Cost of Capital

Cost of Capital

CONCEPT OF COST OF CAPITAL

The term cost of capital refers to the maximum rate of return a firm must earn on its investment so that the market value of company's equity shares does not fall. This is an consonance with the overall firm's objective of wealth maximization. This is possible only when the firm earns a return on the projects financed by equity shareholders' funds at a rate which is at least equal to the rate of return expected by them. If a firm fails to earn return at the expected 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 of return the firm requires from investment in order to increase the 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 really the rate of return that it requires on the projects available. It is merely a 'hurdle rate'. Of course, such rate may be calculated on the basis of actual cost of different components of capital.

(ii) It is the minimum rate of return: A firm's cost of capital represents the minimum rate of return that will result in at least maintaining (if not increasing) the value of its equity shares.

(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 rate of return when a project involves no risk whether business of financial.

(b) Premium for business risk: The term business risk refers to the variability in operating profit (EBIT) due to change in sales. In case a firm selects a project having more than the normal or average risk, the suppliers of funds for the project will expect a higher rate of return than the normal rate. The cost of capital will thus go up. The business risk is generally determined by the capital budgeting decisions.

(c) Premium for financial risk: The term financial risk refers to the risk on account of pattern of capital structure (or debt-equity mix). In general, it may be said that a firm having a higher debt content in its capital structure is more risky as compared to a firm which has a comparatively low debt content. This is because in the former case the firm requires higher operating profit to cover periodic interest payment and repayment of principal at the time of maturity as compared to the latter. Thus, the chances of cash insolvency are greater in case of such firms. The suppliers of funds would therefore expect a higher rate of return from such firms as compensation for hither risk.

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

K = r0 + b + f
where
K = 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 important from the point of view of both capital
budgeting as well as capital structure planning decisions.

(i) Capital budgeting decisions: In capital budgeting decisions, the cost of capital is often used as a discount rate on the basis of which the firm's future cash flows are discounted to find out their present values. Thus, the cost of capital is the very basis for financial appraisal of new capital expenditure proposals. The decision of the finance manger will be irrational and wrong I case of cost of capital is not correctly determined. This is because the business must earn at least at a rate which equals to its cost of capital in order to make at least a break-even.

(ii) Capital structure decisions: The cost of capital is also an important consideration in capital structure decisions. The finance manager must raise capital from different sources in a way that it optimizes the risk and cost factors. The sources of funds which have less cost involved high risk. Raising of loans may, therefore, be cheaper on account of income tax benefits, but it involves heavy risk because a slight fall in the earning capacity of the company may bring the firm near to cash insolvency. It is, therefore, absolutely necessary that cost 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 as the discount rate that equates the present value of the funds received by the firm net of underwriting costs, with the present value of the expected cash outflows. These outflows may be interest payment, repayment of principal or dividend. This may be calculated by computing value according to the following equation:


C1 Cn Cn
Io = (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 are provided
K = Explicit cost of capital.

Thus, the explicit cost of capital may be taken as "the rate of return of the cash flows of financing opportunity". It is, in other words the internal rate of return the firm pays for financing. For example, if a company raised a sum of Rs.l lakh by way of debentures carrying interest at 9% and payable after 20 years, the cash inflow will be a sum of Rs.l lakh. However, annual cash outflow will be Rs.9,000 for 20 years. The explicit cost will, therefore, be that rate of internal return which equates Rs. 1 lakh, the initial cash inflow with Rs.9,000 payable every year for 20 years and Rs.l lakh at the end of 20 years.

The implicit cost may be defined as "the rate of return associated with the best investment opportunity for the firm and its shareholders that will be forgone if the project presently under consideration by the firm were accepted". When the earnings are retained by a company, the implicit cost is the income which the shareholders could have earned if such earnings would have been distributed and invested by them. As a matter of fact explicit costs arise when the funds are raised, while the implicit costs arise whenever they are used. Viewed from this angle, funds raised from any source have implicit costs once they are invested.

