measurement of cost of capital

7/30/2019 measurement of cost of capital

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Amity Business School

1

Chapter 11

Concept and Measurement of

Cost of Capital




2

CONCEPT AND MEASUREMENT OFCOST OF CAPITAL

Importance and Concept

Measurement of Specific Costs

Computation of Overall Cost ofCapital

Solved Problem

Mini Case

Cost of Capital Practices in India




3

Cost of Capital

The cost of capital is an integral part of investment decisions as it is usedto measure the worth of investment proposal. It is used as a discount ratein determining the present value of future cash flows associated withcapital projects. Conceptually, it is the minimum rate of return that a firm

must earn on its investments so as to leave market price of its sharesunchanged. It is also referred to as cut-off rate, target rate, hurdle rate,required rate of return and so on.

In operational terms, it is defined as the weighted average cost of capital(k 0) of all long-term sources of finance. The major long-term sources offunds are

1) Debt,

2) Preference shares,

3) Equity capital, and

4) Retained earnings.




4

Assumptions

The theory of cost of capital is based on certain assumptions. Abasic assumption of traditional cost of capital analysis is that thefirm’s business and financial risks are unaffected by the acceptanceand financing of projects

Business Risk

Business risk is the risk to the firm of being unable to cover fixed

operating costs.Business risk measures the variability in operating profits [earningsbefore interest and taxes (EBIT)] due to change in sales

Financial Risk

Financial risk is the risk of being unable to cover required financial

obligations such as interest and preference dividends.

Capital budgeting decision determines the business riskcomplexion of the firm. The financing decision determines itsfinancial risk.




5

Explicit and Implicit Costs

Explicit Cost

The explicit cost of capital is associated with the raising of funds (fromdebt, preference shares and equity). The explicit cost of any source ofcapital (C ) is the discount rate that equates the present value of thecash inflows (CI o ) that are incremental to the taking of financingopportunity with the present value of its incremental cash outflows(CO t ). Symbolically,

where CI 0 = initial cash inflow, that is, net cash proceeds received bythe firm from the capital source at time O, CO 1 + CO 2 ... + CO n = cashoutflows at times 1, 2 ... n , that is, cash payment from the firm to thecapital source.

)1(C1

COCI

n

1tt

t

0




6

If CI0 is received in instalments, then, CI0

It is evident from the above mathematical formulation that the explicitcost of capital is the ‘rate of return of the cash flows of the financingopportunity

Implicit Cost

Retained earnings involve no future cash flows to, or from, the firm.

Therefore, the retained earnings do not have explicit cost. However,they carry implicit cost in terms of the opportunity cost of theforegone alternative (s ) in terms of the rate of return at which theshareholders could have invested these funds had they beendistributed to them/or not retained by the firm.

)2(C1

CO...

C1

CO

C1

CO

C1

COC1

CI...

C1

CI

C1

CI

C1

CICI

n

n

3

3

2

2

1

1

n

n

3

3

2

2

1

1

0




7

Measurement of Specific Costs

There are four types of specific costs

1) Cost of Debt

2) Cost of Preference Shares

3) Cost of Equity Capital

4) Cost of Retained Earnings




8

Cost of Debt

Cost of debt is the after tax cost of long-term funds

through borrowing. The debt carries a certain rate of

interest. Interest qualifies for tax deduction indetermining tax liability. Therefore, the effective cost

of debt is less than the actual interest payment made

by the firm by the amount of tax shield it provides.

The debt can be either

1) Perpetual/ irredeemable Debt

2) Redeemable Debt




9

Perpetual Debt

In the case of perpetual debt, it is computed dividing effective interestpayment, i.e., I (1 – t ) by the amount of debt/sale proceeds of debentures orbonds (SV ). Symbolically

ki = Before-tax cost of debtkd = Tax-adjusted cost of debt

I = Annual interest payment

SV = Sale proceeds of the bond/debenture

t = Tax rate

)4(SV

t1Ik

)3(SV1k

d

t




10

Solution

(i) Debt issued at par

Before-tax cost, ki = (Rs 10,000 / Rs 1,00,000) = 10 per cent

After-tax cost, kd = ki (1 – t) = 10% (1 – 0.35) = 6.5 per cent

(ii) Issued at discount

Before-tax cost, ki = (Rs 10,000 / Rs 90,000) = 11.11 per centAfter-tax cost, kd = 11.11% (1 – 0.35) = 7.22 per cent

(iii) Issued at premium

Before-tax cost, ki = (Rs 10,000 / Rs 1,10,000) = 9.09 per cent

After-tax cost, kd = 9.09% (1 – 0.35) = 5.91 per cent

Example 1

A company has 10 per cent perpetual debt of Rs 1,00,000.

