e., numbers of years for which debt would be

outstanding after issue.

Q. No.Q. No.Q. No.Q. No. 2222: A company has 10 per cent non-redeemable debentures of

Rs.5,00,000. Tax rate 40 per cent. Determine cost of capital if debt has been

issued: (i) at par, (ii) at 10 per cent discount, and (iii) at 20 per cent premium.

Answer :Answer :Answer :Answer :

(i) Kd [ 50,000(1-0.40)/ 5,00,000] x 100 = 6.00%

(ii) Kd [ 50,000(1-0.40)/ 4,50,000] x 100 = 6.67%

(iii) Kd [ 50,000(1-0.40)/ 6,00,000] x 100 = 5.00%

Q. No.Q. No.Q. No.Q. No. 3333: A company issued Rs.80,000 12 per cent debentures of Rs.100 each. Tax 40 per

cent, redeemable after 10 years. Floating cost 10 per cent of issue price. Find cost of capital if

issued at: (i) par, (ii) 10 per cent discount, and (iii) 10 per cent premium.

AAAAnswernswernswernswer

(i)

Kd

[12(1 0.40)] + [(100 -90)/10]

---------------------------- x 100 = 8.63%

[ (100 + 90 ) / 2 ]

(ii)Kd [12(1 0.40)] + [(100 -81)/10]---------------------------- x 100 = 10.06%

[ (100 + 81 ) / 2 ]

(iii)

Kd

[12(1 0.40)] + [(100 -99)/10]

---------------------------- x 100 = 7.34%

[ (100 + 99 ) / 2 ]

Q. No.Q. No.Q. No.Q. No. 4444: A company has issued 20 per cent debentures of Rs. 1,00,000. The

floating cost 10 per cent. The company has agreed to repay the debt in five equal

installments starting at the end of first year. Tax 50 per cent. Cost of capital?

Answer :Answer :Answer :Answer : See Answer to Example A

Cost of preference share capitalCost of preference share capitalCost of preference share capitalCost of preference share capital:Calculated exactly in the same way in which

cost of debt capital is calculated with two changes: (i) No tax saving on payment

of preference dividend, and (ii) Payment of corporate dividend tax.

COST OF EQUITY SHARECOST OF EQUITY SHARECOST OF EQUITY SHARECOST OF EQUITY SHARE CAPITALCAPITALCAPITALCAPITAL

The computation of the cost of equity share capital is quite complex because

there are no fixed contractual payment for equity share capital as there are for

debt and preference share capital.


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It is taken as the rate of return expected by equity shareholders. Herein lies

the major difficulty in estimating this cost. How to estimate the expectations of

equity shareholders? Here market price of shares provides help to us. Market

price of share is function of the return that the shareholders expect and they are

likely to get Hence we estimate the rate of return expected by equity

shareholder, (i.e., cost of equity share capital) with the help of market price of

shares and what shareholders are likely to get. There are three methods

regarding estimating the cost of equity capital: (i) Dividend price ratio, (ii)

Dividend price ratio plus growth, and (iii) Earning price ratio. None of these three

methods is free from limitations, yet we use them to get reasonable estimate ofcost of equity capital.

Dividend Price RatioDividend Price RatioDividend Price RatioDividend Price Ratio

The theme of this method is that market price of equity share is equal to present

value of future infinite stream of dividends. Accordingly, cost of equity capital is

that discounting rate at which present value of all future dividends is equal to

current market price of share. Hence, given current market price of shares and

future stream of dividends, we can calculate cost of equity capital. This method

assumes that the company will not earn on its retained earnings and that the

retained earnings will results neither in appreciation of market price of share nor

an increase in dividends. In other words, the method assumes dividend per shareto be same year after year.

D D D

P = + + + ...........................

(1 + Ke)1 (1 + Ke)

2 (1 + Ke)3

D

1 + Ke

P =

1

1

1 + Ke

D D

P = Ke =

Ke P

Ke = Cost of equity capital


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D = Dividend per share

F = Market price per share

Suppose market price of an equity share (face value Rs.100) is Rs.125 and

dividend per share is Rs.15, cost of equity capital

15

= = 0.12. = 12%

125

This method may be used when (i) pay out ratio is 100 per cent, and

(ii) business conditions are to remain stable, with the result that dividend per

share is likely to remain stable year after year.