2. Future cost and historical cost

Future cost refers to the expected cost of funds to finance the project, while historical cost is the cost which has already been incurred for financing a particular project. In financial decision making, the relevant costs are future costs and not the historical costs. However, historical costs are useful in projecting the future costs and providing an appraisal of the past performance when compared with standard 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 as specific cost of capital. In order to determine the average cost of capital of the firm, it becomes necessary first to consider the costs of specific methods of financing. This concept of cost if useful in those cases where the profitability 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 share capital is 11%, a project which will be financed out of equity shareholders' funds would be accepted only when it gives a rate of return of at least 11%.

The composite or combined cost of capital is inclusive of all cost 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 be used as a basis for accepting or rejecting the proposal, even though the company may finance one proposal from one source of financing while another proposal from another source of financing. This is because it is overall mix of financing over time, which is important in valuing the firm as an ongoing overall entity.

4. Average cost and marginal cost

The average cost of capital is the weighted average of the costs of each component of funds employed by the firm. The weights are in proportion of the share of each component of capital in the total capital structure.

The computation of average cost involves the following problems:

(i) It requires measurement of costs of each specific source of capital,
(ii) It requires assigning of appropriate weights of each component of capital.
(iii) It raises a question whether the average cost of capital is at all affected by changes in the composite of the capital. The financing experts differ in their approaches. According to the traditional approach, the firm's cost of capital depends upon the method and level of financing, while according to the modern approach as propounded by Modigliani and Miller, the firm's total cost of capital is independent of the method and level of financing.

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



1. Traditional Approach

According to this approach a firm's cost of capital depends upon the method and level of financing or its capital structure. A firm can, therefore, change its overall cost of capital by increasing or decreasing the debt-equity mix. For example, if a company has 9% debentures (issued and payable at par) the cost of funds raised from this source comes to only 4.5% (assuming a 50% tax rate). Funds from other sources, such as equity shares and preference shares, also involve cost. But the raising of funds through debentures 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 tax benefit while dividend is not allowed as an expense while computing taxable profits of the company.

The traditional theorists, therefore argue that the weighted average cost of capital will decrease with every increase in the debt content in the total capital employed. However, the debt content in the total capital employed should be maintained at a proper level because cost of debt is a fixed burden on the profits of the company, it may have adverse consequences in periods when a company has low profitability. Moreover, if the debt content is raised beyond a particular point, the investors will start considering the company too risky and their expectations from equity shares will go up.

2. Modigliani and Miller Approach

According to this approach the corporation's total cost of capital is constant and it is independent of the method and level of financing. In other words, according to this approach a change in the debt equity ratio does not affect the total cost capital. According to traditional approach, as explained above, the cost of capital is the weighted average cost of the debt and the cost of equity. Each change in the debt-equity ratio automatically offsets change in one with the change in the other on account of change in the expectation of equity shareholders. For example, the capital structure of a company is as follows:

9% Debenture Rs. 1,00,000
Equity Share Capital 1,00,000

The company has present an even debt-equity ratio. It has been paying dividend at the rate of 12% on equity shares. In case, the debt equity ratio changes to say 60% debt and 40% equity, the following consequences will follows:

(i) The debt being cheaper, the overall cost of capital will come down.
(ii) The expectation of the equity shareholders from present dividend of 12%, will go up because they will find the company now more risky.

Thus, the overall cost of capital of the company will not be affected by change in the debt-equity ratio. Modigliani and Miller, therefore, argue that within the same risk class, mere change of debt-equity ratio does not affect cost of capital. Their following observations in their article. "Cost of Capital Corporation Finance and Theory of Investment", need careful consideration:

(i) The total market value of the firm and its cost of capital are independent of its capital structure. The total market value of the firm can be computed by capitalizing the expected stream of operating earnings at discount rate considered appropriate for its risk class.
(ii) The cut-off rate for investment purposes is completely independent of the way in which investment is financed.