The tax rate is 35 per cent. Determine the cost of capital(before tax as well as after tax) assuming the debt is issuedat (i) par, (ii) 10 per cent discount, and (iii) 10 per centpremium.




11

Redeemable Debt

In the case of redeemable debt, the repayment of debt principal (COP)

either in instalments or in lump sum (besides interest, COI) is also takeninto account. kd is computed based on the following equations:

where CI 0 = Net cash proceeds from issue of debentures or from raising debtCOI 1 + COI 2 + ... + COI n = Cash outflow on interest payments in time period 1,2 andso on up to the year of maturity after adjusting tax savings on interest payment.

COP n = Principal repayment in the year of maturity k d = Cost of debt.

The cost of debt is generally the lowest among all sources partly because the riskinvolved is low but mainly because interest paid on debt is tax deductible.

(6)k1

COPt1

k1

COICIs,instalmentinpaidisdebtWhen

/2SVRV

SV/N-RVvalue,Redeemablet1IKely, Alternativ

(5)k1

COPt1

k1

COICIsum,lumpinpaidisprincipalWhen

n

1tt

d

t

t

d

t

0

d

n

1tn

d

n

t

d

t

0




12

Example 2

A company issues a new 10 per cent debentures of Rs 1,000face value to be redeemed after 10 years The debenture is

expected to be sold at 5 per cent discount. It will also involvefloatation costs of 5 per cent of face value. The company’stax rate is 35 per cent. What would the cost of debt be?Illustrate the computations using (1) trial and error approachand (2) shortcut method.

Solution

(1) Trial and Error/Long Approach

Cash Flow Pattern of the Debentures

Years Cashflow

0

1-10

10

+ Rs 900 (Rs 1,000 – Rs 100, that is, par valueless flotation cost less discount)

- Rs 100 (interest outgo)

- Rs 1,000 (repayment of principal at maturity)




13

The value of kd for this equation would be the cost of debt. Thevalue of kd can be obtained, as in the case of IRR, by trial and error.

10

1t 10

dk1

1,000Rst

dk1

65Rs 900Rs

:equationfollowingtheindkof valuethedeterminetoareWe

Determination of PV at 7% and 8% Rate of Interest

Year(s) Cashoutflows

PV factor at Total PV at

7% 8% 7% 8%

1 – 10 Rs 65 7.024 6.710

(Table A-4)

Rs 456.56 Rs 436.15

10 1,000 0.508 0.463(Table A-3)

508.00 ______

964.56

463.00 ______

899.15

The value of kd would be 8 per cent.




14

(2) Shortcut Method

The formula for approximating the effective cost of debt can, as a shortcut,be shown in the Equation

where I = Annual interest payment

RV = Redeemable value of debentures/debt

SV = Net sales proceeds from the issue of debenture/debt(face value of debt minus issue expenses)

Nm = Term of debt

f = Flotation cost

d = Discount on issue of debentures

pi = Premium on issue of debentures

pr = Premium on redemption of debentures

t = Tax rate

(7) /2SVRV

m /Npiprdf t1Id

k

7.9% /21,000Rs900Rs

/1050Rs50Rs0.351100Rsk

d




15

Example 3 A company has issued 10 per cent debentures aggregating Rs1,00,000. The flotation cost is 4 per cent. The company has agreed to repay thedebentures at par in 5 equal annual instalments starting at the end of year 1.The company’s rate of tax is 35 per cent. Find the cost of debt.a

SolutionNet proceeds from the sale of debenture = Rs 96,000.

Since the cash outflows are higher in the initial years than the average (Rs24,500), let us try to determine PV at 7 per cent and 8 per cent.

Cash outflows PV factor at Total PV at

7% 8% 7% 8%

26,500 0.935 0.926 Rs 24,777 Rs 24,539

25,200 0.873 0.857 22,000 21,596

23,900 0.816 0.794 19,502 18,977

22,600 0.763 0.735 17,244 16,61121,300 0.713 0.681 15,187 14,505

98,710 96,228

@Rs 20,000 principal + Rs 10,000 interest (1 – 0.35)

The value of k d = 8 per cent.




