UNIT TWO

CHAPTER THREE

CONCEPT &

MEASUREMENT

OF COST OF

CAPITAL

Lesson 19

Chapter 6

Concept and measurement of cost of capital

Unit 2

Long term investment decisions

After reading this lesson you will be able to: -

Understand the concept, importance & significance of cost of capital Understand the types of capital Calculate the specific costs of debt Calculate the specific cost of preferred stock Calculate the specific cost of common equity using dividends model.

Students we discussed Capital budgeting decision in which there were basically two

inputs i.e.,

(i) The cash flows emanating from the projects, and

(ii) The discount rate.

First input has already been discussed; the present lesson focuses attention on the second

input. This discount rates has been denoted as the cut-off rate, the minimum required rate

of return, rate of interest, target rate etc., Technically speaking, this discount rate is

known as the cost of capital. The concept of cost of capital is an important and

fundamental concept of theory financial management.

We know that the main objective of the business firm is to maximize the wealth of

shareholders in the long run. So, keeping in mind this major point, what managers require

is to invest only in those projects, which give return in excess of cost of funds invested in

the projects of the business? Here my point is that we have to determine of cost of funds,

if it is raised from different sources and at different quantum. The various sources of

funds to the company are in the form of equity and debt.

CONCEPT OF COST OF CAPITAL

The concept of cost of capital has been used in capital budgeting as the discount rate or

the minimum required rate of return. In the NPV and PI techniques, the cash flows have

been discounted at this cost of capital to find out the desirability of the proposal. In the

IRR method, although this cost of capital is not directly used, still it was required to make

the accept-reject decisions. If a project's IRR is more than the cost of capital of the firm

then the proposal is considered to be acceptable, otherwise it should be rejected. So, the

concept of cost of capital has been used quite often without providing a good deal of

explanation about how it is obtained.

Theoretically speaking, the cost of capital is the minimum required rate of return; a

project must earn in order to cover the cost of raising funds being used by the firm in

financing of the proposal.

This can be substantiated as follows; if a firm accepts an investment proposal, it will also

need funds for its financing. These funds can be procured from different types of

investor i.e., equity share holders, preference share holders, debt holders, depositors etc.,

These investor while providing the funds to the firm will have, an expectation of

receiving a minimum return from the firm. The minimum return expected by the

investors depends upon the risk perception of the investor as well as on the risk-return

characteristics of the firm. Therefore, in order to procure funds, the firm must pay this

return to the investors. Obviously, this return payable to investors would be earned out of

the revenues generated by the proposal wherein the funds are being used. So, the proposal

must earn at least that much, which is sufficient to pay to the investors of the firm. This

return payable to investor is therefore; the minimum return the proposal must earn other-

wise, the firm need not take up the proposal. In nutshell, therefore, the cost of raising

funds is the minimum required rate of return of the firm i.e., the cost of capital is the

minimum return which the firm must earn on the proposals in order to break-even..

Thus, the minimum rate of return that a firm must earn in order to satisfy the

expectations of its investor is called the cost of capital of the firm. In other words, the

cost of capital is the rate of return; a firm must earn in order to attract the supplier of

funds to make available the funds to the firm.

IMPORTANCE AND SIGNIFICANCE OF COST OF CAPITAL

The importance and significance of the concept of cost of capital can be stated in terms of

the contribution it makes towards the achievement of the objective of maximization of

the wealth of the shareholders. If a firm's actual rate of return exceeds its cost of capital

and if this return is earned without of course, increasing the risk characteristics of the

firm, then the wealth maximization goal will be achieved. The reason for this is obvious.

If the firm's return is more than its cost of capital, then the investor will no doubt be

receiving their expected rate of return from the firm. The excess portion of the return will

however be available to the firm and can be used in several ways

E.g. (i) for distribution among the shareholders in the form of higher than expected

dividends, and

(ii) For reinvestment within the firm for increasing further the subsequent returns. In both

the cases, the market price of the share of the firm will tend to increase & consequently

will result in increase in the shareholders wealth.

