cost of capitl

8/7/2019 cost of capitl

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CONCEPT OF COST OF CAPITAL:

The term cost of capital refers to the maximum rate ofreturn a firm must earn on its investment so that the marketvalue of company's equity shares does not fall. This is anconsonance with the overall firm's objective of wealthmaximization. This is possible only when the firm earns areturn on the projects financed by equity shareholders'funds at a rate which is at least equal to the rate of returnexpected by them. If a firm fails to earn return at theexpected rate, the market value of the shares would fall and

thus result in reduction of overall wealth of the shareholders.

Thus, a firm's cost of capital may be defined as "the rate ofreturn the firm requires from investment in order to increasethe value of the firm in the market place".

There are three basic aspects of concept of cost:

(i) It is not a cost as such: A firm's cost of capital is reallythe rate of return that it requires on the projects available.

It is merely a 'hurdle rate'. Of course, such rate may becalculated on the basis of actual cost of differentcomponents of capital.

(ii) It is the minimum rate of return: A firm's cost of capitalrepresents the minimum rate of return that will result in atleast maintaining (if not increasing) the value of its equityshares.

(iii) It compromises of three components: A firm's cost of

capital comprises of three components.

(a) Return at zero risk level: This refers to the expected rateof return when a project involves no risk whether businessof financial.

(b) Premium for business risk: The term business risk refers


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to the variability in operating profit (EBIT) due to change insales. In case a firm selects a project having more than thenormal or average risk, the suppliers of funds for the projectwill expect a higher rate of return than the normal rate. The

cost of capital will thus go up. The business risk is generallydetermined by the capital budgeting decisions.

(c) Premium for financial risk: The term financial risk refersto the risk on account of pattern of capital structure (ordebt-equity mix). In general, it may be said that a firmhaving a higher debt content in its capital structure is morerisky as compared to a firm which has a comparatively lowdebt content. This is because in the former case the firmrequires higher operating profit to cover periodic interestpayment and repayment of principal at the time of maturityas compared to the latter. Thus, the chances of cashinsolvency are greater in case of such firms. The suppliers offunds would therefore expect a higher rate of return fromsuch firms as compensation for hither risk.

The above three components of cost of capital may be put inthe form of the following equation:

K =r0 +b +fwhereK = Cost of capital,r0= return at zero risk level,

b = Premium for business risk;

f = Premium for financial risk.

IMPORTANCE OF COST OF

CAPITAL:The determination of the firm's cost of capital is importantfrom the point of view of both capital budgeting as well as


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capital structure planning decisions.

(i)Capital budgeting decisions: In capital budgetingdecisions, the cost of capital is often used as a discount rateon the basis of which the firm's future cash flows arediscounted to find out their present values. Thus, the cost ofcapital is the very basis for financial appraisal of new capitalexpenditure proposals. The decision of the finance mangerwill be irrational and wrong I case of cost of capital is notcorrectly determined. This is because the business mustearn at least at a rate which equals to its cost of capital inorder to make at least a break-even.

(ii)Capital structure decisions: The cost of capital is also an

important consideration in capital structure decisions. Thefinance manager must raise capital from different sources ina way that it optimizes the risk and cost factors. The sourcesof funds which have less cost involved high risk. Raising ofloans may, therefore, be cheaper on account of income taxbenefits, but it involves heavy risk because a slight fall inthe earning capacity of the company may bring the firm nearto cash insolvency. It is, therefore, absolutely necessary thatcost of each source of funds is carefully considered and

compared with the risk involved with it.

CLASSIFICATION OF COST OF

CAPITAL:Cost of capital can be classified as follows:

1. Explicit cost and implicit cost

The explicit cost of any source of finance may be defined asthe discount rate that equates the present value of the fundsreceived by the firm net of underwriting costs, with thepresent value of the expected cash outflows. These outflows


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may be interest payment, repayment of principal ordividend. This may be calculated by computing valueaccording to the following equation:

Io= C1 Cn Cn

(1+K) + (1+K)2 + (1+K)n

where

Io = Net amount of funds received by the firm at time zero

C = Cash Outflow in the period concerned

n = Duration or number of years for which the funds areprovided

K = Explicit cost of capital.

Thus, the explicit cost of capital may be taken as "the rate ofreturn of the cash flows of financing opportunity". It is, inother words the internal rate of return the firm pays forfinancing. For example, if a company raised a sum of Rs.llakh by way of debentures carrying interest at 9% and

payable after 20 years, the cash inflow will be a sum of Rs.llakh. However, annual cash outflow will be Rs.9,000 for 20years. The explicit cost will, therefore, be that rate ofinternal return which equates Rs. 1 lakh, the initial cashinflow with Rs.9,000 payable every year for 20 years andRs.l lakh at the end of 20 years.

The implicit cost may be defined as "the rate of returnassociated with the best investment opportunity for the firm

and its shareholders that will be forgone if the projectpresently under consideration by the firm were accepted".When the earnings are retained by a company, the implicitcost is the income which the shareholders could have earnedif such earnings would have been distributed and investedby them. As a matter of fact explicit costs arise when thefunds are raised, while the implicit costs arise whenever


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they are used. Viewed from this angle, funds raised fromany source have implicit costs once they are invested.

2. Future cost and historical cost

Future cost refers to the expected cost of funds to financethe project, while historical cost is the cost which hasalready been incurred for financing a particular project. Infinancial decision making, the relevant costs are future costsand not the historical costs. However, historical costs areuseful in projecting the future costs and providing anappraisal of the past performance when compared withstandard or predetermined cost.