Dividend Price Ratio plus Growth Method (GordonDividend Price Ratio plus Growth Method (GordonDividend Price Ratio plus Growth Method (GordonDividend Price Ratio plus Growth Method (Gordon----Shapiro ModelShapiro ModelShapiro ModelShapiro Model)

While dividend price ratio method (discussed above) assumes constant amount of

dividend per share year after year, this method (D/P+ growth) assumes dividend

per share to change year after year at constant rate. This rate of change of

dividend is estimated by adjusting the average rate of change of dividend in the

past by possible future variations.

D1 D1 (1 + g) D1 (1 + g)2

P = + + + ...........................

(1 + Ke)1 (1 + Ke)

2 (1 + Ke)3

D1 D1

P = Ke = + g

Ke g P

D1 = Dividend per share at the end of first year (after the date on which priceper share is given)

g = Growth rate of dividend

P = Current market price per share

Ke= Cost of equity capital

Q. No.Q. No.Q. No.Q. No. 5555: Dividend per share is expected to be Rs.1.20 at the end of year and is

expected to grow at 6 per cent per year perpetually. Determine cost of equity

capital if market price is Rs.24 per share.


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1.20

AnswerAnswerAnswerAnswer Ke ==== -------------------------------------------- + 0.06 = 11%

24

Q. No.Q. No.Q. No.Q. No. 6666: Mr. Xhas purchased equity shares of a company which paid a dividend

of Rs.5.00 per share last year. The dividends are expected to grow at 6 per cent

for ever. Find cost of equity capital of the company if Mr. Xpurchased shares at

the rate of Rs.88.33 per share.

5.30

AnswerAnswerAnswerAnswer Ke ==== -------------------------------------------- + 0.06 = 12%

88.33Q. No.Q. No.Q. No.Q. No. 7777: A company paid a dividend of Rs.3 per share last year. Dividends are

expected to growth at 5 per cent per year for next 5 years and at 6 per cent per

year for ever after that. If required rate of return on equity shares is 10 per cent,

find market price of the shares . Suppose today is 1.4.2007. What will be the

market price on the following dates : 31.3.2008, 1.4.2008, 311.3.2009, 1.4.2009,

31.3.2010 and 1.4.2010.


P =P =P =P = [3.15(0.909) + 3.3075(0.826) + 3.4729 (0.751) + 3.6465(0.683) +

3.8288(0.621)] + 3.8288(1.06)1/(1.10)6 +3.8288(1.06)2/(1.10)7 +

3.8288(1.06)3/(1.10)8 +

=

3.8288(1.06)/(1.10)6 2.289

[13.07] + -------------------- = 13.07 + ----------- = 76.03

1.06 0.03636

1 - -------------

1.10

Date Share Price

1.4.2007 76.0300 (Ex 2006-2007 dividend )

31.3.2008 83.6330 (cum 2007-2008 dividend)

1.4.2008 80.4830 (Ex 2007-2008 dividend )

31.3.2009 88.5313 (cum 2008-2009 dividend)

1.4.2009 85.2238 (Ex 2008-2009 dividend )

31.3.2010 93.7462 (Cum 2009-2010 dividend)

1.4.2010 90.2733 (Ex 2009 2010 dividend)


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Q No.Q No.Q No.Q No. 8888: The MD of Smartdeal Ltd has just attended a meeting with an

investment analyst who has suggested that Smartdeals shares are overvalued by

10%. The data used by the investment analyst is shown as below;

Year Total dividend No. of shares Total earnings

2000 1,13,000 57,200 3.65,200

2001 1,22,680 57,200 4,26,400

2002 1,62,160 70,000 5,34,200

2003 2,00,140 80,000 5,72,400

Current share price of Smartdeal equity share is Rs.75. Ke. 12%. Are the shares

overvalued? (ICWA Dec. 2004)


Dividend per share ( 2000) = Rs.1.9755

Dividend per share ( 2003) = Rs.2.5018

g = (2.5018/1.9755)1/3 1

= AL[1/3(log2.5018 log1.9755)] -1

= AL[1/3(0.3982 0.2958)] 1 = 0.081 = 8.10 %

= 1.081 1 = 0.081 = 8.10%

2.50(1.081)

P = ------------------ = 69.29

0.12 0.081

% overvaluation = (5.71/67.50) x 100 = 8.46%

Q. No. 9Q. No. 9Q. No. 9Q. No. 9 On the basis of the following information:

Current Dividend (D0) = Rs.2,50Discount rate (k) = 10.50%

Growth rate (g) = 2%

Calculate the present value of stock of ABC Ltd. Is its stock overvalued if the

stock price is Rs.35, ROE =9% and EPS = Rs.2.25? Show the detailed

calculations. ( Nov.2007)( Nov.2007)( Nov.2007)( Nov.2007)


2.50(1.02)

Value of stock of ABC Ltd. = -------------- = Rs.30

0.1050 0.02


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Payout ratio = 2,50/2,25 = 1.1111

b= -0.1111

r = 0.09

g = -0.009999

2.50(1-.009999)

Value of stock: ---------------------- = 21.52

0.1050 (-0.009999)

The stock is overpriced.

