Capital Structure ,Cost of Capital and Value

8/13/2019 Capital Structure ,Cost of Capital and Value

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Capital structure ,cost of capital

and Value of the firm

Prof. Prapti Paul


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Concept of value of firm:

The value of the firm depends on the earnings of the firm and

the earnings of the firm depends upon the investment decisionsof the firm. The earnings of the firm are capitalized at a rateequal to the cost of capital in order to find out the value of thefirm. Thus the value of the firm depends upon 2 factors, i.e.earnings of the firm and cost of capital.


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Capital structure theories Divergent views can been expressed on the relationship

between leverage, cost of capital and value of the firm.Establishing the relationship between the 3 is one of the mostcontroversial issue in financial management. Different views inthe form of theories of capital structure, can be studied and

analyzed by grouping into,i. The capital structure matters for the valuation of the firm,

presented by Net Income Approach.

ii. The capital structure does not matter for the valuation of thefirm.

iii. A more pragmatic approach between the two, presented byTraditional Approach.

iv. Modigliani- Miller approach which provides justification forNOI approach.


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The relationship between the leverage, cost of capital and value of thefirm has been analyzed in terms of the approaches and MM Model.Following assumptions are made to understand this relationship:

1) There are only 2 sources of funds, i.e. the equity and the debt, whichis having fixed interest.

2) The total assets of the firm are given and there would be no change inthe investment decisions of the firm.

3) The firm has a policy of distributing the entire profits among thesh.hol i.e. there is no retained earnings.

4) The operating profits of the firm are given and not expected to grow.

5) The business risk is given and is constant and not affected byfinancing mix.

6) No corporate or personal taxes.

7) Investors have the same subjective probability distribution of

expected operating profits of the firm.


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The following definitions and notations have been used for discussingcapital theories:

E= Total market value of equity.

D=Total market value of debt.

V=Total market value of the firm i.e. D+E

I=Total interest payment

NOP=Net operating profit i.e. EBIT

NP=Net profit or profit after tax (PAT) D0= Dividend paid by the co. at time 0 (i.e. now).

D1= Expected dividend at the end of Year 1 (from now).

P0=Current market price of the share

P1=Expected market price of the share after 1 year.

kd= after tax cost of debt i.e. I/D ke= cost of equity i.e. D1/P0

k0= overall cost of capital i.e. WACC

= [D/(D+E)]kd +[E/(D+E)]ke

= NOP/V = EBIT/V


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Net Income Approach: capital structure matters Suggested by Durand, this theory states that there is a relationship between

capital structure and value of the firm and therefore the firm can affect itsvalue by increasing or decreasing the debt proportion in the overall financingmix. The NI approach makes the foll assumptions:

1) The total capital requirement of the firm is given and is constant.

2) That kdis less than ke.

3) Both kdand keremain constant and increase in financial leverage i.e. use ofmore and more debt financing in the capital structure does not affect the riskperception of the investors.

The NI approach starts from the argument that change in financing mix of a

firm will lead to change in WACC, ko

, of the firm resulting in the change inthe value of the firm. As Kdis less than kethe increasing use of cheaper debt(and simultaneous decrease in equity proportion) in the overall capitalstructure will result in magnified returns available to the shareholders. Theincreased returns to sh.hol will increase the total value of the equity and thusincrease the total value of the firm. The WACC, ko, will decrease and the

value of the firm will increase.


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On the other hand, if the financial leverage is reduced by the decrease in debtfinancing, the WACC , ko of the firm will increase and the total value of the

firm will decrease.

Under NI approach, the firm will have maximum value capital structure at apoint where ko is minimized. A firm can increase its value by increasing thedebt proportion in the capital structure. So higher the degree of debt financing,better it is. The optimal capital structure is the one at which WACC, ko is

minimum resulting in maximum value of the firm.


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illustration 1: The expected EBIT of a firm is Rs.2,00,000. it has issued equity share capital

with ke@ 10% and 6% debt of Rs.5,00,000. find out the value of the firm and

the overall cost of capital, WACC.