3. Specific cost and combined cost

The cost of each component of capital (i.e., equity shares,preference shares, debentures, loans etc.) is known asspecific cost of capital. In order to determine the averagecost of capital of the firm, it becomes necessary first toconsider the costs of specific methods of financing. Thisconcept of cost if useful in those cases where theprofitability of a project is judged on the basis of the cost of

the specific sources from where the project will be financed.For example, if a company's estimated cost of equity sharecapital is 11%, a project which will be financed out of equityshareholders' funds would be accepted only when it gives arate of return of at least 11%.

The composite or combined cost of capital is inclusive of allcost of capital from all sources, i.e., equity shares,preference shares, debentures and other loans. In capital

investment decisions, the composite cost of capital will beused as a basis for accepting or rejecting the proposal, eventhough the company may finance one proposal from onesource of financing while another proposal from anothersource of financing. This is because it is overall mix offinancing over time, which is important in valuing the firm asan ongoing overall entity.


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4. Average cost and marginal cost

The average cost of capital is the weighted average of thecosts of each component of funds employed by the firm. The

weights are in proportion of the share of each component ofcapital in the total capital structure.

The computation of average cost involves the followingproblems:

(i) It requires measurement of costs of each specific sourceof capital,

(ii) It requires assigning of appropriate weights of each

component of capital.(iii) It raises a question whether the average cost of capitalis at all affected by changes in the composite of the capital.The financing experts differ in their approaches. According tothe traditional approach, the firm's cost of capital dependsupon the method and level of financing, while according tothe modern approach as propounded by Modigliani andMiller, the firm's total cost of capital is independent of themethod and level of financing.

Marginal cost of capital, on the other hand, is the weightedaverage cost of new funds raised by the firm. For capitalbudgeting and financing decision, the marginal cost ofcapital is the most important factor to be considered.

1. Traditional Approach

According to this approach a firm's cost of capital dependsupon the method and level of financing or its capitalstructure. A firm can, therefore, change its overall cost ofcapital by increasing or decreasing the debt-equity mix. Forexample, if a company has 9% debentures (issued andpayable at par) the cost of funds raised from this sourcecomes to only 4.5% (assuming a 50% tax rate). Funds from


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other sources, such as equity shares and preference shares,also involve cost. But the raising of funds throughdebentures is cheaper because of following reasons:

(i) Interest rates are usually lower than dividend rates,

(ii) Interest is allowed as an expense resulting in a taxbenefit while dividend is not allowed as an expense whilecomputing taxable profits of the company.

The traditional theorists, therefore argue that the weightedaverage cost of capital will decrease with every increase inthe debt content in the total capital employed. However, thedebt content in the total capital employed should be

maintained at a proper level because cost of debt is a fixedburden on the profits of the company, it may have adverseconsequences in periods when a company has lowprofitability. Moreover, if the debt content is raised beyond aparticular point, the investors will start considering thecompany too risky and their expectations from equity shareswill go up.

2. Modigliani and Miller Approach

According to this approach the corporation's total cost ofcapital is constant and it is independent of the method andlevel of financing. In other words, according to this approacha change in the debt equity ratio does not affect the totalcost capital. According to traditional approach, as explainedabove, the cost of capital is the weighted average cost of thedebt and the cost of equity. Each change in the debt-equityratio automatically offsets change in one with the change inthe other on account of change in the expectation of equity

shareholders.

For example, the capital structure of a company is asfollows:

9% Debenture Rs. 1,00,000

Equity Share Capital 1,00,000


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The company has present an even debt-equity ratio. It hasbeen paying dividend at the rate of 12% on equity shares.In case, the debt equity ratio changes to say 60% debt and40% equity, the following consequences will follows:

(i) The debt being cheaper, the overall cost of capital willcome down.

(ii) The expectation of the equity shareholders from presentdividend of 12%, will go up because they will find thecompany now more risky.

Thus, the overall cost of capital of the company will not beaffected by change in the debt-equity ratio. Modigliani and

Miller, therefore, argue that within the same risk class, merechange of debt-equity ratio does not affect cost of capital.Their following observations in their article. "Cost of CapitalCorporation Finance and Theory of Investment", needcareful consideration:

(i) The total market value of the firm and its cost of capitalare independent of its capital structure. The total marketvalue of the firm can be computed by capitalizing theexpected stream of operating earnings at discount rate

considered appropriate for its risk class.

(ii) The cut-off rate for investment purposes is completelyindependent of the way in which investment is financed.

Assumptions under Modigliani-MillerApproach

The Modigliani-Miller Approach is subject to the followingassumptions:

(i) Perfect capital market: The securities are traded inperfect capital markets. This implies that:

(a) The investors are free to buy or sell securities.

(b) The investors are completely knowledgeable and rational


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persons. All information and changes in conditions areknown to them immediately.

(c) The purchase and sale of securities involve no costs suchas broker's commission, transfer, fees, etc.

(d) The investors can borrow against securities withoutrestrictions on the same conditions as the firms can.

(ii) Firms can be grouped in homogeneous risk classes:Firms should be considered to belong to a homogeneousclass if their expected earnings have identical riskcharacteristics. In other words, all firms can be categorizedaccording to the return that they give and a firm in each

class is having the same degree of business and financialrisk.

(iii)Same expectations: All investors have the sameexpectation of the firm's net operating income (EBIT) whichis used for evaluation of a firm. There is 100% dividend payout, i.e., firms distribute all of their net earnings to theshareholders.

(iv)No corporate taxes: In the original formulation Modigliani

and Miller hypothesis assumes that there are no corporatetaxes. This assumption has been removed later.