16

Cost of Preference Shares

The cost of preference share (k p ) is akin to k d .

However, unlike interest payment on debt, dividend

payable on preference shares is not tax deductiblefrom the point of view assessing tax liability. On the

contrary, tax (D t ) may be required to be paid on the

payment of preference dividend.

• Irredeemable Preference Shares

• Redeemable Preference Shares




17

Irredeemable Preference Shares

The cost of preference shares in the case of irredeemablepreference shares is based on dividends payable on them and thesale proceeds obtained by issuing such preference shares, P0 (1 – f ). In terms of equation:

where k p = Cost of preference capitalD p = Constant annual dividend payment

P 0 = Expected sales price of preference shares

f = Flotation costs as a percentage of sales price

D t = Tax on preference dividend

)A8(f 1P

D1Dk

)8(f 1P

DK

0

tp

p

0

p

p




18

Example 4

A company issues 11 per cent irredeemable preference shares of the facevalue of Rs 100 each. Flotation costs are estimated at 5 per cent of theexpected sale price. (a) What is the k

p , if preference shares are issued at (i)

par value, (ii) 10 per cent premium, and (iii) 5 per cent discount? (b) Also,compute k p in these situations assuming 13.125 per cent dividend tax

Solution

%2.12

05.0195Rs

11Rs

)iii(

%5.1005.01110Rs

11Rs

)ii(

%6.1105.01100Rs

11Rs

)i()a(

p

p

p

k

DiscountatIssued

k

PremiumatIssued

k

paratIssued

%8.1325.90Rs

44.12Rs

)iii(

%9.115.104Rs

44.12Rs

)ii(

%1.1395Rs

44.12Rs)13125.1(11Rs

)i()b(

p

p

p

k

DiscountatIssued

k

PremiumatIssued

k

paratIssued




19

Redeemable Preference Shares

The cost of redeemable preference shares requiring lump sumrepayment (P ) is determined on the basis of the following equation:

where P 0 = Expected sale price of preference shares

f = Floatation cost as percentage of P 0

D p = Dividends paid on preference shares

P n = Repayment of preference capital amount

(9)

k1

P

k1

1Df 1P

:sinstalmentinrequiredrepaymentof casetheIn

k1

P

k1

1Df 1P

n

1tt

p

t

t

p

tp

0

n

1tn

p

n

t

p

tp

0

D

D




20

Example 5

ABC Ltd has issued 11 per cent preference shares of the face value of Rs100 each to be redeemed after 10 years. Flotation cost is expected to be 5per cent. Determine the cost of preference shares (k

p ).

Solution

cent.per11isdividendofratetheascentper12and11betweenbetolikelykofvalueThe p is

k 1

100Rs

k 1

11Rs95Rs

10

1t10

pt

p

Determination of PV at 11% and 12%

Year Cashoutflows

PV factor at Total PV at

11% 12% 11% 12%

1 – 10 Rs 11 5.889 5.65 Rs 64.78 Rs 62.1510 100 0.352 0.322 35.15

99.93

32.20

94.35

Kp=11.9 per cent




21

The computation of cost of equity capital (k e ) isconceptually more difficult as the return to the equity-holders solely depends upon the discretion of the

company management. It is defined as the minimumrate of return that a corporate must earn on theequity-financed portion of an investment project inorder to leave unchanged the market price of the

shares. There are two approaches to measure k e :

1) Dividend Valuation Model Approach

2) Capital Asset Pricing Model (CAPM) Approach.

Cost of Equity Capital

Di id d V l ti A h




22

As per the dividend approach, cost of equity capital is defined as the

discount rate that equates the present value of all expected futuredividends per share with the net proceeds of the sale (or the currentmarket price) of a share.

The cost of equity capital can be measured with the following equations:

(A) When dividends are expected to grow at a uniform rate perpetually:

where D 1 = Expected dividend per share

P 0 = Net proceeds per share/current market price

g = Growth in expected dividends

Dividend Valuation Approach

(12)gP

Dk(11)

gk

DP

getwe10,Eq.gSimplifyinequation.theof

sidestwotheequateswhichrate)(discountreturnof ratetheis10Eq.ink

(10)k1

g1D

k1

g1D...k1

g1D

k1

g1Df 1P

0

1

e

e

1

0

e

n

1tt

e

1t

1n

e

n

02

e

2

01

e

1

00




23

The calculation of k e on the basis of Eq. 12 is based on certain

assumptions with respect to the behaviour of investors and their

ability to forecast future values:

the market value of shares depends upon the expected dividends;

investors can formulate subjective probability distribution of

dividends per share expected to be paid in various future periods;

the initial dividend, D 0, is greater than zero (D 0 > 0);

the dividend pay-out ratio is constant;

investors can accurately measure the riskiness of the firm so as

to agree on the rate at which to discount the dividends.