Solution: EBIT Rs.2,00,000

- Interest 30,000

Net Profit 1,70,000

ke 10%Value of equity, E=1,70,000/.10 17,00,000

Value of debt, D, 5,00,000

Total value of the firm, V, 22,00,000

WACC, ko EBIT/V

= 2,00,000/22,00,000= .09 OR 9%

The WACC could also be calculated as: [D/(D+E)]kd+[E/(D+E)]ke

= [5/(5+17)].06+[17/(5+17)].10

=.09 or 9%


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Now if the firm has issued 6% Debt of Rs. 7,00,000 instead of Rs. 5,00,000, theposition would have been as follows:

EBIT Rs. 2,00,000

- Interest 42,000Net profit 1,58,000

ke 10%

Value of equity, E=1,58,000/.10 15,80,000

Value of debt, D, 7,00,000

Total value of the firm, V, 22,80,000WACC, ko, EBIT/V

=2,00,000/22,80,000

=.087 or 8.7%

So when the 6% debt is increased from Rs.5,00,000 to Rs. Rs.7,00,000 the valueof the firm increases from Rs.22,00,000 to Rs. 22,80,000 and the WACCdecreases from 9% to 8.7%.


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Now suppose the firm has issued 6% debt of Rs.2,00,000 only instead ofRs.5,00,000, the position would be as follows:

EBIT Rs.2,00,000- Interest 12,000

Net Profit 1,88,000

ke 10%

Value of equity, E=1,88,000/.10 18,80,000

Value of debt, D, 2,00,000Total value of the firm, V 20,80,000

WACC, k0 EBIT/V

= 2,00,000/20,80,000

= .096 or 9.6%

So when the proportion of 6% debt is reduced to Rs.2,00,000 only, the valueof the firm reduces to Rs.20,80,000 and the WACC increases from 9% to9.6%. Thus as per the NI approach, a firm is able to increase its value anddecrease its WACC by increasing the debt proportion in the capital structure.


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The effect of changing proportions of debt on the market price of the sharecan also be analyzed. Initially the value of equity, E is Rs.17,00,000 and thefirm has 1,00,000 shares outstanding. So the market price of the share would

be Rs.17. now if the firm increases its debt proportion from Rs.5,00,000 toRs.7,00,000 and uses its proceed to retire 11,764.70 shares

(i.e. Rs.2,00,000/Rs.17) of the firm. In this case, the total value of equity isRs. 15,80,000(already calculated) represented by 88,235.30 shares or themarket price of Rs. 17.90 per share (Rs.15,80,000/88,235.30). The EPS in thiscase would be Rs.1.79 (i.e.Rs.1,58,000/88,235.30) giving 10% yield on the

market price of Rs.17.90.

However if the firm wishes to reduce the debt from Rs.5,00,000 toRs.2,00,000 it will be required to issue additional shares at the market priceof Rs. 17. the no. of new shares to be issued is Rs.3,00,000/17 = 17,647.05 ,

making total no. of outstanding shares to be 1,17,647.05. in this case the totalmarket value of the equity shares is Rs.18,80,000 and the market price of theshare would be Rs.15.98 and the EPS would be Rs. 1.59 giving a yield of 10%on the market price. Thus the market price of the share also moves in linewith the value of the firm in response to the variations in debt proportions ofthe capital structure.


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Under NI Approach, the value of the firm can be defined as:

Conclusion: easy to understand and its too simple to be realistic. It ignores,

perhaps the most important aspects of leverage, that the market price dependsupon the risk which varies in direct relation to the changing proportion of debtin the capital structure.

Value of firm= value of equity + value of debt


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Net Operating Income Approach: capital structure

does not matter According to NOI approach, the market value of the firm depends upon the

net operating profit or the EBIT and the overall cost of capital, WACC.

The financing mix or the capital structure does not affect the value of the firm.

The NOI approach makes the following assumptions:

1) The investors see the firm as a whole and thus capitalize the total earnings ofthe firm to find out the value of the firm.

2) k0of the firm is constant and depends upon the business risk which also isassumed to be unchanged.

3) kd is taken as constant.

4) The use of more and more debt in the capital structure increases the risk ofthe sh.hol and thus results in the increase in the cost of the equity capital,i.e., ke. The increase in keis such as to completely off set the benefits ofemploying cheaper debt.

5) There are no taxes.


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The NOI Approach is based on the argument that the market values the firm asa whole for a given risk complexion. Thus for a given value of EBIT, the valueof the firm remain same irrespective of the capital composition and instead

depends upon the overall cost of capital. The value of the equity maybe foundout by deducting the value of debt from the total value of the firm i.e.