In conclusion, it may be said that in spite of the correctnessof the basic reasoning of Modigliani and Miller, the traditionalapproach is more realistic on account of the followingreasons:

(i) The corporations are subject to income-tax and,therefore, due to tax effect, the cost of debt is lower than

cost of equity capital.

(ii) The basic assumptions of Modigliani and Millerhypothesis that capital markets are perfect, is seldom true.

On account of the above reasons the Modigliani and Millerapproach has come under severe criticism. Mr. Ezra


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Solomon has observed. "The thesis that the company's costof capital is independent of its financial structure is not valid.As far as the leverage effect alone is concerned (andignoring all other considerations that might affect the choice

between debt and equity) there does exist a clearlydefinable optimum position-namely, the point at which themarginal cost of more debt is equal to or greater than acompany's average cost of more debt is equal to or greaterthan a company's average cost of capital". However, Mr.E.W. Walker's remarks very aptly explain the utility ofModigliani and Miller's approach. According to him, "thecriticisms lodged against Modigliani and Miller's thesis arevalid thus limiting its use in actual situations. Nevertheless,

the propositions as well as their criticisms should becarefully studied, since they will serve as an aid tounderstanding capital structure theory".

DETERMINATION OF COST OF CAPITAL

Problems in determination

It has already been stated that the cost of capital is one ofthe most crucial factors in most financial managementdecisions. However, the determination of the cost of capitalof a firm is not an easy task. The finance manager isconfronted with a large number of problems, bothconceptual and practical, while determining the cost ofcapital of a firm. These problems can briefly be summarizedas follows:

1. Controversy regarding the dependence of cost of

capital upon the method and level of financing

There is a, major controversy whether or not the cost ofcapital dependent upon the method and level of financing bythe company. According to the traditional theorists, the costof capital of a firm depends upon the method and level offinancing. In other words, according to them, a firm can


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change its overall cost of capital by changing its debt-equitymix. On the other hand, the modern theorists such asModigliani and Miller argue that the firm's total cost ofcapital is independent of the method and level of financing.

In other words, the change in the debt-equity ratio does notaffect the total cost of capital.

An important assumption underlying MM approach is thatthere is perfect capital market. Since perfect capital marketdoes not exist in practice, hence the approach is not of muchpractical utility.

2. Computation of cost of equity

The determination of the cost of equity capital is anotherproblem. In theory, the cost of equity capital may be definedas the minimum rate of return that a company must earn onthat portion of its capital employed, which is financed byequity capital so that the market price of the shares of thecompany remains unchanged. In other words, it is the rateof return which the equity shareholders expect from theshares of the company which will maintain the presentmarket price of the equity shares of the company.

This means that determination of the cost of equity capitalwill require quantification of the expectations of the equityshareholders. This is a difficult task because the equityshareholders value the equity shares of a company on thebasis of a large number of factors, financial as well aspsychological. Different authorities have tried in differentways to quantify the expectations of the equityshareholders. Their methods and calculations differ.

3. Computation of cost of retained earnings anddepreciation funds

The cost of capital raised through these sources will dependupon the approach adopted for computing the cost of equitycapital. Since there are different views, therefore, a financemanager has to face difficult task in subscribing and


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selecting an appropriate approach.

4. Future costs versus historical costs

It is argued that for decision-making purposes, the historical

cost is not relevant. The future costs should be considered.It, therefore, creates another problem whether to considermarginal cost of capital, i.e., cost of additional funds or theaverage cost of capital, i.e., the cost of total funds.

5. Problem of weights

The assignment of weights to each type of funds is acomplex issue. The finance manager has to make a choicebetween the risk value of each source of funds and the

market value of each source of funds. The results would bedifferent in each case.

It is clear from the above discussion that it is difficult tocalculate the cost of capital with precision. It can never be asingle given figure. At the most it can be estimated with areasonable range of accuracy. Since the cost of capital is animportant factor affecting managerial decisions, it isimperative for the finance manager to identify the range

within which his cost of capital lies.

Computation of cost of capitalComputation of cost of capital involves: (i) Computation ofcost of each specific source of finance- termed ascomputation of specific costs and (ii) Computation ofcomposite cost termed as weighted average cost.

Computation of specific costsCost of each specific source of finance, viz., debt, preferencecapital and equity capital, can be determined as follows:

Cost of Debt


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Debt may be issued at par, at premium or discount. It maybe perpetual or redeemable. The technique of computationof cost in each case has been explained later.

(a) Debt issued at par: The computation of cost of debtissued at par is comparatively an easy task. It is the explicitinterest rate adjusted further for the tax liability of thecompany. It may be computed according to the followingformula:

Kd = (l-T)R

where Kd = Cost of debt;

T = Marginal tax rate;

R = Debenture interest rate.

For example, if a company has issued 90% debentures andthe tax rate is 50%, the after tax cost of debt will be 4.5%,calculated as given below:

Kd = (l-T)R

= (1 -.5) 9 = .5x9 = 4.5%

The tax is deducted out of the interest payable, becauseinterest is treated as an expense while computing the firm'sincome for tax purposes. However, the tax adjusted rate ofinterest should be used only in those cases where the"earning of the firm before interest and tax" (EBIT) is equalto or exceed the interest. In case, EBIT is in negative, thecost of debt should be calculated before adjusting theinterest rate for tax. For example, in the above cases, thecost of debt before adjusting for tax effect will be 9%.

(b) Debt issued at premium or discount: In case thedebentures are issued at premium or discount, the cost ofdebt should be calculated on the basis of net proceedsrealized on account of issue of such debentures or bonds.Such cost may further be adjusted keeping in view the taxapplicable to the company.