Note: Under the provisions of Section 115(O), of the Income Tax Act,

1961, a domestic company is liable to pay tax at a flat rate of 11.5 percent (plus surcharge) on dividends declared/distributed/paid on/after

April 1, 2003. The payment of the dividend tax will reduce the growth

(g ) in dividends:




24

(B) Under different growth assumptions of dividends over theyears:

Equation 12 will have to be modified to take into account two (ormore, if necessary) growth rates. The solution in the followingEquation 13 for k e would give the cost of equity capital:

higher.bewouldDtwithoutgObviously,

A)(12P

D1DPSEPS

EPS

Dt1DPSEPS

P

EPSb.r g

EPS/Pr

taxDividendDtwhere

EPS

Dt1DPSEPS

EPS

Dt1DPS1b

return.of rater rate,retentionbwhereb.r,g

0

t

0

0

yearslater ingrowthConstantg

yearsearlier ingrowthof Ratewhereg

(13)k1

g1D

k1

g1DP

c

h

n

1t 1ntt

e

1t

cn

t

e

1t

b0

0




25

Example 6

Suppose that dividend per share of a firm is expected to be Re 1 per sharenext year and is expected to grow at 6 per cent per year perpetually.Determine the cost of equity capital, assuming the market price per share is

Rs 25.

Solution: This is a case of constant growth of expected dividends. The k e canbe calculated by using Equation

The dividend approach can be used to determine the expectedmarket value of a share in different years. The expected value of ashare of the hypothetical firm in Example 6 at the end of years 1 and2 would be as follows

%1006.025Rs1Rs

g

0

P1

D

ek

28Rs0.060.10

1.124Rs

gek3

D

2P(ii)

26.50Rs0.060.10

1.06Rs

gek2

D)

1(Pyearfirsttheof endtheatPrice(i)




26

Example 7

From the undermentioned facts determine the cost of equity shares ofcompany X:

(i) Current market price of a share = Rs 150.

(ii) Cost of floatation per share on new shares, Rs 3.

(iii) Dividend paid on the outstanding shares over the past five years:

Year Dividend per share

1

2

3

4

5

6

Rs 10.50

11.02

11.58

12.16

12.76

13.40

(iv) Assume a fixed dividend pay out ratio.(v) Expected dividend on the new shares at the end of the current year is Rs

14.10 per share.




27

Solution

As a first step, we have to estimate the growth rate in

dividends. Using the compound interest table (Table A-1), the

annual growth rate of dividends would be approximately 5 per

cent. (During the five years the dividends have increased from

Rs 10.50 to Rs 13.40, giving a compound factor of 1.276, that is,

Rs 13.40/Rs 10.50. The sum of Re 1 would accumulate to Rs

1.276 in five years @ 5 per cent interest).

%6.14%53Rs150Rs147Rs

10.14Rske




28

CAPITAL ASSET PRICING MODEL

(CAPM) APPROACH

The CAPM describes the relationship between the required rate of return orthe cost of equity capital and the non-diversifiable or relevant risk of thefirm as reflected in its index of non-diversifiable risk, that is, beta.Symbolically,

Ke = Rf + b (Km – Rf ) (14)

Rf = Required rate of return on risk-free investmentb = Beta coefficient**, and

Km = Required rate of return on market portfolio, that is, the average rate orreturn on all assets

M = Excess in market return over risk-free rate,

J = Excess in security returns over risk-free rate,

MJ = Cross product of M and J and

N = Number of years

22 MNM

JMNMJ**




29

Example 8

The Hypothetical Ltd wishes to calculate its cost of equity

capital using the capital asset pricing model approach. From

the information provided to the firm by its investment advisors

along with the firms’ own analysis, it is found that the risk-free

rate of return equals 10 per cent; the firm’s beta equals 1.50

and the return on the market portfolio equals 12.5 per cent.

Compute the cost of equity capital.