V=EBIT/ko

and E= V-D

and ke= EBIT-Interest

V-D

Thus the financing mix is irrelevant and does not affect the value of the firm.The value remains the same for all types of debt-equity mix. Since there will bechange in risk of the sh.hol as a result of a change in debt-equity mix,therefore, the ke, will be changing linearly with change in debt proportions.

The NOI Approach considers koto be constant and therefore there is nooptimal capital structure; rather every capital structure is as good as any other.


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illustration 2: A firm has an EBIT of Rs. 2,00,000 and belongs to the risk class of 10%. What

is the value of the cost of equity capital if it employs 6% debt to the extent of30%, 40% or 50% of the total capital fund of Rs. 10,00,000.

Solution:Particulars 30% debt 40% debt 50% debt

EBIT 2,00,000 2,00,000 2,00,000

ko 10% 10% 10%

Value of the firm, V 20,00,000 20,00,000 20,00,000

Value of 6% debt, D 3,00,000 4,00,000 5,00,000

Value of equity, E=(V-D) 17,00,000 16,00,000 15,00,000

Net profit(EBIT-Interest) 1,82,000 1,76,000 1,70,000

ke, NP/E 10.7% 11% 11.33%


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The ke of 10.7%, 11% and 11.33% can be verified for different proportions ofdebt by calculating WACC, ko, as follows:

For 30% debt, ko = [D(D+E)]kd+[E(D+E)]ke

=[ 3(3+17)].06+[17(3+17)].107=10%

For 40% debt, ko= [D(D+E)]kd+[E(D+E)]ke

=[ 4(4+16)].06+[16(4+16)].107

=10%

For 50% debt, ko= [D(D+E)]kd+[E(D+E)]ke= [ 5(5+15)].06+[15(5+15)].107

= 10%

The calculations of WACC testify that the benefit of employment of more andmore debt in the capital structure is offset by the increase in equitycapitalization rate ke. The above analysis shows that under the NOI approach,the value of the firm is found by capitalizing the EBIT at the rate koand fromthis value, the value of debt is deducted to find out the value of the equity.

Value of equity = value of firm value of debt


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Traditional Approach: a practical view point In practical situation both NI and NOI Approach are extreme in view and seem

to be unrealistic. The traditional approach takes a compromising view betweenthe two and incorporates the basic philosophy of both. It takes midwaybetween the NI approach ( that the value of the firm can be increased byincreasing leverage) and the NOI approach (that the value of the firm isconstant irrespective of the degree of financial leverage).

As per the traditional approach, a firm should make judicious use of both debtand the equity to achieve a capital structure which maybe called the optimalcapital structure. At this capital structure, the overall cost of capital, WACC ofthe firm will be minimum and value of the firm maximum. The traditionalviewpoint states that the value of the firm increases with increase in financialleverage but upto a certain limit only. Beyond this limit, the increase in

financial leverage will increase its WACC also and hence the value of the firmwill decline.

Under traditional approach, kd is assumed to be less than ke.


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Thus as per the traditional approach, a firm can be benefitted from a moderatelevel of leverage when the advantages of using debt (having lower cost) out

weigh the disadvantages of increasing ke (as a result of higher financial risk).The overall cost of capital ko, therefore is a function of the financial leverage.The value of the firm can be affected by the judicious use of debt and equity inthe capital structure.


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illustration 3:

ABC Ltd. having a EBIT of Rs.1,50,000 is contemplating to redeem a part of the

equity by introducing debt financing. Presently its a 100% equity firm with keof16%. The firm is to redeem the capital by introducing debt financing uptoRs.3,00,000 i.e.30% of the total funds or upto Rs.5,00,000 i.e. 50% of totalfunds. It is expected that for the debt financing upto 30% the rate of interest willbe 10% and the kewill increase to 17%. However if the firm opts for 50% debtfinancing then the interest will be payable at the rate of 12% and the kewill be20%. Find out the value of the firm and its WACC under different levels of debtfinancing.