In capital budgeting decision it helps accepting those proposals whose rate of

return is more than the cost of capital of the firm and hence results in increasing the value

of the firm. Similarly, the firm's value is reduced when the rate of return on the proposal

falls below the cost of capital. Thus, the concept of cost of capital is consistent with the

goal of maximization of shareholders wealth and it works as a tool to achieve this goal.

Further, the cost of capital has a useful role to play in deciding the financial plan or

capital structure of the firm. It may be noted that in order to maximize the value of the

firm, the cost of all the different sources of funds must be minimized. The cost of capital

of different sources usually varied and the firm will like to have a combination of these

sources in such a way so as to minimize the overall cost of capital of the firm.

What impacts the cost of capital?

FINANCIAL SOUNDNESS OF THE FIRM

THE DEBT TO EQUITY MIX OF THE

FIRM

INTEREST

RATE LEVELS

IN THE

MARKET

RISKINESS OF EARNINGS

The Cost of Capital becomes a guideline for measuring the profitability of different investments.

Remember that: The goal of the corporation is to maximize

the value of shareholders equity!

Therefore cost needs to come down.

TYPES OF COST OF CAPITAL

Explicit cost & implicit cost

The explicit cost of capital of a particular source may be defined in terms of the interest

or dividend that the firm has to pay to the suppliers of funds. There is an explicit flow of

return payable by the firm to the supplier of fund. For example, the firm has to pay

interest on debentures, dividend at fixed rate on preference share capital and also some

expected dividend on equity shares. These payments refer to the explicit cost of capital.

There is one source of funds, which does not involve any payment or flow i.e., the

retained earnings of the firm. The profits earned by the firm but not distributed along the

equity shareholders are ploughed back and reinvested within the firm. These profits

gradually result in a substantial source of funds to the firm. Had these profits been

distributed to equity shareholders, they could have invested these funds (return for them)

elsewhere and would have earned some return. The investors forego this return when the

profits are ploughed back. Therefore, the firm has an implicit cost of these retained

earnings and this implicit cost is the opportunity cost of investors. Thus, the, implicit cost

of retained earning is the return which could have been earned by the investor, had the

profit been distributed to them. This is also called opportunity cost of capital.

Except the retained earnings, all other sources of funds have explicit cost of

capital.

Specific cost & overall cost

We know that a company obtains capital from various sources. The cost of capital of each

source differs because of the risk differences and the contractual agreements. The cost of

capital of each, source of capital is known as component or specific cost of capital.

And when we take combined cost of all the components it is called overall cost of capital.

The components are assigned certain weights & then the weighted average cost of capital

is determined. The advantage of using the overall cost of capital is its simplicity. Once it

is computed, projects can be evaluated using a single rate that does not change unless

underlying business and financial market condition change.

The overall cost of capital of a firm is a proportionate average of the costs of the various

components of firms financing. The cost of equity capital is the most difficult to

measure. Our concern will be with the marginal or specific cost of capital. We will

determine specific costs first & then will move our attention to overall cost of capital.

MEASUREMENT OF COST OF CAPITAL As discussed for measuring firms overall cost of capital specific cost of capital need to

be determined component wise.

Component of Cost of capital

I. Cost of Debt (KD)

II. Cost of Preferred Capital (KP)

III. Cost of Equity (KE)

IV. Cost of Retained Earnings (KR)

I. Cost of Debt (KD)

We know it very well that the capital structure of a firm normally includes the debt

component also. Debt may be in the form of Debentures, Bonds; Term Loans form

Financial Institutions and Banks etc. The debt is carried a fixed rate of interest payable to

them, irrespective of the profitability of the company since the coupon rate is fixed. The

firm increases its earnings through debt financing. Then after payment of fixed interest

charges more surpluses is available for equity shareholders, and hence EPS will increase.

An important point to be remembered that dividends payable to equity shareholders and

preference shareholders is an appropriation of profit, whereas the interest payable on

debt it is a charge against profit. Therefore, any payment towards interest will reduce

the profit and ultimately the companys tax liability would decrease. This phenomenon is

called Tax shield. The tax shield is viewed as a benefit accruing to the company,

which is geared. Geared, here means inclusion of debt capital to the total capital

requirement of the form/company. To gain the full tax shield the following condition

apply:

The company must be able to show a taxable profit every year to take full advantage of the tax shield.