SolutionKe = 10% + [1.5 × (12.5% – 10%)] = 13.75 per cent




30

Example 9: As an investment manager you are given the following

information

Investment in equity

shares of

Initial

price

Dividends Year-end

market price

Beta risk

factor

A Cement Ltd

Steel Ltd

Liquor Ltd

B Government of India

Bonds

Risk-free return, 8 per cent

Rs 25

35

45

1,000

Rs 2

2

2

140

Rs 50

60

135

1,005

0.80

0.70

0.50

0.99

You are required to calculate (i) expected rate of returns of market portfolio,and (ii) expected return in each security, using capital asset pricing model

S l ti




31

Solution

(i) Expected Returns on Market Portfolio

Security Return Investment

Dividends Capital

Appreciation

Total

A Cement Ltd

Steel Ltd

Liquor Ltd

B Government

of India Bonds

Rs 2

2

2

140

146

Rs 25

25

90

5

145

Rs 27

27

92

145

291

Rs 25

35

45

1,000

1.105

Rate of return (expected) on market portfolio = Rs 291/Rs 1,105 = 26.33 percent

(ii) Expected Returns on Individual Security (in percent)

k e = R f + b (k m – R f )Cement Ltd = 8% + 0.8 (26.33% – 8%) 22.66

Steel Ltd = 8% + 0.7 (26.33% – 8%) 20.83

Liquor Ltd = 8% + 0.5 (26.33% – 8%) 17.16

Government of India Bonds = 8% + 0.99 (26.33% – 8%) 26.15




32

The capital assets pricing model (CAPM) approach to calculate thecost of equity capital is different from the dividend valuationapproach in some respects. In the first place, the CAPM approachdirectly considers the risk as reflected in beta in order to determine

the K e . The valuation model does not consider the risk; it rather usesthe market price as a reflection of the expected risk-return preferenceof investors in the market.

Secondly, the dividend model can be adjusted for flotation cost toestimate the cost of the new equity shares. The CAPM approach is

incapable of such adjustment as the model does not include themarket price which has to be adjusted.

Both the dividend and CAPM approaches are theoretically sound. Butmajor problems are encountered in the practical application of theCAPM approach in collecting data—which may not be readily

available or in a country like India may be altogether absent—regarding expected future returns, the most appropriate estimate ofthe risk-free rate and the best estimates of the security’s beta .




33

Cost of Retained Earnings

The cost of retained earning (k r ) is equally difficult to

calculate in theoretical terms. Since retained earnings

essentially involves use of funds, it is associated with an

opportunity/implicit cost. The alternative to retained earnings

is the investment of the funds by the firm itself in a

homogeneous outside investment. Therefore, k r is equal to

k e . However, it might be slightly lower than k e in the case of

new equity issue due to flotation costs.




34

Computation of Overall Cost of Capital

Weighted Average Cost of Capital

Weighted average cost of capital is the expected averagefuture cost of funds over the long run found by weighting thecost of each specific type of capital by its proportion in the

firm;s capital structure.

Assignment of Weights

The aspects relevant to the selection of appropriate weightsare:

1) Historical weights

a) Book value weights or

b) Market value weights

2) Marginal Weights




35

Historical Weights Historic weights either book ormarket value weights are based on actual capital

structure proportion to calculate weights.

Market Value Weights Market value weights use market

values to measure the proportion of each type of capitalto calculate weighted average cost of capital.

Book Value Weights Book value weights use accounting

(book) values to measure the proportion of each type of

capital to calculate the weighted average cost of capital

Marginal Weights Marginal weights use proportion of

each type of capital to the total capital to be raised.




36

Mechanics of Computation

Example 10: Book Value Weights

(a) A firm’s after-tax cost of capital of the specific sources is as

follows:Cost of debt

Cost of preference shares (including dividend tax)

Cost of equity funds

8%

14

17

(b) The following is the capital structureSource Amount

Debt

Preference capital

Equity capital

Rs 3,00,000

2,00,000

5,00,000

10,00,000

(c) Calculate the weighted average cost of capital, k0 usingbook value weights.

Table 1: Solution Computation of weighted average cost of capital (Book




37

Table 1: Solution Computation of weighted average cost of capital (BookValue Methods)

Source of funds

(1)

Amount

(2)

Proportion

(3)

Cost (%)

(4)

Weighted cost(3 x 4)

(5)

Debt

Preference capital

Equity capital

Rs 3,00,000

2,00,000

5,00,000

10,00,000

0.3 (30)

0.2 (20)

0.5 (50)

1.00 (100)

0.08

0.14

0.17

0.024

0.028

0.085

0.137

Weighted average cost of capital 13.7%

An alternative method of determining the k 0 is to compute, as shown in Table 2, the totalcost of capital and then divide this figure by the total capital. This procedure obviouslyavoids fractional calculations.

