8. cost of capital

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Financial Management I

8. Cost of Capital

Dr. Suresh

[email protected]

Phone: 40434399, 25783850


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Course Content - Syllabus

*Book reference

Sr Title ICMR Ch. PC Ch. IMP Ch.

1 Introduction to Financial Management 1* 1 12 Overview of Financial Markets 2* 2 -3 Sources of Long-Term Finance 10* 17 20, 214 Raising Long-term Finance - 18* 20, 21, 235 Introduction to Risk and Return 4* 8, 9 4, 56 Time Value of Money 3* 6 27 Valuation of Securities 5* 7 38 Cost of Capital 11* 14 99 Basics of Capital Expenditure

Decisions 18* 11 810 Analysis of Project Cash Flows - 12* 10, 11

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Cost of Capital

Reference Books

1. Financial Management, ICMR Book, Chapter 11

2. Financial Management, Prasanna Chandra, 7th

Edition,

Chapter 14

3. Financial Management, I. M. Pandey, 9th Edition,

Chapter 9


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SyllabusCost of Capital

1. Concept and Importance

2. Cost of Debenture

3. Term Loans

4. Equity Capital and Retained Earnings

5. Calculation of Weighted Average Cost of Capital

6. Weighted Marginal Cost of Capital Schedule


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Major components of capital are equity, preference anddebt. Let us find out the costs of these various types of

finances. Capital has a cost. Various sources of capital

has varied costs and implications.

Companys cost of capital is weighted average cost of

various sources of finance that a company uses e. g.

equity, preference, debentures, term loans, retained

earnings etc.

Cost of capital is used for evaluating projects, determining

capital structure etc.


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Suppose a company uses equity, preference and debt inproportions of 50, 10 and 40. If the cost of these

components is 16%, 12% and 8% resp.

Then weighted average cost of capital (WACC) will be

= Proportion of equity x cost of equity +

proportion of preference x cost of preference +proportion of debt x cost of debt

= 0.5 x 16 + 0.10 x 12 + 0.40 x 8

= 12.4%


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Cost of debenture is defined as the discount rate which

equates the net proceeds from issue of debentures to the

expected cash outflows in the form of interest and

principle repayments, i. e.

(1)

Where, kd = post-tax cost of debenture capital

I =annual interest payment per debenture capitalt = corporate tax rate

F = redemption price per debenture

P = net amount realized per debenturen = maturit eriod

nd

n

1tt

d )k(1

F

)k(1

t)-I(1P


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Interest payment I is multiplied by factor (1-t) because

interest on debt is a tax-deductible expense and only post

tax costs are considered.

Same formula can be used for different types of debt

instruments such as bank loans and commercial paper.

Computation of kd requires a trial-and-error method.


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Example: A company issued a debenture of Rs. 100 face

value, 14% interest rate p.a. The debenture is

redeemable at a premium of 5% after 10 years.

Company realizes Rs. 97 per debenture and the

corporate tax rate is 50%. Calculate the cost of thisdebenture to the company.

Solution

nd

n

1tt

d )k(1

F

)k(1

t)-I(1P

10d

10

1tt

d )k(1

5100

)k(1

0.5)-14(197

10d

10

1tt

d )k(1

105

)k(1

797

(kd,10)(kd,10) PVIFx105PVIFAx797


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To find out the value of kd

in the above equation, several

values of kd will have to be tried out in order to reach the

input value. Therefore to start, consider a discount rate

of 8% for kd. The expression becomes

Rs. 7 x PVIFA(8%,10yrs)+ Rs.105 x PVIF(8%,10yrs)

= Rs. 7 x 6.71 + Rs. 105 x 0.463

= Rs. 95.585

Since the above value is less than Rs. 97 realized price, we

have to try with a less discounting rate kd

. So let kd

=

7% then


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Rs. 7 x PVIFA(7%,10yrs)

+ Rs.105 x PVIF(7%,10yrs)

= Rs. 7 x 7.024 + Rs. 105 x 0.508

= Rs. 102.508

From above, it is clear that kd lies between 7% and 8%.

We have to use linear interpolation between 7% and 8%.

= 7 + 0.796 = 7.796

Yield to maturity is 7.796%

95.585-102.50897-102.508x)7(87kd


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By computer Excel

In Excel, put all values of cash flows including initial

outflow with minus sign in a row or column e. g.-95 7 7 7 7 7 7 7 7 7 112

Then use the formula

=irr(values)

e. g.

=irr(a1:k1)

You get the answer as 7.791%



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3. Term Loans

Cost of term loans will be simply equal to the interest ratemultiplied by (1 - tax rate). The interest is multiplied by

(1tax rate) as interest on term loans is also tax

deductible.