Q. No.Q. No.Q. No.Q. No. 10101010: A company is contemplating an issue of new equity shares. The

current market price is Rs.225 per share. The dividend per share for last fiveyears, has been as follows:

2000 Rs.10.70

2001 Rs.10.30

2002 Rs.13.20

2003 Rs.12.10

2004 Rs.14.03

The floating costs are expected to be 5 per cent of issue price which is

Rs.225.

Determine (a) growth rate in dividends, (b) cost of equity capital assuminggrowth rate calculated by you, (c) cost of equity capital (new shares).

Teaching Note not to be given in the exam. When a firm raises capital by

issuing new shares, it has to incur issue expenses. In this case, the rate of return

the firm should earn on net equity raised should be higher than the rate expected

by equity shareholders. The reason is quite simple. The net funds available to

the firm are less than what equity shareholders contribute. For example, if issue

expenses are 5 per cent and shareholders expected 19 per cent, the firm would

be earning on Rs.95 while shareholders would expect return on Rs.100.

Answer;Answer;Answer;Answer;Growth rate of dividend = [14.03/10.70]

1/4 = 7%

14.03(1.07)

Ke = ----------- + 0.07 = 13.67%

225

14.03(1.07)

Ke ( New Issue) = ----------- + 0.07 = 14.02%

225(1-0.05)

Earning Price RatioEarning Price RatioEarning Price RatioEarning Price Ratio


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As per this method, rate of return required by equity shareholders is equal to

E1 /P where E1 = EPS of first year and P = Market price per share. The

advocates of this approach opine that market price of share depends upon EPS

and is not influenced by dividend policy (i.e., payout ratio). If the payout ratio is

low, there would be lower amount of dividend per share in earlier years but it

will result in higher growth in EPS (low payout ratio means higher retained

earnings, which when invested will push up EPS), the consequence of which will

be higher dividend per share with same payout ratio. If payout ratio is higher,

there should be higher dividend per share in earlier years but its consequence

would be lower growth rate of dividend. In other words, lower payout ratio

results in lower dividends in earlier years but higher dividends in later years.

Higher payout ratio results in higher dividends in earlier year but lower growth

rate in dividends later years. Lower dividends of earlier years (in case of low

payout ratio) are compensated by higher dividends of later years. Higher

dividends of earlier years (in case of high payout ratio) get compensated by

lower growth rate of dividends in later year. Market price of the share is present

value of all future dividends (earlier years as well as later years). Hence it is not

influenced by dividend policy, i.e., pay out ratio. It is influenced by EPS. Hence,

under this method rate of return expected by shareholders is estimated with the

help of EPS and market price of share.

COST OF RETAINED EARCOST OF RETAINED EARCOST OF RETAINED EARCOST OF RETAINED EARNINGSNINGSNINGSNINGS

Retained earnings belong to equity shareholders. Hence, cost of retained

earnings (Kr) is equal to cost of equity (Ke).

OVERALL COST OF CAPIOVERALL COST OF CAPIOVERALL COST OF CAPIOVERALL COST OF CAPITALTALTALTAL

The overall cost of capital of firm is determined by finding the weighted average

cost of different sources of capital. Weights may be based either on book values

of various components of capital or on present market values of various

components of capital. Book value weights are used to find the Ko of existing

capital. Market value weights are used to find the Ko of funds to be raised.

Q.No.Q.No.Q.No.Q.No.11111111: Determine cost of capital using market value weights as well as book

value weights using following data:

Book value of capital structure: Rs.

Debenture (Rs. 1000 each) 16,00,000

Preference shares (Rs. 10 each) 4,00,000

Equity shares (Rs. 100 each) 20,00,000

Market price:


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Debentures Rs.1,100 each

Preference shares Rs.12 each

Equity shares Rs.200 each

Debentures carry 8 per cent interest. Issued at par. Redeemable at par

maturity period 10 years. Floatation cost 10 per cent.