TABLE 2 Computation of Weighted Average Cost of Capital (Alternative Method)

Sources Amount Cost (%) Total cost (2 × 3)

(1) (2) (3) (4)DebtPreference capitalEquity capital

Total

Rs 3,00,0002,00,0005,00,000

10,00,000

81417

Rs 24,00028,00085,000

1,37,000

Weighted average cost of capital = [(Rs 1,37,000 / Rs 10,00,000) x 100] = 13.7 per cent

Example 11 (Market Value Weights)




38

Example 11 (Market Value Weights)

From the information contained in Example 10, calculate the weighted averagecost of capital, assuming that the market values of different sources of fundsare as follows:

Source Market valueDebt Rs 2,70,000

Preference shares 2,30,000

Equity and retained earnings 7,50,000

Total 12,50,000

Solution

(1) The determination of the market value of retained earnings presentsoperational difficulties. The market value of retained earnings can be indirectlyestimated. A possible criterion has been suggested by Gitman,19 according towhich, since retained earnings are treated as equity capital for purpose of

calculation of cost of specific source of funds, the market value of the ordinaryshares may be taken to represent the combined market value of equity sharesand retained earnings. The separate market values of retained earnings andordinary shares may be found by allocating to each of these a percentage ofthe total market value equal to their percentage share of the total based onbook values.




39

On the basis of the foregoing criterion, the sum of Rs 7,50,000 in Example 11 is

allocated between equity capital and retained earnings as follows:

Source of funds Book value Per cent of book value Market value

(1) (2) (3) (4)

Equity shares Rs 4,00,000 80 Rs 6,00,000*

Retained earnings 1,00,000 20 1,50,000**

*(0.8 × Rs 7,50,000) **(0.20 × Rs 7,50,000)

(2) After the determination of market value, k0 is calculated as shown in Table 3.

TABLE 3 Computation of Weighted Average Cost of Capital (Market Value Weights)

Sources Market value Cost (per cent) Total cost (3 × 2)

(1) (2) (3) (4)

Debt Rs 2,70,000 8 Rs 21,600

Preference shares 2,30,000 14 32,200

Equity capital 6,00,000 17 1,02,000

Retained earnings 1,50,000 17 25,500

Total 12,50,000 1,81,300

k0 = (Rs 1,81,300/Rs 12,50,000) × 100 = 14.5 per cent




40

Solution The computation is illustrated in Table 4.

TABLE 4 Weighted Average Cost of Capital (Marginal Weights)

Sources of funds Amount Proportion Cost (%) (2 × 4) Total cost

(1) (2) (3) (4) (5)

Debt Rs 3,00,000 0.60 (60) 8 Rs 24,000

Preference

shares

1,00,000 0.20 (20) 14 14,000

Retained earnings 1,00,000 0.20 (20) 17 17,000

5,00,000 1.00 (100) 55,000

Weighted average cost of capital = (Rs 55,000/Rs 5,00,000) × 100 = 11 per cent

Example 12 The firm of Example 10 wishes to raise Rs 5,00,000 for expansion of its

plant. It estimates that Rs 1,00,000 will be available as retained earnings and thebalance of the additional funds will be raised as follows:

Long-term debt Rs 3,00,000

Preference shares 1,00,000Using marginal weights, compute the weighted average cost of capital.




41

COST OF CAPITAL PRACTICES IN INDIA

The main features of the cost of capital practices followed by the corporates in Indiaare as follows:

The most frequently used (67 per cent of cases) discount rate (i.e., minimum

acceptable/required rate of return) to evaluate capital budgeting decision isbased on the overall cost (WACC) of the corporate.

Depending on the risk characteristics of the project, multiple risk-adjusteddiscount rates are used by about one-fifth of the corporate enterprises.

The specific cost of capital used to finance the project (i.e. if the discount rate fora project that will be financed entirely with retained earnings is the cost of

retained funds) is used by one-fourth of the sample corporates.The CAPM is the most popular method of estimating the cost of equity capital (54

per cent). The Gordon’s dividend model is equally popular method to computethe cost of equity capital (52 per cent). The earnings yield approach is used byone-third of the sample corporates to estimate the cost of equity capital. The useof the multi-factor model is used by very few corporates (7 per cent).