Assumptions under Modigliani-Miller Approach

The Modigliani-Miller Approach is subject to the following assumptions:
(i) Perfect capital market: The securities are traded in perfect capital markets. This implies that:
(a) The investors are free to buy or sell securities.
(b) The investors are completely knowledgeable and rational persons. All information and changes in conditions are known to them immediately.
(c) The purchase and sale of securities involve no costs such as broker's commission, transfer, fees, etc.
(d) The investors can borrow against securities without restrictions 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 homogeneous class if their expected earnings have identical risk characteristics. In other words, all firms can be categorized according to the return that they give and a firm in each class is having the same degree of business and financial risk.
(iii) Same expectations: All investors have the same expectation of the firm's net operating income (EBIT) which is used for evaluation of a firm. There is 100% dividend pay out, i.e., firms distribute all of their net earnings to the shareholders.
(iv) No corporate taxes: In the original formulation Modigliani and Miller hypothesis assumes that there are no corporate taxes. This assumption has been removed later.

In conclusion, it may be said that in spite of the correctness of the basic reasoning of Modigliani and Miller, the traditional approach is more realistic on account of the following reasons:

(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 Miller hypothesis that capital markets are perfect, is seldom true.

On account of the above reasons the Modigliani and Miller approach has come under severe criticism. Mr. Ezra Solomon has observed. "The thesis that the company's cost of capital is independent of its financial structure is not valid. As far as the leverage effect alone is concerned (and ignoring all other considerations that might affect the choice between debt and equity) there does exist a clearly definable optimum position-namely, the point at which the marginal cost of more debt is equal to or greater than a company's average cost of more debt is equal to or greater than a company's average cost of capital". However, Mr. E.W. Walker's remarks very aptly explain the utility of Modigliani and Miller's approach. According to him, "the criticisms lodged against Modigliani and Miller's thesis are valid thus limiting its use in actual situations. Nevertheless, the propositions as well as their criticisms should be carefully studied, since they will serve as an aid to understanding capital structure theory".

DETERMINATION OF COST OF CAPITAL

Problems in determination

It has already been stated that the cost of capital is one of the most crucial factors in most financial management decisions. However, the determination of the cost of capital of a firm is not an easy task. The finance manager is confronted with a large number of problems, both conceptual and practical, while determining the cost of capital of a firm. These problems can briefly be summarized as 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 of capital dependent upon the method and level of financing by the company. According to the traditional theorists, the cost of capital of a firm depends upon the method and level of financing. In other words, according to them, a firm can change its overall cost of capital by changing its debt-equity mix. On the other hand, the modern theorists such as Modigliani and Miller argue that the firm's total cost of capital is independent of the method and level of financing. In other words, the change in the debt-equity ratio does not affect the total cost of capital.

An important assumption underlying MM approach is that there is perfect capital market. Since perfect capital market does not exist in practice, hence the approach is not of much practical utility.

2. Computation of cost of equity
The determination of the cost of equity capital is another problem. In theory, the cost of equity capital may be defined as the minimum rate of return that a company must earn on that portion of its capital employed, which is financed by equity capital so that the market price of the shares of the company remains unchanged. In other words, it is the rate of return which the equity shareholders expect from the shares of the company which will maintain the present market price of the equity shares of the company.

This means that determination of the cost of equity capital will require quantification of the expectations of the equity shareholders. This is a difficult task because the equity shareholders value the equity shares of a company on the basis of a large number of factors, financial as well as psychological. Different authorities have tried in different ways to quantify the expectations of the equity shareholders. Their methods and calculations differ.




3. Computation of cost of retained earnings and depreciation funds

The cost of capital raised through these sources will depend upon the approach adopted for computing the cost of equity capital. Since there are different views, therefore, a finance manager has to face difficult task in subscribing and 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 consider marginal cost of capital, i.e., cost of additional funds or the average cost of capital, i.e., the cost of total funds.