If the company makes loss, the tax shield goes down and cost of borrowing increases.

Example

Harappa Ltd. has earned a profit before interest and tax of Rs. 6,00,000 for the year ended

31st March 2001. Calculate its profit after tax in the following situation:

The company has entirely financed its project through issue of 3,00,000 equity shares of Rs 10 each.

The company has financed its project through issue of 1,00,000 equity shares of Rs 10 each and 20,000 14% debentures of Rs 100 each.

The companys applicable corporate tax rate is 40%.

Solution

Capital structure Case I Case II

30,00,000

-

10,00,000

20,00,000

Equity share capital

14% Debentures

Total 30,00,000 30,00,000

You can calculate the profit as:

Calculation of profit after tax

Particulars Case I Case II

6,00,000 6,00,000

2,80,000

6,00,000

2,40,000

3,20,000

1,28,000

3,60,000 1,92,000

Profit before interest

Less: Interest charges

Profit after interest before tax

Less: Tax @40%

Profit after tax (PAT)

EPS = PAT/No. Of Equity shares Rs. 1.20 Rs. 1.92

By using the tax shield and advantage of fixed interest bearing funds in the capital

structure, the EPS of the owners i.e. equity shareholders is increase by Re.0.72 (i.e. Rs

1.92-Rs 1.20)

In a situation of loss making, the advantage of tax shield and gearing cannot be gained. It

will further increase the cost of debt.

The explicit cost of debt can be derived by solving for the discount rate that equates the

market price of the debt issue with the present value of interest payments and then be

adjusting the explicit cost obtained for the tax deductibility of interest payments.

To apply the formulation of cost of debt what kind of information do we need?

Inflows (Net cash proceeds by issue of debentures) Outflows (In terms of interest & principal repayment whether in installments or

in lump sum)

IMPORTANT

Interest payment made by the firm on debt qualifies for tax deduction, therefore the

effective cash outflows is less than the actual payment of interest made by the firm.

Debt can be perpetual debt or redeemable debt

(a) Cost of Perpetual Debt

The cost of perpetual debt is calculated with the following formula:

KD = I (1-T) / D

Where,

KD = Cost of debt

I = Annual interest payment

T = Companys effective corporate tax rate

D = Net proceeds of issue of Debentures, Bonds, Terms loans etc.

Example

Vishwanath Steel Ltd. has issued 30,000 irredeemable 14% debentures of Rs 150 each.

The cost of floatation of debentures is 55 of the total issued amount. The companys

taxation rate is 40%. Calculate the cost of debt.

Here, you see:

Net proceeds from debenture issue

45,00,000

2,25,000

Total issue amount (30,000 debentures X Rs. 150)

Less: Floatation Cost (Rs. 45,00,000 X 5/100)

Net proceeds from issue 42,75,000

Annual interest charge:

(Rs 45,00,000 x 14/ 100)

= Rs. 6,30,000

KD = I (1-T)/D

= Rs. 6,30,000 (1- 0.40)/ (Rs.42,75,000)

= 3,78,000/42,75,000 = 0.0884 or 8.84%

Please note

Net proceeds will change if debentures are issued at discount or at premium.

(b) Cost of Redeemable Debt

The cost of capital of redeemable debt may be ascertained with the help of following

equation

n Ii (1-t) COPi COPn B0 = ---------- + --------- + --------- i=1 (1+kd)i (1+kd)i (1+kd)n Where I = Annual Interest Payment

B0 = Net Proceeds

COPi = Regular Cash Outflow on account of amortization

COPn = Cash Outflow on account of repayment at maturity

Kd = After tax cost of capital of debt.

In case, the debt is repayable only at the time of maturity and there is no annual

amortization then the Equation above will not contain the second element i.e.,

COPi/(1+kd)i. The Equation is to be solved for the value of kd, which will be after tax cost

of capital for debt. This equation is to be solved by trail and error procedure (as the IRR

equation was solved earlier).