Where, kt = post-tax cost of term loansI = interest rate

t = corporate tax rate

t)(1Ikt

2 C f P f C i l


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2. Cost of Preference Capital

Preference capital carries a fixed rate of dividend and isredeemable on maturity period. Preference stock is

much like a bond with fixed commitments, however

preference dividend is not a tax-deductible expense andhence does not produce any tax savings.

Cost of redeemable preference share is defined as that

discount rate which equates the proceeds from

preference capital issue to the payments associated with

the same i.e. dividend payment and principle payments,

i. e.

2 C f P f C i l


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(1)

Where, kp = cost of preference capital

D = preference dividend per share payable

annually

F = redemption price

P = net amount realized per share

n = maturity period

np

n

1tt

p )k(1

F

)k(1

DP

2 C f P f C i l


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Example: A company has issued preference shares with

face value Rs. 100 and carrying a dividend rate of 14%

p.a. The preference shares are redeemable after 12 years

at par. If the net amount realized per share is Rs. 95,

calculate the cost of preference capital.

Solution:

np

n

1tt

p )k(1

F

)k(1

DP

12p

12

1tt

p )k(1

100

)k(1

1495

(kp,12)(kp,12) PVIFx100PVIFAx1495

2 C t f P f C it l


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in the above equation, several

values of kd will have to be tried out in order to reach the

input value. Therefore to start, consider a discount rate

of 15% for kd. The expression becomes


= Rs. 14 x 5.421 + Rs. 100 x 0.187

= Rs. 94.594

Since the above value is less than Rs. 95 realized price, we

have to try with a less discounting rate kd

. So let kd

=

14% then

2 C t f P f C it l


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= Rs. 14 x 5.66 + Rs. 100 x 0.208

= Rs. 100.04

From above, it is clear that kd lies between 14% and 15%.

We have to use linear interpolation between 14% and

15%.

= 14 + 0.93 = 14.93

Yield to maturity is 14.93 %

94.594-100.04

95-100.04x14)-(1514kd

4 E it C it l d R t i d E i


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Cost of equity Capital

Rate of return required by the equity share holders i.e.

cost of equity is difficult to estimate. Because there is no

definite commitment from the firm to pay dividends, nor

specified by any legal contract, unlike in the case ofdebenture holders.

However we come up with reasonably good estimates of

the cost of equity by employing some basic principles.Several approaches are used for estimating cost of equity

such as dividend forecast approach, capital asset pricing

model, realized yield approach, earnings-price ratio

approach and bond yield plus risk premium approach.



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Dividend forecast approach

According to this approach, the present value or intrinsic

value of an equity stock is equal to the sum of present

values of dividends associated with it, i.e.

(2)

Where, Pe = price per equity shareDt = expected dividend per share at the end of

year one

ke = rate of return required by the equity

shareholders or the cost of equity capital

1tt

e

te

)k(1

DP



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In practice, the model suggested in equation (2) cannot beused in its present form because it is not possible to

forecast the dividend stream completely over the life of

the company. Therefore the growth in dividends can be

categorized as nil growth or constant growth or super

normal growth. Equation (2) can be modified

accordingly. For instance, assuming a constant growth

rate (g) in dividends, equation (2) can be simplified as

(3)

This model is called Gordons model.

gk

DP

e

1e



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If the current market price of share is given as Pe, valuesof D1 and g are known, then the equation (3) can be

written as

(4)

Example: Share price of a company is Rs. 125. The

dividend expected a year hence is Rs. 12 and the

dividends are expected to grow at a constant rate of 8%

per annum. Calculate the cost of equity capital of the

company

Solution: 17.6%or0.1760.08125

12kgP

Dk e

e

1

e

gP

D

k e

1e



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Realized Yield ApproachAccording to this approach, past returns on a stock are

taken as proxy for returns in the future by the investors.

Realized return over n year period is calculated as

Where Wt = wealth ratio, calculated as

Dt = dividend per share for year t payable at the

end of year

Pt = price per share at the end of year t

n....32,1,tand

P

PD

1-t

tt

gP

Dk

e

1e



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Example: Calculate the cost of equity by Realized YieldApproach for the data given below. Price per share at

the beginning of the year 1 is Rs. 10.