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Illustration 1: A company issues 10% irredeemabledebentures of Rs. 1,00,000. The company is in 55% taxbracket. Calculate the cost of debt (before as well as aftertax) if the debentures are issued at (i) par; (ii) 10%

discount, and (iii) 10% premium.

Solution:

Cost of debentures can be calculated according to the

following formula:

Kd = I (1-T)

NP

whereKd = Cost of debt after tax.I= Annual interest payment.

NP = Net proceeds of loans or debentures.

T = Tax rate.

(i) Issued at par

Kd= 1000 (1-.55)

1,00,00

= 1 x .45

10

= .045 or 4.5%

(ii) Issued at discount:

Kd = 10,00 (1-.55)90,000

= 1 x .45

9


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= .05 or 5%

(iii) Issued at 10% premium:

Kd =10,00 (1-.55)

1,00,00

=1 x .45

11

= .041 or 4.1%.

(c) Cost of redeemable debt: In the preceding pageswhile calculating cost of debt we have presumed that

debentures/bonds are not redeemable during the lifetime ofthe company. However, if the debentures are redeemableafter the expiry of a fixed period the effective cost of debtbefore tax can be calculated by using the following formula:

Kd(before tax) = I + (P - NP)/n

(N + NP)/2whereI= Annual interest payment,

P = Par value of debentures,NP = Net proceeds of debentures,n = Number of years to maturity.

Illustration 2: A firm issues debentures of Rs. 1,00,000and realises Rs.98,000 after allowing 2% commission tobrokers. The debentures carry an interest rate of 10%. Thedebentures are due for maturity at the end of the 10th year.You are required to calculated the effective cost of debt

before tax.Solution:

Kd (before tax) =I + (P - NP)/n

(P + NP)/2


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=10,000 + (1,00,000 - 98,000) / 10

(1,00,000 + 98,000)72

=10,000+200

99,000

=.103 or 10.30%.

In the above example, if the tax rate is 55%, the cost ofdebt after tax can be calculated as follows:

Kd (after tax)

= Kd (before tax) x ( 1 - T)

= 10.30(1 -.55)= 10.30 x. 45 = 4.64%.

In order to keep sufficient earnings available for equityshareholders for maintaining their present value, thecompany should see that it earns on the funds provided byraising loans at least equal to the effective interest ratepayable on them. In case the firm earns less than theeffective interest rate, earnings available for the equityshareholders will decrease. This would naturally affectadversely the market price of the company's equity shares.

It should be noted that while calculating the real cost ofdebt, not only the contractual interest rate but also certainother imputed costs or raising funds from debts should beconsidered. The more is the financing of funds from the debtthe higher is the expectation of the equity shareholders ontheir capital because of increase in the risk factor. Moreover,with increase in the amount of borrowed funds, the interest

rate is also likely to rise. Thus, the imputed cost of raisingfunds through borrowings includes the increase in theexpectation of the equity shareholders from their capitalemployed in the business. If it had not been so, themanagement would have at all times liked to finance theirrequirements only by means of raising long-term debts.


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Cost of preference capital

The computation of the cost of preference capita howeverposes some conceptual problems. In case of borrowings,

there is legal obligation on the firm to pay interest at fixedrates while in case of preference shares, there is no suchlegal obligation. Hence, some people argue that dividendspayable on preference share capital do not constitute cost.However, this is not true. This is because, though it is notlegally binding on the company to pay dividends onpreference shares, it is generally paid whenever thecompany makes sufficient profits. The failure to pay dividendmay be better of serious concern from the point of view of

equitshareholders. They may even lose control of thecompany because of the preference shareholders getting thelegal right to participate in the general meetings of thecompany with equity shareholders under certain conditionsin the event of failure of the company to pay them theirdividends. Moreover, the accumulation of arrears ofpreference dividends may adversely affect the right of equityshareholders to receive dividends. This is because nodividend can be paid to them unless the arrears of

preference dividend are cleared. On account of thesereasons the cost of preference capital is also computed onthe same basis as that of debentures. The method of itscomputation can be put in the form of the followingequation:

Kp = Dp

NP

whereKp == Cost of preference share capitalDp = Fixed preference dividendNp = Net proceeds of preference shares.

Illustration 3: A company raised preference share


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capital of Rs. 1,00,000 by issue of 10% preference shares ofRs.10 each. Calculate the cost of preference capital thenthey are issued at (i) 10% premium, and (ii) at 10%discount:

Solution:

(i) When preference shares are issued at 10% premium:

Kp = Dp = 10000X100

NP 1,10,000

=9.09%

(ii) When preference shares are issued at 10% discount:

Kp =Dp = 10,000 X 100

NP 9,0000

=11.11%.

Cost of redeemable preference shares

In case of redeemable preference shares, the cost of capital

is the discount rate that equals the net proceeds of sale ofpreference shares with the present value of future dividendsand principal repayments. Such cost can be calculatedaccording to the same formula which has been given in thepreceding pages for calculating the cost of redeemabledebentures.

Illustration 4: A company has 10% redeemable preferenceshares redeemable at the end of the 10th year from the yearof their issue. The underwriting costs came to 2%. Calculatethe effective cost of preference share capital:

Solution:

Kd (before tax) =Dp + (P - NP)/n

(P + NP)/2


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=10.000 + (1,00,000 - 98,000) / 10

(1,00,000 + 98,000) / 2

=10,200

99,000 = 10.30%.

It should be noted that the cost of preference capital is notadjusted for taxes, since dividend on preference capital istaken as an appropriation of profits and not as a chargeagainst profits. Thus, the cost of preference capital issubstantially greater than the cost of debt.