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Solution: 0% debt 30% debt 50% debt

Total debt ----- Rs.3,00,000 Rs.5,00,000

Rate of interest ------ 10% 12%

EBIT Rs.1,50,000 1,50,000 1,50,000

-interest ------- 30,000 60,000

PBT 1,50,000 1,20,000 90,000

ke .16 .17 .20

Value of equity, E 9,37,500 7,05,882 4,50,000

Value of debt ----- 3,00,000 5,00,000

Total value 9,37,500 10,05,882 9,50,000

ko (EBIT/Total value) .16 .149 .158

With the increase in leverage from 0% to 30%, the firm is able to reduce itsWACC from 16% to 14.9% & the value of the firm increases from Rs. 9,37,500 to

Rs.10,05,882. This happens as the benefits of employing cheaper debt are

available and ke does not rise too much. Thereafter when the leverage is

increased further to 50%, the cost of debt as well as equity both rise to 12% and

20% resp. The eq. investors have increased the eq. capitalization rate to 20% as

they are now finding the firm to be more risky (as a result of 50% leverage).


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The increase in cost and debt and the eq. capitalization rate has increased the koand hence as a result the value of the firm has reduced from Rs.10,05,882 toRs.9,50,000 and the ko has increased from 14.9% to 15.8%.

Thus the above example shows that that the value of the firm increases upto aparticular level of leverage only and further increase would reduce the value ofthe firm . So by judicious use of financial leverage the firm can optimize its value.

Thus the traditional approach seems to a workable position on the theoreticalgrounds. The kdand keboth maybe expected to increase beyond a particular levelof leverage. However the traditional approach is criticized on the point that thevalue of the firm is a factor of its profitability rather than its financial mix.


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Modigliani-Miller Model: extension of the NOI

approach The MM model maintains that under a given set of assumptions, the capital

structure and its composition has no effect on the value of the firm. The modelshows that the financial leverage does not matter and the cost of capital andthe value of the firm are independent of the capital structure. There is nothingwhich maybe called the optimal capital structure.

Assumptions of MM Model:

1. The capital markets are perfect and complete information is available to allthe investors free of cost. The implication of this assumption is that investorscan borrow and lend funds at same rate and can move quickly from onesecurity to another without incurring any transaction cost.

2. The securities are infinitely divisible.

3. Investors are rational and well informed about the risk return of all the

securities.

4. All the investors have same probability distribution about expected futureearnings.

5. There is no corporate income tax.

6. The personal leverage and corporate leverage are perfect substitutes.


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On the basis of these assumptions, the MM Model derived that :

a) The total value of the firm is equal to the capitalized value of the operatingearnings of the firm. The capitalization is to be made at a rate appropriate to

the risk class of the firm.b) The total value of the firm is independent of the financing mix i.e. the

financial leverage.

c) The cut off rate for the investment decision of the firm depends upon the riskclass to which the firm belongs and thus is not affected by the financingpattern of these investments.

The MM Model argues that if 2 firms are alike in all respects except that theydiffer in respect of their financing pattern and their market value, then theinvestors will develop a tendency to sell the shares of the over valued firm(creating a selling pressure) and to buy the shares of the under valued firm

(creating a demand pressure). This buying and selling pressure will continuetill the two firms have the same market value.


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There are 2 firms, LEV &Co. and ULE & Co. These firms are alike and identical inall respects except that the LEV &Co. is a levered firm and has 10% debt ofRs.30,00,000 in its capital structure. On the other hand, the ULE &Co. is anunlevered firm and had raised funds only by the issue of equity sh.cap. Both thesefirms have an EBIT of Rs. 10,00,000 and the equity capitalization rate ,ke of 20%.Under these parameters, the total value and the WACC of both the firms will beascertained as follows:

LEV & Co. ULE &Co.

EBIT 10,00,000 10,00,000

-Interest 3,00,000 Nil

Net profit 7,00,000 10,00,000

Equity capitalization rate .20 .20

Value of equity 35,00,000 50,00,000

Value of debt 30,00,000 Nil

Total value, V 65,00,000 50,00,000

WACC, ko= EBIT/V 15.38% 20%


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Though, both LEV &Co. and ULE& Co. have the same EBIT of Rs.10,00,000and the same ke of 20% and still the LEV &Co.., the levered firm has a lower koand a higher value as against the ULE & Co.., which is an unlevered firm. MMargue that this position cannot persist for long and soon there will be equalityin the values of the two firms. MM Model proves the above point by thearbitrage mechanism.