Solution: Wealth ratios are

Realized yield = (1.35 x 1.08 x 1.23)1/3 -1

= 0.2149 or 21.49%

Year 1 2 3

DPS (dividend per share) Rs. 1.5 2 1.5

Price per share at the end of the year 12 11 12

Year 1 2 3

Wealth ratio 1.35 1.08 1.23

4 Eq it Capital and Retained Earnings


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Capital Asset Pricing Model (CAPM) ApproachThis is a popular approach for estimating the cost of

equity. According to this approach, the cost of equity is

calculated as

Where ki = rate of return required on equity or the cost

of equity

Rf= risk free rate of return

i = beta of security i

Rm = rate of return on market portfolio

)R(RRk fmifi

4 Equity Capital and Retained Earnings


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Example: Consider a risk free rate of return as 6%, rate ofreturn on market portfolio as 12% and value of beta for

a stock as 1.2. Calculate the cost of equity.

Solution

According to CAPM approach, the cost of equity is

ki = 6 + 1.2 (126)

= 6 + 7.2

= 13.2 %

)R(RRk fmifi



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Bond Yield Plus Risk Premium Approach

According to this approach, return required by the

investors is based on risk profile of a company. Risk

profile is adequately reflected in the return earned by the

bondholders or debt. Since the risk borne by the equity

investors is higher than the bondholders or debt, the

return expected by equity holders is also higher. Hence

this return is calculated as

Cost of equity = Yield on long term bonds of thecompany + Risk premium

Risk premium based on operating and financial risks of

the company and it is a subjective figure normally rangesbetween 2% and 6%.



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Earnings Price Ratio ApproachAccording to this approach, cost of equity is equal to

Where E1 = expected EPS for the next year

P0 = current market price per share

E1 can be estimated by multiplying current EPS by

(1+ growth rate)

0

1

P

E

4 Cost of Retained Earnings and Cost of


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4. Cost of Retained Earnings and Cost ofExternal Equity

Cost of Retained EarningsEarnings of a firm can be reinvested or paid as dividends

to shareholders. If the firm retains part of its earnings

for future growth of the firm, the shareholder will

demand compensation from the firm for using that

money. As a result, the cost of retained earnings

represents a shareholders expected returns from the

firms common stock. Thus the firms cost of retainedearnings is equal to the cost of equity capital i.e.

Cost of retained earnings is always less than the cost of new

issue of common stock due to absence of floatin costs.

er kk



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Cost of External EquityCost of external equity includes certain floatation costs

involved in the process of raising equity from the

market. It is the rate of return required by the equity

holders or the cost of equity on the net funds raised.With the dividend capitalization model, following

formula is used for calculating the cost of external equity.

Method 1

Where ke = cost of external equity

f = floatation costs as a % of current market price

g = constant growth rate applicable to dividends

D1

= dividend expected at the end of year1

P = current market rice er share

g

f)(1P

Dk

0

1e

'



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Cost of External Equity

For all other approaches, there is no particular method

for accounting for the floatation costs. Following formula

can be used as an approximation in such cases

Where ke = cost of external equity

ke = rate of return required by the equity holders

f = floatation costs as a % of current market price

f)(1

kk

ee

'

5 Calculation of Weighted Average Cost of


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5. Calculation of Weighted Average Cost ofCapital

Weighted Average Cost of Capital (WACC) is calculatedby multiplying the specific cost of each source of

financing by its proportion in the capital structure and

adding these weighted values. WACC is calculated for

various components of capital such as equity, preference,debentures, term loans, retained earnings etc. depending

on their proportions and their cost of capital values.

Where We, Wp, Wd, Wt and Wr are the weights or the

proportions of equity, preference, debentures,

term loan and retained earnings resp.

ke, k , kd, kt and kr are the corresponding costs

rrttddppee kWkWkWkWkWWACC



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Example: A company has a following capital structure

Market price per equity share is Rs. 25. Next expected dividend

per share is Rs. 2 and DPS is expected to grow at a constant

rate of 8%. Preference shares are redeemable after 7 years at

par and are currently quoted at Rs. 75 per share. Debentures

are redeemable after 6 years at par and their current market

price is Rs. 90 per share. Tax rate is 50%. Calculate WACC.

Capital Rs. In lakhs

Equity capital (10 lakh shares at par value) 100

12% Preference capital (10,000 shares at par value) 10

Retained earnings 120

14% Non-convertible Debentures (70,000 debentures at par) 70

14% term loan from SFC 100

Total 400



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SolutionWe will adopt a three step procedure to solve this

problem

Step 1: Determine the costs of various sources of finance.

We shall define symbols ke, kr, kp, kd and kt to denote the

costs of equity, retained earnings, preference capital,

debentures and term loans resp.