Example

ABC Ltd. issues 15% debentures of face value of Rs.100 each, redeemable at the end of 7

years. The debentures are issued at a discount of 5% and the flotation cost is estimated to

be 1%. Find out the cost of capital of debentures given that the firm has 50% tax rate.

Solution B0 = Rs.100 Rs.5 Rs1 = Rs.94.

I = Rs.15 (1-.5) = 7.50.

Putting these values in Equation 12.3

94 = 7.50 (PVAF (r, n)) + 100 (PVF(r, n))

The value of right hand side of the equation is to be made equal to the amount of Rs.94

and can be derived by trail and error procedure as follows:

At kd = 9% = 7.5(5.033) + 100 (.547)

= 39.05 + 54.30 = 92.45

Since the amount is less than Rs.94, the rate of discount may be reduced to 8% and

therefore,

At kd = 8% = 7.5(5.206) + 100(.583)

= 39.05 + 58.30 = 97.35

By interpolating between 8% and 9%, the value of kd comes to 8.68%. So, the cost of

capital (after tax) of debenture is 8.68%.

In order to avoid the cumbersome procedure of trial and error we can use an

approximation to after tax cost of capital of debt.

I (1-t) + (RV B0) / N

kd = --------------------------

(RV + B0) / 2

Where RV = Redemption Value of debenture

kd = After Tax Cost of Debt

t = Tax rate

N = Life of debenture

Now, applying the same

15 (1-.5) + (100 94) / 7

kd = ------------------------------

(100 + 94) / 2

= .861 or 8.61%.

II. Cost of Preference Share Capital (KP)

Preferred Stock has a higher return than bonds, but is less costly than common

stock. WHY?

In case of default, preferred stockholders get paid before common stock holders.

However, in the case of bankruptcy, the holders of preferred stock get paid only after

short and long-term debt holder claims are satisfied.

Preferred stock holders receive a fixed dividend and usually cannot vote on the firms

affairs.

(a) Cost of Perpetual Preference shares

Preferred stock dividend Market price of preferred stock (1 flotation cost)

Example

If Cowboy Energy Services is issuing preferred stock at $100 per share, with a stated

dividend of $12, and a flotation cost of 3%, then:

Solution

$12

$100 (1-0.03)

= 12.4 %

Unlike the situation with bonds, no adjustment is made for taxes, because preferred stock

dividends are paid after a corporation pays income taxes. Consequently, a firm assumes

the full market cost of financing by issuing preferred stock. In other words, the firm

cannot deduct dividends paid as an expense, like they can for interest expenses.

(b) Cost of Redeemable Debt

The cost of redeemable preference share is defined as that discount rate which equates the

proceeds from preference share capital issue to the payment associated with the same i.e.

dividend payment and principal payment. It is calculated as follows:

n D F P = ----------- + ----------- t =1 (1 + kp)t (1 + kp)n Where Kp = cost of preference capital D = preference dividend per share payable annually F = redemption price P = net amount realized per share

And n = maturity period An approximation formula as given below can also be used. F P D + ------ n

F + P ------- 2

Example The terms of the preference share issue made by Color-Dye-Chem are as follows: Each

preference share has a face value of Rs.100 and carries a rate of dividend of 14 percent

payable annually. The share is redeemable after 12 years at par. If the net amount realized

is Rs.95, what is the cost of the preference capital?

Solution Given that D = 14, F = 100, P = 95 and n = 12 100 95 14 + ---------- 12

= 0.148 or 14.8 percent 100 + 95 ----------- 2 Example

ABC Ltd issues 15% preference shares of the face value of Rs. 100 each at a flotation

cost of 4%. Find out the cost of capital of preference share if

i. The preference shares are irredeemable and

ii. If the preference shares are redeemable after 10 years at a premium of 10%

Solution

i. If the preference shares are irredeemable the cost of capital is

15 96

= 15.63%

ii. If the preference shares are redeemable after 10 years at a premium of 10%

Given that D = 15, F = 100, P = 96 and n = 10 100 96 15 + ----------

10 = 0.1571 or 15.71% percent

100 + 96 ----------- 2 III. Cost of Equity (KE)

Equity capital is that capital, which we generate from the owners of the company. These

funds are not repaid during the lifetime of the organization; hence are also called

permanent source of funds. The equity shareholders are the owners of the company and

we know it very well that the main objective of the firm is maximization of wealth of the

equity shareholders.