The arbitrage process: refers to undertaking by a person of two relatedactions simultaneously in order to derive some benefit. Continuing with the

above example suppose an investor is holding 10% equity sh.cap of LEV &Co.The value of his ownership right is Rs.3,50,000 i.e.10% of Rs.35,00,000.further out of the total net profit of Rs.7,00,000 of LEV &Co. he is entitled to10%, i.e.Rs.70,000 p.a. and getting a return of 20%, his ke , on his worth. Inorder to avail the opportunity of making a profit he decides to convert hisholdings from LEV &Co. to ULE & Co.,. He disposes off his holdings in LEV

&Co. for Rs.3,50,000, but in order to buy 10% holdings of ULE &Co. he needstotal funds of Rs.5,00,000, whereas his proceeds are only Rs.3,50,000. So hetakes a loan @10% of an amount equal to Rs.3,00,000 ( i.e. 10% debt of theLEV & Co.) and now he is having total funds of Rs. 6,50,000 (i.e. proceeds ofRs.3,50,000 and the loan of Rs.3,00,000).


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Out of the total funds of Rs.6,50,000 he invests Rs.5,00,000 to buy 10% holdings ofULE &Co. still he has funds of Rs. 1,50,000 available with him. Assuming that theULE &Co. continues to earn the same EBIT of Rs. 10,00,000 the net returnsavailable to the investor from ULE &Co. are:

Profit available from ULE &Co. Rs.1,00,000(being 10% of net profit)

- Interest payable@ 10% on Rs.3,00,000 loan 30,000

Net return 70,000

So the investor is able to get the same return of Rs.70,000 from ULE &Co. also,which he was receiving as an investor of LEV &Co.., but he has funds ofRs.1,50,000 left over for investment else where. Thus his total income maybe morethan Rs.70,000 (inclusive of some income on investment of Rs.1,50,000).Moreover his risk is the same as before. Though his new outlet i.e. ULE &Co. is anunlevered firm (hence no risk) but the position of the investor is levered because of

his borrowing of Rs.3,00,000 from the market. He has replaced corporate leverageby his personal leverage.

Thus an investor who originally owns a part of the levered firm and enters into anarbitrage process as above, will be better off selling the holding in levered firm andbuying the holding in unlevered firm using his homemade leverage.


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The MM Model argues that this opportunity to earn extra income througharbitrage process, will attract many investors. The gradual increase in sales of theshares of the levered firm, LEV& Co. will push its prices down and the tendencyto purchase the shares of the unlevered, ULE &Co. will drive its prices up. Theselling and purchasing pressure will continue until the market value of the 2firms are equal. At this stage, the value of the levered firm and unlevered firmand also their cost of capital are same; thus the overall cost of capital, ko, isindependent of the financial leverage.


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The arbitrage process described above involves a transfer of investment from alevered firm to unlevered firm. The arbitrage process will work in the reversedirection also, when the value of the levered firm is less than the value of the

unlevered firm. Say the total value of LEV &Co. is Rs.45,00,000 (consisting ofRs.30,00,000 debt capital and Rs. 15,00,000 equity sh.cap) and the value of ULE&Co. is same as before i.e. Rs.50,00,000. Now the investor holding 10% sh.cap ofULE &Co. sells his ownership right for Rs.5,00,000. Out of these proceeds hebuys 10% of share capital of LEV &Co. for Rs. 1,50,000 and invests Rs.3,00,000(i.e. 10% of Rs.30,00,000) in 10% government bonds. Still he would be having

funds of Rs.50,000 with him and his position in respect of incomes from the 2firms would be as under:

ULE &Co. LEV &CO.

10% profits 1,00,000 70,000

10% interest on bonds ---- 30,000

Total income 1,oo,ooo 1,00,000

Thus by performing the arbitrage process, the investor will not be able to

maintain his income level, but also be having additional cash flows of

Rs.50,000 at his disposal. The prices of the share of ULE &Co. and LEV &Co.

must adjust until the values of both the firms are equal.


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Critical evaluation of MM Model: theoretically the MM Model and itsemphasis of no relationship between the leverage and the value of the firm seemsto be good enough in the light of the assumptions underlying the model.

However most of the assumptions are unrealistic and untenable. Moreover, thearbitrage process which provides behavioral justification for the model, is itselfquestionable in real life as perfect competition is never found and the transactioncosts are inevitable.