Cost of equity capital

The computation of the cost of equity capital is a difficulttask. Some people argue, as observed in case of preferenceshares, that the equity capital does not involve any cost. Theargument put forward by them is that it is not legallybinding on the company to pay dividends to the equityshareholders. This does not seem to be a correct approachbecause the equity shareholders invest money in shares withthe expectation of getting dividend from the company. The

company also does not issue equity shares without havingany intention to pay them dividends. The marketprice of theequity shares, therefore, depends upon the return expectedby the shareholders.

Conceptually cost of equity share capital may be defined asthe minimum rate of return that a firm must earn on theequity financed portion of an investment in a project in orderto leave unchanged the market price of such shares. Forexample, in case the required rate of return on equity sharesis 16% and cost of debt is 12%, and the company has thepolicy of financing with 75% equity and 25% debt, therequired rate of return on the project could be estimated asfollows:

16% x .75 = 12%


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12% x .25 = 3%15%

This means that if the company accepts a project involvingan investment of Rs.l0,000, and giving an annual return ofRs. l,500, the project would provide a return which is justsufficient to leave the market value unchanged of thecompany's equity shares. The rate of return on equityfinanced portion can be calculated as follows:

Total Return Rs. 1,500

Less: Interest on debentures 0.25 x 12 x 100 Rs. 300Amount Available for equity shareholders

Rate of return on equity= 1,200 x 100 Rs. 1,2007,500

= 16%

Thus, the expected rate of return is 16% which just equalsthe required rate of return on investment. If the projectearns less than Rs. l,500 a year, it would provide a returnless than required by the investors. As a result, the marketvalue of the company's shares would fall. Theoretically, thisrate of return could be considered as the cost of equitycapital.

In order to determine the cost of equity capital, it may bedivided into the following two categories:

1. The external equity or new issue of equity shares.

2. The retained earnings.

The computation of the cost of each of these is explainedbelow:

The external equity or new issue of equity

shares


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From the preceding discussion, it is implied that in order tofind out the cost of equity capital, one must be in a positionto determine what the shareholders as a class expect fromtheir investment in equity shares. This is a difficult

proposition because shareholders as a class are difficult topredict or quantify. Different authorities have conveyeddifferent explanations and approaches. The following aresome of the appropriate according to which the cost ofequity capital can be worked out:

1. Dividend price (D/P) approach

According to this approach, the investor arrives at themarket price of an equity shares by capitalizing the set of

expected dividend payments. Cost of equity capital hastherefore been defined as "the discount rate that equatesthe present value of all expected future dividends per sharewith the net proceeds of the sale (or the current marketprice) of a share".

In other words, the cost of equity capital will be that rate ofexpected dividends which will maintain the present marketprice of equity shares.

This approach rightly emphasizes the importance ofdividends, but it ignores the fact that the retained earningshave also an impact on the market price of the equityshares. The approach therefore does not seem to be verylogical.

Illustration 5: A company offers for public subscription

equity shares of Rs.10 each at a premium of 10%. Thecompany pays 5% of the issue price as underwritingcommission. The rate of dividend expected by the equityshareholders is 20%.

You are required to calculate the cost of equity capital.Willyour cost of capital be different if it is to be calculated on thepresent market value of the equity shares, which is Rs.15?


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Solution:

The cost of new equity can be determined according to thefollowing formula:

Ke = D

NPwhereKe = Cost of equity capital;D = Dividend per equity share;NP = Net proceeds of an equity share,

Ke = 2

10.45 = 0.19 or 19%Rs. 11 - Re. 0.55.

In case of existing equity shares, it will be appropriate tocalculate the cost of equity on the basis of market price ofthe company's shares. In the present case, it can becalculated according to the following formula:

Ke = D

MP

whereKe = Cost of equity capital;D = Dividend per equity share;MP = Market price of an equity share.

Ke = 2

15 =0.133 or 13.3%.

2. Dividend price plus growth (D/P + g) approach

According to this approach, the cost of equity capital isdetermined on the basis on the expected dividend rate plusthe rate of growth in dividend. The rate of growth individend is determined on the basis of the amount of


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dividends paid by the company for the last few years. Thecomputation of cost of capital according to this approach canbe done by using the following formula:

Ke = D +g

NP

whereKe = Cost of equity capital;D = Expected dividend per share;NP = Net proceeds of per share;g = Growth in expected dividend.

It may be noted that in case of existing equity shares, the

cost of equity capital can also be determined by using theabove formula. However, the market price (MP) should beused in place of net proceeds (NP) of the shares as givenabove.

Illustration 6: The current market price of an equity shareof a company is Rs.90. The current dividend per share isRs.4.50. In case the dividends are expected to grow at therate of 7% , calculate the cost of equity capital.

Solution:

Ke =D +g

MP

=4.50 + .07

90

= 0.5+ .07 = .12 or 12%.

Illustration 7: From the following details of X Limited,calculate the cost of equity capital:(i) Each share is of Rs. 150 each(ii) The underwriting cost per share amounts to 2%.

(iii) The following are the dividends paid by the company for


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the last five years:

Year Dividend per share per share

1987 10.50

1988 11.00

1989 12.50

1990 12.75

1991 13.40

(iv) The company has a fixed dividend pay out ratio,

(v) The expected dividend on the new shares amounts to Rs.14.10 per share.