Equity share capital is treated as the risk capital of the company. Because of the

following reasons:

1. If the company is doing well then the ultimate beneficiaries are the equity

shareholders who will get the return in the form of dividends from the company, and

the capital appreciation for their investment

2. If the company is liquidated due to losses, the ultimate and worst sufferers are the

equity shareholders.

3. Sometimes they may not even get their investment back during the liquidation

process.

The profits after taxation, less dividends paid out to the shareholders, are funds that

belong to the equity shareholders. These funds are reinvested in the company and

therefore, you should note that those retained funds should be included in the category of

equity. These funds are known as retained earnings.

The cost of equity is defined as the minimum rate of return that a company must earn on

the equity. You should remember that you have to earn this minimum rate on your

investment in any project so that market price of the shares remains unchanged. Now I

will explain the various methods, which are used in calculation of Cost of Equity.

The cost of equity capital is by far the most difficult cost to measure. In the case of equity

share, the cost has to be viewed in the opportunity framework. The investor has provided

funds to the firm expecting to receive the combined return of dividends and the

appreciation in market value. The investment was made, presumably on a logical basis,

because the type of risk embodied in the firm reasonably matched with the investors on

risk preference and because the expectations about earnings, dividends and market

appreciation were satisfactory. The investor made this choice by foregoing other

investment opportunities. The problem of measuring, the cost of equity capital to a firm

arises from the need to measure the investors expectations about the risk and return in

relation to the firm. There are various models that we use for determining cost of equity.

Let us discuss these models one by one.

Ways to Calculate

1. Dividend discount models 2. CAPM 3. Price earning method 4. Bond yield plus risk premium

1. DIVIDEND DISCOUNT MODELS

Dividend discount models are designed to compute the intrinsic value of a share of

common stock under specific assumption as to the expected growth pattern of future

dividends and the appropriate discount rate to employ. Merrill Lynch, CS First Boston,

and a number of other investment banks routinely make such calculations based on their

own particular models and estimates. What follows is an examination of such models,

beginning with the simplest one.

The value of a share of common stock can be viewed as the discounted value of all

expected cash dividends provided by the issuing firm until the end of the time. In other

words,

D1 D2 Dx V = (1 + ke)1 + (1 + ke)2

+ . + (1 + ke)x

Constant Growth

Future dividends of a company could jump all over the place; but, if dividends are

expected to grow at a constant rate, what implication does this hold for our basic stock

valuation approach? If this constant rate is g, then Equation written above will become

D0(1 + g) D0(1 + g)2 D0(1 + g)x V = (1 + ke)1 + (1 + ke)2

+ . + (1 + ke)x

Where D0 is the present dividend per share. Thus, the dividend expected at the end of

period n is equal to the most recent dividend times the compound growth factor, (1 + g)n.

Assuming that ke is greater than g (a reasonable assumption because a dividend growth

rate that is always greater than the capitalization rate would imply an infinite stock

value), Equation can be reduced to

V = D1/(Ke g)

Rearranging, the investors required return can be expressed as

ke = (D1/V) + g

The critical assumption in this valuation model is that dividends per share are expected to

grow perpetually at a compound rate of g. For many companies this assumption may be a

fair approximation of reality.

An allowance for future growth in dividend is to add to the current dividend yield. It is

recognized that the current market price of a share reflects expected future dividends.

This dividend growth model is also called as Gordons dividend growth model.

Let us do some questions to understand the concept better.

Example

LKN, Inc.s dividend per share at t = 1 is expected to be $4, that it is expected to grow at

a 6 percent rate forever, and that the appropriate discount rate is 14 percent. What will be

the value of one share of LKN stock?