5. Problem of weights
The assignment of weights to each type of funds is a complex issue. The finance manager has to make a choice between the risk value of each source of funds and the market value of each source of funds. The results would be different in each case.

It is clear from the above discussion that it is difficult to calculate the cost of capital with precision. It can never be a single given figure. At the most it can be estimated with a reasonable range of accuracy. Since the cost of capital is an important factor affecting managerial decisions, it is imperative for the finance manager to identify the range within which his cost of capital lies.

Computation of cost of capital

Computation of cost of capital involves: (i) Computation of cost of each specific source of finance-termed as computation of specific costs and (ii) Computation of composite cost termed as weighted average cost.

Computation of specific costs

Cost of each specific source of finance, viz., debt, preference capital and equity capital, can be determined as follows:

Cost of Debt

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

(a) Debt issued at par: The computation of cost of debt issued at par is comparatively an easy task. It is the explicit interest rate adjusted further for the tax liability of the company. It may be computed according to the following formula:
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 and the 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, because interest is treated as an expense while computing the firm's income for tax purposes. However, the tax adjusted rate of interest should be used only in those cases where the "earning of the firm before interest and tax" (EBIT) is equal to or exceed the interest. In case, EBIT is in negative, the cost of debt should be calculated before adjusting the interest rate for tax. For example, in the above cases, the cost of debt before adjusting for tax effect will be 9%.

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

Illustration 1: A company issues 10% irredeemable debentures of Rs. 1,00,000. The company is in 55% tax bracket. Calculate the cost of debt (before as well as after tax) 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
where
Kd = Cost of debt after tax.
I = Annual interest payment.
NP = Net proceeds of loans or debentures.
T = Tax rate.

(i) Issued at par
1000 (1-.55)
Kd = 1,00,00

= 1 x .45
10 = .045 or 4.5%

(ii) Issued at discount:
10,00 (1-.55)
Kd = 90,00


= 1 x .45
9 = .05 or 5%

(iii) Issued at 10% premium:
10,00 (1-.55)
Kd = 1,00,00
= 1 x .45
11 = .041 or 4.1%.

(c) Cost of redeemable debt: In the preceding pages while calculating cost of debt we have presumed that debentures/bonds are not redeemable during the lifetime of the company. However, if the debentures are redeemable after the expiry of a fixed period the effective cost of debt before tax can be calculated by using the following formula:

I + (P - NP)/n
Kd(before tax) = (N + NP)/2
where
I = 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. 1,00,000 and realises Rs.98,000 after allowing 2% commission to brokers. The debentures carry an interest rate of 10%. The debentures are due for maturity at the end of the 1 0th year. You are required to calculated the effective cost of debt before tax.

Solution
I + (P - NP)/n
Kd (before tax) = (P + NP)/2
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 of debt 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 equity shareholders for maintaining their present value, the company should see that it earns on the funds provided by raising loans at least equal to the effective interest rate payable on them. In case the firm earns less than the effective interest rate, earnings available for the equity shareholders will decrease. This would naturally affect adversely the market price of the company's equity shares.

It should be noted that while calculating the real cost of debt, not only the contractual interest rate but also certain other imputed costs or raising funds from debts should be considered. The more is the financing of funds from the debt the higher is the expectation of the equity shareholders on their 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 raising funds through borrowings includes the increase in the expectation of the equity shareholders from their capital employed in the business. If it had not been so, the management would have at all times liked to finance their requirements only by means of raising long-term debts.