Solution:

In order to calculate the cost of funds raised through equityshare capital, calculation of growth rate will be necessary.During the last 4 years (and not 5 years, since dividends atthe end of 1987 are being compared with dividends at theend of 1991) the dividends declared by the company have

increased from Rs.10.50 to Rs.13.40 giving a compoundbefore of 1.276 (i.e., 13.40/10.50). By looking to the"compound sum of one rupee tables" in the line of 4 yearsone can find out that a sum of Re.l would accumulate to1.276 in 4 years at 6% interest. This means that growthrate of dividends is 6%. The cost of equity funds can now bedetermined as follows:

Ke = D +g

MP

= 14.10 + 6%

147

= 9.6% + 6% = 15.6%.


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The "dividend price growth approach" is, to a great extent,helpful, in determining satisfactorily the expectation of theinvestors. However, the quantification of the expectations ofgrowth of dividends is a difficult matter. Usually, it ispresumed that the growth in dividends will be equal to thegrowth rate in earnings per share.

3. Earning price (E/P) approach

According to this approach, it is the earning per share whichdetermines the market price of the shares. This is based onthe assumption that the shareholders capitalize a stream of

future earnings (as distinguished from dividends) in order toevaluate their shareholdings. Hence, the cost of capitalshould be related to that earnings percentage which couldkeep the market price of the equity shares constant. Thisapproach, therefore, takes into account both dividends aswell as retained earnings. However, the advocates of thisapproach differ regarding the use of both earnings and themarket price figures. Some simply use of current earningrate and the current market price of the share of the

company for determining the cost of capital. While othersrecommend average rate of earnings (based on the earningsof the past few years) and the average market price(calculated on the basis of market price for the last fewyears) of equity shares.

The formula for calculating the cost of capital according tothe approach is as follows:-

Ke = E

NP

whereKe = Cost of equity capital;D = Earning per share;NP = Net proceeds of an equity share,


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However, in case of existing equity shares, it will beappropriate to use market price (MP) instead of net proceeds(NP) for determining the cost of capital.

Illustration 8: The entire capital employed by a companyconsists of one lakh equity shares of Rs.100 each, its currentearnings are Rs. 10 lakhs per annum. The company wants toraise additional funds of Rs.25 lakhs by issuing new shares.The floatation costs are expected to be 10% of the facevalue of the shares. You are required to calculated the costof equity capital presuming that the earnings of thecompany are expected to remain stable over the next fewyears.

Solution:

Ke = E = 10

NP 90

= 0.11 or 11%.

4. Realised yield approach

According to this approach, the cost of equity capital should

be determined on the basis of the returns actually realizedby the investors in a company on their equity shares. Thus,according to this approach the past records in a given periodregarding dividends and the actual capital appreciation inthe value of the equity shares held by the shareholdersshould be taken to compute the cost of equity capital.

This approach gives fairly good results in case of companieswith stable dividends and growth records. In case of suchcompanies, it can be assumed with reasonable degree ofcertainty that the past behaviour will be repeated in thefuture also.

Illustration 9: A purchased 5 shares in a company at a

cost of Rs.240 on January 1, 1987. He held them for 5 yearsand finally sold them in January, 1992 for Rs.300. The


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amount of dividend received by him in each of these 5 yearswere as follows:

Year Dividend

1987 Rs. 14

1988 Rs. 14

1989 Rs. 14.50

1990 Rs. 14.50

1991 Rs. 14.50

You are required to calculate the cost of equity capital.

Solution:

In order to calculate the cost of capital, it is necessary tocalculate the internal rate of return. This rate of return canbe calculated by "trial and error method" as explainedearlier. The rate comes to 10% as shown below:

Year Dividend Sales Discount Present

(Rs.) Proceeds factor at Value

(Rs.) 10% (Rs.)

1987 14.00 .909 12.7

1988 14.00 .826 11.6

1989 14.50 .751 10.9

1990 14.50 .683 9.9

1991 14.50 .621 9.0

1992 300 .621 186.3

240.4

The purchase price of the 5 shares on January 1, 1987 wasRs.240. The present value of cash inflows (as on January


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1,1987) amounts to Rs.240.40. Thus, at 10%, the presentvalue of the cash inflows over a period of 5 years is equal tothe cash outflow in the year 1987. The cost of equity capitalcan, therefore, be taken as 10%.

The realized yield approach can be helpful in determining therate of return required by the investors provided thefollowing three conditions are satisfied:

(i) The company will fundamentally remain the same asregards risk,

(ii) The shareholders continue to expect the same rate ofreturn for bearing this risk,

(iii) The shareholders reinvested opportunity rate is equal tothe realized yield.

Cost of retained earnings

The companies do not generally distribute the entire profitsearned by them by way of dividend among theirshareholders. Some profits are retained by them for futureexpansion of the business. Many people feel that such

retained earnings are absolutely cost free. This is not thecorrect approach because the amount retained by company,if it had been distributed among the shareholders by way ofdividend, would have given them some earning. Thecompany has deprived the shareholders of this earnings byRetaining a part of profit with it. Thus, the cost of retainedearnings is the earning forgone by the shareholders. Inother words, the opportunity cost of retained earnings maybe taken as the cost of the retained earnings. It is equal to

the income that the shareholders could have otherwiseearned by placing these funds in alternative investments.For example, if the shareholders could have invested thefunds in alternative channels, they could have got a returnof 10%. This return of 10% has been forgone by thembecause of the company is not distributing the full profits tothem. The cost of retained earnings may, therefore, be


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taken at 10%.

The above analysis can also be understood in the followingmanner. Suppose the earnings not retained by the companyis passed on to the shareholders, and are invested by theshareholders in the new equity shares of the same company,the expectation of the shareholders from the new equityshares would be taken as the opportunity cost of theretained earnings. In other words, if earnings were paid asdividends and simultaneously an offer for the right shareswas made, the shareholders would have subscribed to theright shares on the expectation of certain return. Thisexpected return can be taken as the cost of retainedearnings of the company.