Solution

The value of one share of LKN stock would be

V = $4/(.14 - .06) = $50 For companies in the mature stage of their life cycle, the perpetual growth model is often

reasonable.

D1

+ g

PE

Where,

D1 = current dividend per Equity share

PE = Market price per equity share

g = Growth in expected dividend

Example

The equity of Survy limited is traded in the market at Rs. 90 each. The current year

dividend per share is Rs 18.The subsequent growth in dividend is expected at the rate of

6%. Calculate the cost of equity capital.

Solution

KE = D1 + g

PE

Rs. 18

= + 0.06

Rs. 90

= 0.20 + 0.06 = 0.26 or 26 %

Example

Sunlight Ltd. has its share of Rs. 10.each quoted on the stock exchange; the current price

per share is Rs. 24. The gross dividends per share over the last year have been Rs.1.20,

Rs1.45 and Rs 1.60. Calculate the cost of equity shares.

Solution

Expected current year dividend:

110

Rs. 1.60 X = Rs. 1.76.

100

The dividends are growing @ 10 % and are expected to continue to grow at this rate.

D1

KE = + g

PE

Where,

D1 = Current year equity dividend i.e., Rs.1.76

PE = Market price of equity share i.e., Rs. 24

g = Expected growth rate in dividend i.e. 10% or 0.10

Rs. 1.76

KE = ------------------- + 0.10 [0.07 + 0.10 = 0.17 or 17 %]

24

Some times the dividend growth model formula for calculation of cost of equity

share capital is also written as follows:

D0 (1+g)

KE = + g

PE

Where,

D0 = Last dividend paid per share

g = Constant annual growth rate of dividends

PE = Ex. Dividend market price per share.

Example

Full moon Ltd. has its equity share of Rs. 10 each quoted in a stock exchange has market

price of RS. 56. A constant expected annual growth rate of 6%, and dividend of Rs.3.60

per share has been paid for the current year. Calculate the cost of capital.

Solution

D0 (1+g)

KE = + g

PE

3.60 (1+ 0.06)

= + 0.06

56

= 0.0681 + 0.06 = 0.1281 or 12.81%

Example

ABC ltd has just declared & paid a dividend at the rate 15% on the equity share of Rs.

100 each. The expected future growth rate in dividends is 12%. Find out the cost of

capital of equity shares given that the present value of share is Rs. 168.

Solution

The cost of equity capital in this case will be ascertained as follows

D0 (1+g)

P0 =

KE --g

168 = 15(1+.12)

KE -- 12

KE = 16.8/168 + .12

= .22or 22%

No growth

A special case of the constant growth model calls for an expected growth rate, g, of zero.

Here the assumption is that dividends will be maintained at their current level forever.

The dividend per share is expected on the current market price per share. As per this

method, the cost of 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 share. Not many

stocks are expected to maintain a constant dividend forever. However, when a stable

dividend is expected to be maintained for a long period of time this equation does provide

a good approximation of value.

D1

KE = -----------------

PE

Where,

KE = Cost of equity

D1 = Annual dividend per share

DE = Ex-dividend market price per share

Example

Hindustan Manufacturing Ltd. has distributed a dividend of Rs. 30 on each Equity share

of Rs 10. The current market price of share is Rs. 80. Calculate the cost of equity

Solution

Applying the above formula:

D1

KE =

PE

Where,

D1 = Dividend per share of the current period i.e, Rs. 30

PE = Market price per share i.e, Rs. 80

Rs.30

KE =

Rs. 80

= 0.357 or 37.5 %

Example

FMD Ltd issued 10,000 equality of Rs. 10 each at a premium of Rs. 2 each. The company

has incurred issue expenses of Rs 5,000. The equity shareholders expect the rate of

dividend to 18% p.a. Calculate the cost of equity share capital. Will your answer be

different if the current market price of the share is Rs 21.1?

Solution

Since the Equity share are newly issued, the cost of capital of it can be calculated as

follows:

D1

KE = ------------

NP

D1 = Expected dividend per share of the current year

NP = Net proceeds of each equity share.

