© tata mcgraw-hill publishing company limited, financial management 11-1 concept and measurement of...

© Tata McGraw-Hill Publishing Company Limited, Financial Management © Tata McGraw-Hill Publishing Company Limited, Financial Management © Tata McGraw-Hill Publishing Company Limited, Financial Management © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-11-11

11-11-11

Concept and Measurement Concept and Measurement of Cost of Capitalof Cost of Capital


11-11-22

Measurement of Specific CostsMeasurement 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


11-11-33

Cost of DebtCost 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 in determining 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


11-11-44

Perpetual DebtPerpetual Debt

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

ki = Before-tax cost of debt

kd = Tax-adjusted cost of debt

I = Annual interest paymentSV = Sale proceeds of the bond/debenturet = Tax rate

)4(

1

)3(

SV

tIk

SV

Ik

d

t


11-11-55

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 cent

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


11-11-66

Redeemable DebtRedeemable 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 taken into account. kd is computed based on the following equations:

where CI0 = Net cash proceeds from issue of debentures or from raising debtCOI1 + COI2 + ... + COIn = Cash outflow on interest payments in time period 1,2 and so on up to the year of maturity after adjusting tax savings on interest payment.COPn = Principal repayment in the year of maturity kd = Cost of debt.

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

(6)

k1

COPt1

k1

COICI s,instalment in paid is debt When

(5) /2SVRV

SV/N-RV value, Redeemablet1IKely,Alternativ

n

1tt

d

tt

d

t0

d


11-11-77

Example 2

A company issues a new 10 per cent debentures of Rs 1,000 face value to be redeemed after 10 years The debenture is expected to be sold at 5 per cent discount. It will also involve floatation costs of 5 per cent of face value. The company’s tax rate is 35 per cent. What would the cost of debt be? Illustrate the computations using shortcut method.


11-11-88

(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 paymentRV = Redeemable value of debentures/debtSV = Net sales proceeds from the issue of debenture/debt

(face value of debt minus issue expenses)Nm= Term of debt

f = Flotation costd = Discount on issue of debenturespi = Premium on issue of debenturespr = Premium on redemption of debenturest = Tax rate

(7)

/2SVRVm/Npiprdft1I

dk

7.9%

/21,000Rs900Rs

/1050Rs50Rs0.351100Rsk d


11-11-99

Example 3 A company has issued 10 per cent debentures aggregating Rs 1,00,000. The flotation cost is 4 per cent. The company has agreed to repay the debentures 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

Solution

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

Since the cash outflows are higher in the initial years than the average (Rs 24,500), 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 16,611

21,300 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 kd = 8 per cent.


11-11-1010

Cost of Preference SharesCost of Preference Shares

The cost of preference share (kp) is akin to kd. However, unlike interest payment on debt, dividend payable on preference shares is not tax deductible from the point of view assessing tax liability.

n Irredeemable Preference Shares

n Redeemable Preference Shares


11-11-1111

Irredeemable Preference SharesIrredeemable Preference Shares

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

where kp = Cost of preference capitalDp = Constant annual dividend paymentP0 = Expected sales price of preference

sharesf = Flotation costs as a percentage of sales

priceDt = Tax on preference dividend

)A8(

f1P

D1Dk

)8(f1P

DK

0

tp

p

0

p

p


11-11-1212

Example 4

A company issues 11 per cent irredeemable preference shares of the face value of Rs 100 each. Flotation costs are estimated at 5 per cent of the expected sale price. (a) What is the kp, if preference shares are issued at (i) par value, (ii) 10 per cent premium, and (iii) 5 per cent discount? (b) Also, compute kp in these situations assuming 13.125 per cent dividend tax

Solution

%2.1205.0195Rs

11Rs

)iii(

%5.1005.01110Rs

11Rs

)ii(

%6.1105.01100Rs

11Rs

)i()a(

p

p

p

k

Discountat Issued

k

Premiumat Issued

k

parat Issued

%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

Discountat Issued

k

Premiumat Issued

k

parat Issued


11-11-1313

Redeemable Preference SharesRedeemable Preference Shares

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

where P0 = Expected sale price of preference shares

f = Floatation cost as percentage of P0

Dp = Dividends paid on preference sharesPn = Repayment of preference capital

amount

(9)

k1

P

k1

1Df1P

:sinstalment in required repayment of case the Ink1

P

k1

1Df1P

n

1tt

p

tt

p

tp0

n

1tn

p

nt

p

tp0

D

D


11-11-1414

Example 5

ABC Ltd has issued 11 per cent preference shares of the face value of Rs 100 each to be redeemed after 10 years. Flotation cost is expected to be 5 per cent. Determine the cost of preference shares (kp).