Cost of equity

Cost of retained earnings

gPDk

0

1e

16%or0.160.0825

2

16%or0.16kk er



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To find out the value of kp

By trial-and-error method, start kp = 19%, the

expression becomes


= Rs. 12 x 3.706 + Rs. 100 x 0.296 = Rs. 74.072

Next, try k = 18%, then

np

n

1tt

p )k(1

F

)k(1

DP

7p

7

1ttp )k(1

100

)k(1

12

75

(kp,7)(kp,7) PVIFx100PVIFAx1275



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= Rs. 12 x 3.812 + Rs. 100 x 0.314 = Rs. 77.144

kp lies between 19% and 18%.

By linear interpolation between 19% and 18%.

= 18 + 0.70 = 18.70 %

74.072-77.144

75-77.144x)18(1918kp



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By trial-and-error method, start kp = 10%, the

expression becomes


= Rs. 7 x 4.355 + Rs. 100 x 0.564 = Rs. 86.885

Next, try k = 9%, then

nd

n

1tt

d )k(1

F

)k(1

t)-I(1P

6d

6

1tt

d )k(1

100

)k(1

0.5)-14(1

90




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= Rs. 7 x 4.486 + Rs. 100 x 0.596 = Rs. 91.002

kd lies between 10% and 9%.

By linear interpolation between 10% and 9%.

= 9 + 0.24 = 9.24 %

Cost of term loan kt = 0.14 (1-0.5) = 0.07 or 7%

86.885-91.002

90-91.002x)9(109kp



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Step 2: Determine weights associated with various sources

of finance. Let We, Wr, Wp, Wd and Wt represent the

weights of various sources of finance.

25.0400100We

025.040010Wp

30.0400

120Wr

175.0400

70Wd

25.0100Wt



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Step 3: Multiply the costs of various sources of finance

with corresponding weights and add these weighted costs

to determine WACC.

ttddpprree kWkWkWkWkWWACC

0.187x0.0250.16x0.300.16x0.25

0.07x0.250.0924x0.175

12.63%or0.1263

6 Weighted Marginal Cost of Capital


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6. Weighted Marginal Cost of CapitalSchedule

WACC tends to rise as the firm seek more and more

capital. As the suppliers provide more capital, the rate

of return required by them tends to increase. A schedule

(Table) or a graph showing the relationship between

additional financing and the WACC is called the

weighted marginal cost of capital schedule.

Determining Weighted Marginal Cost of Capital Schedule

The procedure involves following steps

1. Estimate the cost of each source of finance for

various levels of its use

6. Weighted Marginal Cost of Capital


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2. Identify the levels of new financing at which the cost

of new components would change, as per capital

structure policy of the firm (ratios of different

sources of finance). These levels called the breaking

points and they can be calculated asBreaking point on account of financing source i =

3. Calculate the WACC for various ranges of totalfinancing between the breaking points

4. Prepare the weighted marginal cost of capital

schedule which reflects the WACC for each level of

total new financing

structurecapitalin theisourcefinancingofProportion

pointberakingat theisourcefromfinancingnewTotal



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Example: A company is planning to raise equity, preference

and debt capital in the following proportions:Equity : 0.50Preference : 0.20Debt : 0.30

The costs of the three sources of finance for different levels ofusage has been estimated as below

Source of FinanceRange of new financing from the source

(Rs. In lakh)Cost %

Equity 015 16

1525 1725 and above 18

Preference 03 14

3 and above 15

Debt 020 8

20 and above 10



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Calculation of Breaking Point

Source of

Finance

Cost

%

Range of new

financing from the

source (Rs. In lakh)

Breaking Point

(Rs. in lakh)

Range of total

new financing

(Rs. in lakh)

Equity 16 015 15 / 0.5 = 30 030

17 1525 25 / 0.5 = 50 3050

18 25 and above - 50 and above

Preference 14 03 3 / 0.2 = 15 015

15 3 and above - 15 and above

Debt 8 020 20 / 0.3 = 66.67 066.67

10 20 and above - 66.67 and above



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Calculation of WACC for various ranges of total new financing

Range of totalnew financing(Rs. in lakh)

Source offinance

ProportionCost%

WeightedCost %

WACC

015 Equity 0.5 16 8

13.2Preference 0.2 14 2.8

Debt 0.3 8 2.4

1530 Equity 0.5 16 8

13.4Preference 0.2 15 3

Debt 0.3 8 2.4

3050 Equity 0.5 17 8.5


Debt 0.3 8 2.45066.67 Equity 0.5 18 9


Debt 0.3 8 2.4

66.67 and above Equity 0.5 18 9

15Preference 0.2 15 3

Debt 0.3 10 3



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Weighted Marginal Cost of Capital Schedule

Range of Total New Financing

(Rs. In Lakh)

Weighted Marginal Cost of Capital

(%)

015 13.2

1530 13.4

3050 13.9

5066.67 14.4

66.67 and above 15

8. cost of capital

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