NET Proceeds per share:

(10,000 Equity share Rs.12) - Rs 5,000 =

10,000

1,15,000

=

10,000

= 11.50 per share

Rs 1.80

KE = X 100 = 15.65 %

Rs 11.50

But in case of the existing equity share, market price is to be taken as basis for calculation

of cost of equity capital as follows:

D1

KE =

PE

Where,

D1 = Current dividend per Equity share

PE = Market price of equity share

Rs. 1.80

KE = = 0.0857 or 8.57 %

RS. 21

Varying Growth Rate in Dividends:

Dividends may also be assumed to grow at different rates for different years. For

example, for first 5 years the growth rate may be 10% per annum, then for the next 5

years the growth rate may be 15% per annum and thereafter the dividends may grow at

20% per annum infinitely. This means that the dividend will grow at 10% per annum for

year 1 to 5, and at 15% for years 6 to 10 and at 20% for the year 11 and thereafter.

Equation can be modified to take care of such situations of dividend stream and the cost

of capital may therefore be calculated with the help of following Equation.

D0 (1 + g1)i D5 (1 + g2)i-5 D10 (1 + g3)i-10

P0 =

5 i = 1

(1 + ke)i +

10 i = 6

(1 + ke)i .+

i = 11

(1 + ke)i

Where P0 = Current market price of the equity share

D0 = Dividend just paid by the company

D5 = Dividend payable at the end of year 5

D10 = Dividend payable at the end of year 10

g1, g2 and g3 = Different growth rates, and

ke = Cost of equity share capital.

This Equation can be solved by trail and error procedure to find out the value of ke.

Note: Calculation of Ke as per Equations above, is a standard formulation in financial

management. This however, may be adjusted in the light of relevant tax laws. In India,

Equity Dividend is subject to Corporate Dividend Tax at 20%. For example, a company

declares a dividend of Rs. 5 on equity shares, then it has to pay a tax of Rs. 1 to the

government and the total cash outflow of the company would be Rs. 6. So, in the above

equations, the term Di may be replaced by Di (I+t) where t is the Corporate Dividend

Tax Rate.

The value of ke may be calculated as follows:

D1(1 + t)

ke = ------------ + g

P0

16.8 (1 + .2)

= --------------- + .12

168

= 24%

In may be observed that the Ke has increased from 22% to 24% as a result of

inclusion of Corporation Dividend Tax.

Zero Dividends:

It may also be assumed that the firm may not pay any dividend and instead reinvests its

entire earnings. The investors, even if no dividend is expected, will not change their

required rate of return. Instead, the investor must be expecting a capital gain in the form

of increase in market price. Thus, the required rate of return accrues to the investors in

the form of capital gain, which they receive when they sell their shares at a later date at a

price say, Pn, against the current price, P0. In such a case, the cost of capital, ke, may be

calculated with the help of following equation.

Pn

P0 = --------------

(1 + ke)n

An important assumption in Equation above is that Pn >P0. The value of ke in Equation

can be derived as

ke n (Pn P0) 1

The main problem in applying this equation is that it is difficult, if not impossible to

estimate value of Pn i.e.,, the expected market price at the end of year n.

Criticism of dividend discount models

The dividend growth model is criticized on the following reason:

The future growth pattern is impossible to predict because it will be inconsistent and uneven.

Due to uncertainty of future and imperfect information, only historic growth is to be used for prediction for future growth.

Calculating only cost of equity capital, and ignoring the cost of other forms of capital may not be valid

The dividend growth depends on retained earnings of the company, and the growth is difficult to assume.

Long term investment decisionsIMPORTANCE AND SIGNIFICANCE OF COST OF CAPITAL

Therefore cost needs to come down.TYPES OF COST OF CAPITALExplicit cost & implicit costSpecific cost & overall costMEASUREMENT OF COST OF CAPITALComponent of Cost of capital

ExampleExample

SolutionExampleSolutionExampleSolution

1. DIVIDEND DISCOUNT MODELSExampleSolutionExampleSolutionExampleSolutionExampleSolutionExample

SolutionNo growthExampleSolutionSolutionCriticism of dividend discount models