Solution

cent. per 11 is dividend of rate the ascent per 12 and 11 between be to likely k of value The p is

k1

100Rs

k1

11Rs95Rs

10

1t10

pt

p

Determination of PV at 11% and 12%

Year Cash outflows

PV factor at Total PV at

11% 12% 11% 12%

1 – 10 Rs 11 5.889 5.65 Rs 64.78 Rs 62.15

10 100 0.352 0.322 35.15

99.93

32.20

94.35

Kp=11.9 per cent


11-11-1515

The computation of cost of equity capital (ke) is conceptually more difficult as the return to the equity-holders solely depends upon the discretion of the company management. It is defined as the minimum rate of return that a corporate must earn on the equity-financed portion of an investment project in order to leave unchanged the market price of the shares. There are two approaches to measure ke:

1) Dividend Valuation Model Approach 2) Capital Asset Pricing Model (CAPM)

Approach.

Cost of Equity CapitalCost of Equity Capital


11-11-1616

As per the dividend approach, cost of equity capital is defined as the discount rate that equates the present value of all expected future dividends per share with the net proceeds of the sale (or the current market 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 D1 = Expected dividend per share

P0 = Net proceeds per share/current market price

g = Growth in expected dividends

Dividend Valuation ApproachDividend Valuation Approach

(12)gP

Dk(11)

gk

DP

get we10, Eq. gSimplifyin equation. the of

sides two the equates whichrate) (discount return of rate the is 10 Eq. in k

(10)k1

g1D

k1

g1D...

k1

g1D

k1

g1Df1P

0

1e

e

10

e

n

1tt

e

1t

1n

e

n

02

e

2

01

e

1

00


11-11-1717

Example 6

Suppose that dividend per share of a firm is expected to be Re 1 per share next 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 ke can be calculated by using Equation

The dividend approach can be used to determine the expected market value of a share in different years. The expected value of a share of the hypothetical firm in Example 6 at the end of years 1 and 2 would be as follows

%1006.025Rs1Rsg

0P

1D

ek

28Rs0.060.10

1.124Rsgek

3D

2P (ii)

26.50Rs0.060.10

1.06Rsgek

2D

)1

(Pyear first the of end theat Price(i)


11-11-1818

Example 7

From the undermentioned facts determine the cost of equity shares of company 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.


11-11-1919

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

10.14Rsk e


11-11-2020

CAPITAL ASSET PRICING MODEL CAPITAL ASSET PRICING MODEL (CAPM) APPROACH(CAPM) APPROACH

The CAPM describes the relationship between the required rate of return or the cost of equity capital and the non-diversifiable or relevant risk of the firm 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 investment

b = Beta coefficient**, and

Km = Required rate of return on market portfolio, that is, the average rate or return 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 andN = Number of years

22 MNM

JMNMJ**


11-11-2121

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.

Solution

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


11-11-2222

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


11-11-2323

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 per cent

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

ke = Rf + b(km – Rf)

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


11-11-2424

Cost of Retained Earnings

The cost of retained earning (kr) 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, kr is equal to ke.

However, it might be slightly lower than ke in the

case of new equity issue due to flotation costs.


11-11-2525

Computation of Overall Cost of CapitalComputation of Overall Cost of Capital

Weighted Average Cost of Capital

Weighted average cost of capital is the expected average future cost of funds over the long run found by weighting the cost 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 weights are:

1) Historical weights

a) Book value weights or

b) Market value weights

2) Marginal Weights


11-11-2626

Historical Weights Historic weights either book or market

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 capital to

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.


11-11-2727

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 structure

Source 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 using book value weights.


11-11-2828

Table 1: Solution Computation of weighted average cost of capital (Book Value 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 k0 is to compute, as shown in Table 2, the total cost of capital and then divide this figure by the total capital. This procedure obviously avoids fractional calculations.

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

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

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

Debt Preference capital Equity capitalTotal

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


11-11-2929

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 the balance of the additional funds will be raised as follows:

Long-term debt Rs 3,00,000

Preference shares 1,00,000

Using marginal weights, compute the weighted average cost of capital.


11-11-3030

SOLVED PROBLEMSOLVED PROBLEM


11-11-3131

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


11-11-3232

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 cent dividend 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%0.0720 Rs

2Rsg

f1P

D)(k sharesequity of (iii)Cost

12.8%100295Rs100Rs

105Rs12Rs

2SVRV

NfD )(k shares preference of (ii)Cost

7.7%100296Rs100Rs

104Rs0.35 11 Rs

2SVRV

Nft)-1(1 )(k debt, of (i)Cost

0

1e

mp

md


11-11-3333

Using these specific costs we can calculate the book value and market value weights 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 61,600

Preference 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

© tata mcgraw-hill publishing company limited, financial management 11-1 concept and measurement of...

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