Tax Adjusted Return

In the example given above, we have presumed that theshareholders will have with them the amount of retainedearnings available when distributed by the company. Inactual practice, it does not happen. The shareholders haveto pay tax on the dividends received, incur brokerage costfor making investments, etc. The funds available with the

shareholders are, therefore, less than what they would havebeen with the company, had they been retained by it. Onaccount of this reason, the cost of retained earnings to thecompany would be always less than the cost of new equityshares issued by the company.

The following adjustments are made for ascertaining thecost of retained earnings:

(i)Income tax adjustment: The dividends receivable by the

shareholders are subject to income tax. Hence, thedividends actually received by them are not the amount ofgross dividends but the amount of net dividend, i.e., grossdividends less income tax.

(ii)Brokerage cost adjustment: Usually, the shareholdershave to incur some brokerage cost for investing the


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dividends received. Thus, the funds available with them forreinvesting will be reduced by this amount.

The opportunity cost of retained earnings to theshareholders is, therefore, the rate of return that they canobtain by investing the net dividends (i.e., after tax andbrokerage) in alternative opportunity of equal quality.

Illustration 10: ABC Ltd. is earning a net profit ofRs.50,000 per annum. The shareholders required rate ofreturn is 10%. It is expected that retained earnings, ifdistributed among the shareholders, can be invested bythem in securities of similar type carrying return of 10% perannum. It is further expected that the shareholders will have

to incur 2% of the net dividends received by them asbrokerage cost for making new investments. Theshareholders of the company are in 30% tax bracket.

You are required to calculate the cost of retained earnings tothe company.

Solution:

In order to calculate the cost of retained earnings to the

company, it is necessary to calculate the net amountavailable to the shareholders for investment and the likelyreturn earned by them. This has been done as follows:

Rs.

Dividends payable to the shareholders 50,000

Less: Income tax @ 30% 15,000

After tax dividends

35,000

Less: Brokerage cost @ 2% 700

Net amount available for investment 34,300

Since the shareholders have the investment opportunity ofearning 10%, the amount of earning received by them on


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their investment will amount to Rs.3,430 (i.e. 10% ofRs.34,300).

In case the earnings had not been distributed by thecompany among its shareholders, the company could havefull Rs.50,000 for investment, since no income tax andbrokerage cost, as above, would have been payable. Thecompany could have paid a sum of Rs.3,430 to theshareholders if it could earn a return of 6.86% calculated asfollows:

Rs. 3430 X 100

50,000 = 6.86%.

The rate of return expected by the shareholders from thecompany on their retained earnings comes to 6.86%. Itmay, therefore, be taken as the cost of the retainedearnings.

The cost of retained earnings after making adjustment forincome tax and brokerage cost payable by the shareholderscan be determined according to the following formula:

kr = Ke(1-T) (1-B)whereKr = Required rate of return on retained earnings.Ke = Shareholder's required rate of return.T = Shareholders' marginal tax rate.B = Brokerage cost.

The cost of retained earnings using the data given in theabove illustration can be calculated according to the aboveformula, as follows:

kr = Ke(1-T)(1-B)

= 10%(1 - .3) (1 - .02) = 10% x .7 x .98

= 6.86%.

The computation of the cost of retained earnings, after


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making adjustment for tax liabilities, is a difficult processbecause personal income tax rates will differ fromshareholder to shareholder. Thus, it will be necessary to findout the personal income-tax rates of the different

shareholders of the company in case cost of retainedearnings it to be calculated according to the aboveapproach. In case of a widely held public company, there area large number of shareholders of varying means andincomes. It is, therefore, almost impossible to determine asingle tax rate that would correctly reflect the opportunitycost of retained earnings to every shareholder. Evencomputation of a weighted average tax would also not givesatisfactory results. Some authorities have, therefore,

recommended the use of another approach termed by themas external yield criterion. According to this approach theopportunity cost of retained earnings is the rate of returnthat can be earned by investing the funds in anotherenterprise by the firm. Thus, according to this approach, thecost of retained earnings is simply the return on directinvestment of funds by the firm and not what theshareholders are able to obtain on their investments. Theapproach represents an economically justifiable opportunity

cost that can be applied consistently. Moreover, the need fordetermining the marginal tax rate for investors will not arisein case the approach is follows.

The "External Yield Criterion", suggested above, has not yetbeen universally accepted. In the absence of a universallyacceptable and practically feasible method for determiningseparately the cost of retained earnings, many accountantscalculate the cost of retained earnings on the same patternas that of equity shares. Moreover, when the cost of fundsraised by equity shares, the need for determining theseparate cost for retained earnings does not at all arise.Some calculate it on the Dividend Payout Basis.

Weighted average cost of capital


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After calculating the cost of each component of capital, theaverage cost of capital is generally calculated on the basis ofweighted average method. This may also be termed asoverall cost of capital. The computation of the weighted

average cost of capital involves the following steps:

1.Calculation of the cost of each specific source offunds: This involves the determination of the cost of debt,equity capital, preference capital, etc., as explained before.This can be done either on "before tax" basis or "after tax"basis. However, it will be more appropriate to measure thecost of capital on "after tax basis". This is because the returnto the shareholders is an important figure in determining thecost of capital and they can get dividends only after thetaxes have been paid.

2. Assigning weights to specific costs: This involvesdetermination of the proportion of each source of funds inthe total capital structure of the company. This may be doneaccording to any of the following method.