Preference shares carry 10 per cent dividend rate. Issue and redemption at par.

Maturity period 10 years. Floatation cost 10 per cent.

Equity dividend expected at the end of year, i.e., Rs. 20 per share.Anticipated growth rate in dividends is 5 per cent. Corporate tax 30 %. CDT 15%


Cost

Debentures [8(1 0.30)] + [(100 -90)/10]

---------------------------- x 100 = 6.95%

[ (100 + 90 ) / 2 ]

Preference

shares

[1(1 + 0.15)] + [(10 -9)/10]

---------------------------- x 100 = 13.16%

[ (10 + 9 ) / 2 ]

Equity

shares

20

----------- + 0.05 = 15.00%

200

Computation of Overall cost of capital ( Book value weights)

Source of Finance Cost (X) Book Values (W) XW

Debentures 6.95 16L 111.20L

Preference shares 13.16 4L 52.54L

Equity shares 15.00 ( 1.15) 20L 345.00L

W = 40L XW = 508.74L

Ko = XW / W = 508.74L / 40L = 12.72%

Computation of Overall cost of capital ( Market value weights)


Debentures 6.95 17.60L 122.320L

Preference shares 13.16 4.80L 63.168L

Equity shares 15.00 ( 1.15) 40.00L 690.00L

W = 62.40L XW = 875.488


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Ko = XW / W = 875.488L / 62.40L = 14.03%

Q. No.Q. No.Q. No.Q. No. 12121212 : The following items have been extracted from the liabilities side of

balance sheet of XYZ Ltd. as at 31st December 1986.

Paid-up capital: Rs.

4,00,000 equity shares of Rs.10 each 40,00,000

Reserve and surplus 60,00,000

Loans:

15% Non-convertible debentures 20,00,000

14% Loans 60,00,000

Other relevant information:

Year ended

(31st Dec.)

Dividend per

share (Rs.)

EPS

(Rs)

Market price per share in the

beginning of the year (Rs.)

1986 4.00 7.50 50

1985 3.00 6.00 40

1984 4.00 4.50 30

Find weighted average cost using book value weights and earning price ratiomethod as basis of cost of equity.


Growth rate of EPS = (7.50/4.50)1/2 -1= 29.10%

Growth rate of Market Price = (50/30)1/2 -1= 29.10%

7.50(1.291)

Ke = ------------- x 100 = 15%

50(1.291)

Computation of Overall cost of capital ( Book value weights)


Debentures 10.50 20L 210L

Loan 9.80 60L 588L

Equity shares 15.00 100L 1500L

W = 180L XW = 2298L

Ko = XW / W = 2298L / 180L = 12.77%

Q. No.Q. No.Q. No.Q. No. 13131313: GREG Ltd. paid the following equity dividends over the last five years

:


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2000 20

2001 21

2002 29

2003 23

2004 28

Mr. Pinto is considering buying some shares in GREG as he believes that the

dividend will continue to grow. He requires a return of 17 per cent from this type

of investment. How much should he be prepared to pay if the 2004 dividend has

just been paid?


Growth rate of Dividend = (28/20)1/4 -1= 8.78%

D1 28(1.0878)

P = ---------- = ------------- = 370.54

Ke g 0.17 0.0878

Q. No.Q. No.Q. No.Q. No. 14141414: A Ltd. needs finance of Rs.10lakh for meeting its investment plans. It

has Rs.2,10,000 in the form of retained earnings available for investment

purposes. The following are the further details:

1. Debt/equity mix 30%/70%

2. Cost of debt

Up to Rs. 1,80,000 10% (before tax)

Additional amount 16% (before tax)

3. Earnings per share Rs. 4

4. Dividend pay out 50% of earnings

5. Expected growth rate of dividend 10%

6. Current market price per share Rs. 44

7. Tax rate 30%

8. CDT 15%

Compute overall weighted average after tax cost of additional finance.


2.20

Ke = ------------- + 0.10 = 15%

44

Computation of Overall cost of capital

Source of Finance Cost (X) % Weights (W) XW

Debt 7.00 1.80L 12.600L


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Debt 11.20 1.20L 13.440L

Equity shares 15.00(1.15) 4.90L 84.525L

Retained earnings 15.00 2.10L 31.500L

W = 10L XW = 142.065

(It is assumed that the return on retained earnings will be provided by issuing

Bonus shares and not by increasing the dividend.)

Ko = XW / W = 142.065L / 10L = 14.2065%

Documents

Appendix B - Cost of Capital