A significant feature of the methods used to estimate the cost of equity capital isthat while the CAPM is significantly used by the large corporates, the Gordon’s discount model is more popular with small firms. Moreover, the highly profitablecorporate (based on ROCE and EAV) give significantly low importance todividend yield and earnings yield to compute the cost of equity capital than theless profitable corporates.

CONTD.




42

The Government of India (GOI) 10-year bonds are the most widely used risk-freerate to compute the cost of capital using the CAPM approach. The industryaverage beta is the most popular measure of the systematic risk used by thecorporates. Each of the published sources of beta and the self-calculated betaare also used by about one-fifth of the corporates respectively.

The self-calculated beta is more popularly used by the large and/highly profitablecorporates. The small and low profitable corporates rely more on the publishedsources of beta.

The majority of corporates (two-thirds) considers the last 5-year monthly shareprice data to estimate the equity beta. The highly profitable firms use weeklyshare price data for the purpose.

The average market risk premium (9-10 per cent) is the most widely usedmeasure by the corporates. The average of historical return and the impliedreturn on the market portfolio are also fairly popular as an input while using theCAPM.

As regards the cost of debt, the most widely used method is the interest taxshield (i.e., tax advantage of interest on debt).

While the majority of the corporates revise their estimates of cost of capitalannually, some of the sample corporates continuously revise it with everyinvestment.

Apart from project choice criterion, the cost of capital is also used widely for (a)divisional performance measurement , (b) EVA computation and (c) CVAcomputations.

CONTD




43

Majority of the sample companies adopt theoretically sound andconceptually correct basis of determining the cost of capital, namely, theweighted average cost of long-term sources of finance. However, there is no

systematic procedure followed to compute it. It is more likely to be subjectivein nature. The Indian corporates use of mix of the WACC, marginal cost ofcapital of additional funds and management judgment in this regard.

There is wide divergence in the corporate practices as regards thecomputation of the cost of equity capital. About one-tenth of the corporatesdo not attach any cost to equity capital. Another one-tenth treat the cost of

equity capital as equivalent to primary rate of return available on securities ofbalanced mutual funds and debentures issued by blue chip companies.

However, the vast majority of companies (two-thirds of the sample) follow theconceptually sound methods (i.e. primary rate of return plus risk premium,dividend valuation model and CAPM) of determining the cost of equitycapital.

About one-fifth of the sample corporates consider retained earnings as acost-free source of finance. However, a sizeable proportion of the samplecompanies (75 per cent) regard cost of retained earnings either as equivalentto opportunity cost of using these funds by the corporate/equity-holders orequal to the cost of equity capital.

CONTD.




44

SOLVED PROBLEM




45

As a financial analyst of a large electronics company, you are required to

determine the weighted average cost of capital of the company using (a) book

value weights and (b) market value weights. The following information is

available for your perusal.

The company’s present book value capital structure is:

Debentures (Rs 100 per debenture) Rs 8,00,000

Preference shares (Rs 100 per share) 2,00,000

Equity shares (Rs 10 per share) 10,00,000

20,00,000

All these securities are traded in the capital markets. Recent prices are:

Debentures, Rs 110 per debenture

Preference shares, Rs 120 per share

Equity shares, Rs 22 per share




46

Anticipated external financing opportunities are:

(i) Rs 100 per debenture redeemable at par; 10 year maturity, 11 per cent

coupon rate, 4 per cent flotation costs, sale price, Rs 100.

(ii) Rs 100 preference share redeemable at par; 10 year maturity, 12 per centdividend rate, 5 per cent flotation costs, sale price, Rs 100.

(iii) Equity shares: Rs 2 per share flotation costs, sale price = Rs 22.

In addition , the dividend expected on the equity share at the end of the year is

Rs 2 per share; the anticipated growth rate in dividends is 7 per cent and the

firm has the practice of paying all its earnings in the form of dividends. The

corporate tax rate is 35 per cent.