(a)Marginal weights method: In case of this method weightsare assigned to each source of funds, in the proportion of

financial inputs the firm intends to employ. The method isbased on the logic that our concern is with the new orincremental capital and not with capital raised in the past. Incase the weights are applied in a ratio different than theratio in which the new capital is to be raised, the weightedaverage cost of capital so calculated may be different fromthe actual cost of capital. This may lead to wrong capitalinvestment decisions. However, the method of marginalweighting suffers from one major limitation. It does not

consider the long-term implications of the firm's currentfinancing. A firm should give due attention to long-termimplications while designing the firm's financing strategy.For example, a firm may accept a project giving an aftertaxreturn of 6% because it intends to raise the funds requiredby issue of debentures having an after-tax cost of 5%. Incase next year the firm intends to raise funds by issue of


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equity shares having a cost of 9%, it will have to reject aproject which gives a return of only 8%. Thus, marginalweighting method does not consider the fact that to-day'sfinancing affects tomorrow's cost.

(b) Historical weights method: According to this method therelative proportions of various sources to the existing capitalstructure are used to assign weights. Thus, in case of thismethod the basis of weights is the proportion of fundsalready employed by the firm. This is based on theassumption that the firm's present capital structure isoptimum and it should be maintained in the future also.

Weights under historical system may be either (i) book value

or (ii) market value weights. The weighted average cost ofcapital will be different, depending upon whether book valueweights are used or market value weights are used.

The use of market value weights for calculating the cost ofcapital is theoretically more appealing on account of thefollowing reasons:

(i) The market values of the securities are closelyapproximate to the actual amount to be received from the

sale of such securities.

(ii) The cost of each specific source of finance whichconstitutes the capital structure is calculated according tothe prevailing market price.

However, the use of market value as weights is subject tothe following practical difficulties:

(i) The market values of the securities may fluctuate

considerably.

(ii) Market values are not readily available as compared tothe book values. The book values can be taken from thepublished records of the firm.

(iii)The analysis of the capital structure of the company, in


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terms of debt-equity ratio, is based on the book values andnot on the market-values.

Thus, market value weights are operationally inconvenientas compared to book value weights. However, market valueweights are theoretically consistent and sound, hence theyare a better indicator of the firm's cost of capital.

3. Adding of the weighted cost of all sources of fundsto get on overall weighted average cost of capital.

Illustration 11: From the following capital structure of acompany, calculate the overall cost of capital, using

(a) book value weights and (b) market value weights.

Source Book value Market value

Equity share capital Rs.45000 Rs.90000

(Rs. 10 shares)Retained earnings 15000Preference share capital 10000 10000

Debentures 30000 30000

The after-tax cost of different sources of finance is asfollows:

Equity share capital: 14%; Retained earnings:13%;

Preference share capital: 10%; Debenture: 5%.

Solution:

(a) COMPUTATON OF WEIGHTED AVERAGECOST OF CAPITAL

(BOOK VALUE WEIGHTS)

Source Amount Proportion AfterTax Weighted Cost

(1) (Rs.)(2) (3) (4) (5) = (3) X (4)


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Equity Share 45,000 .45 14% 6.30%

Capital

Retained 15,000 .15 13% 1.95%

Earnings

Prefrence 10,000 .10 10% 1.00%

Share Capital

Debentures 30,000 .30 5% 1.50%

Weighted average cost of capital (K0) 10.75%

Alternatively, the weighted average cost of capital can alsobe found as follows:

COMPUTED OF WEIGHTED AVERAGE COST OF CAPITAE(BOOK VALUE WEIGHTS)

Source Amount After tax Total after

(Rs.) Cost (Rs.) tax cost

(1) (2) (3) (4)=(2)X(3)

Equity Share Capital 45,000 14% 6,300

Retained Earnings 15,000 10% 1,950

Preference Share

Capital 10,000 10% 1,000

Debenture 30,000 5% 1,500

Total 1,00,000 10750

Weighted average cost of capital (K0)


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= Rs.10,750 X 1000

1,00,000

= 10.75%.

(b) COMPUTATON OF WEIGHTED AVERAGE COST OFCAPITAL (MARKET VALUE WEIGHTS)

Source Amount Propotion After Tax Weighted

(Rs.) Cost

(1) (2) (3) (4) (5)=(3)X (4)

Equity 90,000 0.692 14% 9.688Share Capital

Retained Earnings - - - -

Preference Share 10,000 0.77 10% 0.770

CapitalDebentures 30,000 0.231 5% 1.155

Weighted average cost of capital (K0) 11.613%

Illustration 12: Your company' share is quoted in themarket at Rs.20 currently. The company pays a dividend ofRe. 1 per share and the investor expects a growth rate of 5per cent per year. Compute:

(a) the company's cost of equity capital.

(b) If the anticipated growth rate is 6% p.a., calculate theindicated market price per share.

(c) If the company's cost of capital is 8% and the anticipatedgrowth rate is 5% p.a., calculate the indicated market price


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if the dividend of Re.l per share is to be maintained.

Solution:

The relationship among cost of capital, dividend, price and

expected growth rate is given by the formula:

(a) Cost of Equity Capital =

Dividend X 100 + Growth Rate %

Market Price

Company's cost of equity capital = Re.l X 100 + 5%

Rs. 20

= 10%

(b) Market price = Dividend

Cost of Equity -Growth Rate %

Company's cost of equity capital = Re.1

10% - 6%

=Re. 1 =Rs.25

4%

(c) Market price =

Re.l = Re. 1

8%-5% 3%

= Rs. 33.33

cost of capitl

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