Cost of preference capital

The computation of the cost of preference capita however poses some conceptual problems. In case of borrowings, there is legal obligation on the firm to pay interest at fixed rates while in case of preference shares, there is no such legal obligation. Hence, some people argue that dividends payable on preference share capital do not constitute cost. However, this is not true. This is because, though it is not legally binding on the company to pay dividends on preference shares, it is generally paid whenever the company makes sufficient profits. The failure to pay dividend may be better of serious concern from the point of view of equity shareholders. They may even lose control of the company because of the preference shareholders getting the legal right to participate in the general meetings of the company with equity shareholders under certain conditions in the event of failure of the company to pay them their dividends. Moreover, the accumulation of arrears of preference dividends may adversely affect the right of equity shareholders to receive dividends. This is because no dividend can be paid to them unless the arrears of preference dividend are cleared. On account of these reasons the cost of preference capital is also computed on the same basis as that of debentures. The method of its computation can be put in the form of the following equation:

Dp
Kp = NP

where Kp == Cost of preference share capital
Dp = Fixed preference dividend
Np = Net proceeds of preference shares.

Illustration 3: A company raised preference share capital of Rs. 1,00,000 by issue of 10% preference shares of Rs.10 each. Calculate the cost of preference capital then they are issued at (i) 10% premium, and (ii) at 10% discount:


Solution
(i) When preference shares are issued at 10% premium:
Dp 10,000 X 100
Kp = NP = 1,10,000 =9.09%

(ii) When preference shares are issued at 10% discount:
Dp 10,000 X 100
Kp = NP = 90,000 =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 of preference shares with the present value of future dividends and principal repayments. Such cost can be calculated according to the same formula which has been given in the preceding pages for calculating the cost of redeemable debentures.

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




Solution:
Dp + (P - NP)/n
Kd (before tax) = (P + NP)/2

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 not adjusted for taxes, since dividend on preference capital is taken as an appropriation of profits and not as a charge against profits. Thus, the cost of preference capital is substantially greater than the cost of debt.

Cost of equity capital

The computation of the cost of equity capital is a difficult task. Some people argue, as observed in case of preference shares, that the equity capital does not involve any cost. The argument put forward by them is that it is not legally binding on the company to pay dividends to the equity shareholders. This does not seem to be a correct approach because the equity shareholders invest money in shares with the expectation of getting dividend from the company. The company also does not issue equity shares without having any intention to pay them dividends. The market price of the equity shares, therefore, depends upon the return expected by the shareholders.

Conceptually cost of equity share capital may be defined as the minimum rate of return that a firm must earn on the equity financed portion of an investment in a project in order to leave unchanged the market price of such shares. For example, in case the required rate of return on equity shares is 16% and cost of debt is 12%, and the company has the policy of financing with 75% equity and 25% debt, the required rate of return on the project could be estimated as follows:

16% x .75 = 12%
12% x .25 = 3%
15%

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




Total Return
Less: Interest on debentures 0.25 x 12 x 100

Amount Available for equity shareholders

Rate of return on equity = 1,200 x 100
7,500
= 16% Rs. 1,500
Rs. 300

Rs. 1,200



Thus, the expected rate of return is 16% which just equals the required rate of return on investment. If the project earns less than Rs. l,500 a year, it would provide a return less than required by the investors. As a result, the market value of the company's shares would fall. Theoretically, this rate of return could be considered as the cost of equity capital.

In order to determine the cost of equity capital, it may be divided 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 explained below:


The external equity or new issue of equity shares

From the preceding discussion, it is implied that in order to find out the cost of equity capital, one must be in a position to determine what the shareholders as a class expect from their investment in equity shares. This is a difficult proposition because shareholders as a class are difficult to predict or quantify. Different authorities have conveyed different explanations and approaches. The following are some of the appropriate according to which the cost of equity capital can be worked out:

1. Dividend price (D/P) approach

According to this approach, the investor arrives at the market price of an equity shares by capitalizing the set of expected dividend payments. Cost of equity capital has therefore been defined as "the discount rate that equates the present value of all expected future dividends per share with the net proceeds of the sale (or the current market price) of a share".

In other words, the cost of equity capital will be that rate of expected dividends which will maintain the present market price of equity shares.