Solution: Determination of specific costs:

17%0.0720Rs

2Rsg

f 1P

D)(ksharesequityof (iii)Cost

12.8%100295Rs100Rs

105Rs12Rs

2SVRV

Nf D )(ksharespreferenceof (ii)Cost

7.7%100296Rs100Rs

104Rs0.3511Rs

2SVRV

Nf t)-1(1 )(kdebt,of (i)Cost

0

1

e

m

p

m

d

Using these specific costs we can calculate the book value and market value




47

Using these specific costs we can calculate the book value and market valueweights as follows:

(a) k0 based on book value weights

Source of capital Book value (BV) Specific cost (k) (%) Total costs [BV (×) k]

Debentures Rs 8,00,000 7.7 Rs 61,600Preference shares 2,00,000 12.8 25,600

Equity shares 10,00,000 17.0 1,70,000

20,00,000 2,57,200

k0 = Rs 2,57,200/Rs 20,00,000 = 12.86 per cent

(b) k0 based on market value weights

Source of capital Market value

(MV)Specific cost (k) (%) Total costs [MV (×) k]

Debentures Rs 8,80,000 7.7 Rs 67,760

Preference shares 2,40,000 12.8 30,720

Equity shares 22,00,000 17.0 3,74,000

Total capital 33,20,000 4,72,480

k0 = Rs 4,72,480/Rs 33,20,000 = 14.23 per cent




48

MINI CASE



D t Sh i f

Sh i f S&P CNX




50

Date Share price ofInfotech Ltd

Share price ofCantaxy Ltd

S&P CNXNifty

February 28 Rs 115 Rs 28 976

March 29 125 26 985

April 30 140 21 991

May 31 167 20 1035

June 28 189 20 1049

July 31 177 15 989

August 30 142 19 977September 30 121 21 965

October 31 102 32 956

November 29 94 29 951

December 31 102 31 957

January 31 126 28 962

February 28 149 39 975

Calculate beta for Infotech Limited and Cantaxy Limited. Use S&P CNX Nifty data asa proxy for market portfolio and comment.




51

Solution

Y = Return on security

X = Return on market portfolio (index)

N = Total number of observations

X = (Market index level on last trading day of ‘t’ month – Market index

level on last trading day of ‘t – 1’ month) × 100]/Market index

level on last trading day of ‘t – 1’ month.

Y = Price of share on last trading day of ‘t’ month – Price of share on

last trading day of ‘t – 1’ month) × 100)/Price of share on last

trading day of ‘t – 1’ month.

22 XXN

YXN

BETA

-XY

Determination of beta in respect of equity shares of Infotech Limited




52

Determination of beta in respect of equity shares of Infotech Limited

Date Infotechlimited

S&PCNXNifty

Return onInfotech limited

Return onNifty index

Y X X × Y X2

February 28March 29April 30May 31June 28July 31

August 30September 30October 31November 29December 31January 31February 28

115125140167189177

14212110294102126149

976985991

10351049989

977965956951957962975

8.7012.0019.2913.17 –6.35

–19.77 –14.79 –15.70 –7.848.51

23.53

18.25

0.920.614.441.35 –5.72

–1.21 –1.23 –0.93 –0.520.630.52

1.35

8.027.31

85.6317.8236.32

23.9918.1614.644.105.37

12.29

24.67

0.850.37

19.711.83

32.72

1.471.510.870.270.400.27

1.83Sum 38.99 0.21 258.33 62.10

Average 3.25 0.02

Observations (N) 12

BETA = 12 × 258.33 – (0.21 × 38.99)/12 × 62.10 – (0.21 × 0.21) = 4.15

Determination of beta in respect of equity shares of Cantaxy Limited



Amity Business SchoolDate Cantaxy

limitedS&P CNXNifty

Return onInfotechlimited

Return onNifty index

Y X X × Y X2

February 28March 29April 30May 31June 28July 31August 30September 30October 31November 29December 31January 31February 28SumAverage

Observations(N)

28262120201519213229312839

97698599110351049989977965956951957962975

–7.14 –19.23 –4.76 –0.00 –25.0026.6710.5352.38 –9.386.90 –9.6839.2960.575.05

12

0.920.614.441.35 –5.72 –1.21 –1.23 –0.93 –0.520.630.521.350.210.02

–6.59 –11.71 –21.14

0.00142.99 –32.36 –12.93 –48.85

4.904.35 –5.0653.0966.70

0.850.37

19.711.83

32.721.471.510.870.270.400.271.83

62.10

BETA = 12 × 66.70 – (0.21 × 60.57)/12 × 62.10 – (0.21 × 0.21) = 1.06

Comment: Since the beta of Infotech Limited is substantially higher (4.15) than that ofCantaxy Limited (1.06), the equity shares of Infotech Limited are evidently more riskycompared to those of Cantaxy Limited.

measurement of cost of capital

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