1. Non substitutability of personal and corporate leverages

2. Transaction costs3. Institutional investor

4. Availability of complete information

5. Corporate taxes

MM also agreed in their later analysis that the leverage may increase the valueof the firm . The effect of corporate tax on the firm can be explained with anexample. Say A Ltd. and B Ltd. both alike in all respect, except that out of totalcapital fund of Rs. 10,00,000, B Ltd raised Rs. 5,00,000 by the issue of 10%deb. Both the firms have to pay tax @ 30%. The position of their EBIT and itsappropriation under two types of economic conditions is:


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Eco. condition

A Ltd.Avg.

A Ltd.Good

B Ltd.Avg.

B Ltd.Good

EBIT 50,000 1,50,000 50,000 1,50,000

-Interest ----- ------ 50,000 50,000

PBT 50,000 1,50,000 ------ 1,00,000

-Tax@ 30% 15,000 45,000 ------ 30,000

PAT 35,000 1,05,000 ---- 70,000

Total cash flow

for debt & eq.sh.hol 35,000 1,05,000 50,000 1,20,000

A Ltd (unlevered firm) had a tax liability of Rs.15,000 and Rs.45,000 incase of

average and good economic conditions respectively; whereas B ltd (levered firm)

having the same EBIT of Rs.50,000 and Rs. 1,50,000 has to pay only zero or

Rs.30,000 taxes in average and good economic conditions respectively.

So for B Ltd., having 50% leverage in its capital structure, the tax liability becomessmaller under both types of eco. conditions. Similarly the debt holders and the

sh.hol of the firm, who collectively determine the total value of the firm, also receive

a larger share of EBIT in case of leverage firm than their share in the unlevered

firm. This is because of the fact that the interest is tax-deductible in case of the

levered firm.


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The excess cash flow available to the investors of a levered firm can be calculatedas interest charged*tax rate i.e. Rs.50,000*.30= Rs.15,000. This is the differencebetween the cash flows from the levered firm and unlevered firm (i.e.Rs.1,20,000-Rs.1,05,000). This difference of Rs. 15,000 is also known as

Interest tax- shield.

VU= EBIT(1-t)

ko

In the above equation value of EBIT will be equal to PBT because in an unlevered

firm there would be no interest liability.

VL= VU+ PV of interest tax shield

Thus VL= VU+Debt *(t)

The value of the levered firm under MM Model (after incorporating the corporatetax) will be higher than the value of unlevered firm.


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Pecking order theory This theory is based on the assertion that managers have more info about their

firms than investors. This disparity of info is referred to as asymmetric

information. Other things being equal, because of asymmetric info, managers will issue debt

when they are positive about their firms future prospects and will issue equitywhen they are unsure. A commitment to pay a fixed amount of interest andprincipal to debt- holders implies that the co. expects steady cash flows. On theother hand, an equity issue would indicate that the current share price is over

valued. Therefore, the manner in which managers raise capital gives a signal oftheir belief in their firms prospects to investors. This also implies that the firmalways use internal finance when available and choose debt over new issue ofequity when external financing is required.

Myers has called it the pecking order theory since there is not a well defined debtequity target and there are 2 kinds of equity, internal and external, one at the topof the pecking order and the other at the bottom. Debt is cheaper than the costs ofinternal and external equity due to interest deductibility. Internal equity ischeaper and easier to use than external equity.


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internal equity is cheaper because (1) personal taxes might have to paid byshareholders on distributed earnings, and (2) no transaction costs (issue costs)etc, are incurred when earnings are retained.

Managers avoid signaling adverse information about their companies by usinginternal finance. The profitable cos. have lower debt ratios not because they havelower targets but because they have internal funds to finance their activities.They will issue equity sh. cap when they think that the shares are over valued.Because of this, it has been found that the announcement of new issue of sharesgenerally causes share prices to fall.

Thus, the pecking order theory implies that the managers raise finance in the follorder:

1. Managers always prefer to use internal finance.

2. When they do not have internal finance, they prefer issuing debt. They firstissue secured debt and then unsecured debt followed by hybrid securities suchas convertible debentures.

3. As a last resort, managers issue shares to raise finances.

Capital Structure ,Cost of Capital and Value

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