This approach rightly emphasizes the importance of dividends, but it ignores the fact that the retained earnings have also an impact on the market price of the equity shares. The approach therefore does not seem to be very logical.

Illustration 5: A company offers for public subscription equity shares of Rs.10 each at a premium of 10%. The company pays 5% of the issue price as underwriting commission. The rate of dividend expected by the equity shareholders is 20%.

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

Solution:
The cost of new equity can be determined according to the following formula:
D
Ke = NP
where
Ke = Cost of equity capital;
D = Dividend per equity share;
NP = Net proceeds of an equity share,
2
Ke = 10.45 = 0.19 or 19%

Rs. 11 - Re. 0.55.

In case of existing equity shares, it will be appropriate to calculate the cost of equity on the basis of market price of the company's shares. In the present case, it can be calculated according to the following formula:
D
Ke = MP
where
Ke = Cost of equity capital;
D = Dividend per equity share;
MP = Market price of an equity share.

2
Ke = 15 =0.133 or 13.3%.

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

According to this approach, the cost of equity capital is determined on the basis on the expected dividend rate plus the rate of growth in dividend. The rate of growth in dividend is determined on the basis of the amount of dividends paid by the company for the last few years. The computation of cost of capital according to this approach can be done by using the following formula:
D + g
Ke = NP
where
Ke = 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 the above formula. However, the market price (MP) should be used in place of net proceeds (NP) of the shares as given above.

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

Solution
D + g
Ke = 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 the last five years:

Year Dividend per share per share Year Dividend
1987
1988
1989 10.50
11.00
12.50 1990
1991 12.75
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 equity share capital, calculation of growth rate will be necessary. During the last 4 years (and not 5 years, since dividends at the end of 1987 are being compared with dividends at the end of 1991) the dividends declared by the company have increased from Rs.10.50 to Rs.13.40 giving a compound before of 1.276 (i.e., 13.40/10.50). By looking to the "compound sum of one rupee tables" in the line of 4 years one can find out that a sum of Re.l would accumulate to 1.276 in 4 years at 6% interest. This means that growth rate of dividends is 6%. The cost of equity funds can now be determined as follows:
D + g
Ke = MP

14.10 + 6%
= 147
= 9.6% + 6% = 15.6%.

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

3. Earning price (E/P) approach
According to this approach, it is the earning per share which determines the market price of the shares. This is based on the assumption that the shareholders capitalize a stream of future earnings (as distinguished from dividends) in order to evaluate their shareholdings. Hence, the cost of capital should be related to that earnings percentage which could keep the market price of the equity shares constant. This approach, therefore, takes into account both dividends as well as retained earnings. However, the advocates of this approach differ regarding the use of both earnings and the market price figures. Some simply use of current earning rate and the current market price of the share of the company for determining the cost of capital. While others recommend average rate of earnings (based on the earnings of the past few years) and the average market price (calculated on the basis of market price for the last few years) of equity shares.

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

Ke = E
NP
where
Ke = Cost of equity capital;
D = Earning per share;
NP = Net proceeds of an equity share,

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

Illustration 8: The entire capital employed by a company consists of one lakh equity shares of Rs.100 each, its current earnings are Rs. 10 lakhs per annum. The company wants to raise additional funds of Rs.25 lakhs by issuing new shares. The floatation costs are expected to be 10% of the face value of the shares. You are required to calculated the cost of equity capital presuming that the earnings of the company are expected to remain stable over the next few years.

Solution
E 10
Ke = 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 realized by the investors in a company on their equity shares. Thus, according to this approach the past records in a given period regarding dividends and the actual capital appreciation in the value of the equity shares held by the shareholders should be taken to compute the cost of equity capital.

This approach gives fairly good results in case of companies with stable dividends and growth records. In case of such companies, it can be assumed with reasonable degree of certainty that the past behaviour will be repeated in the future 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 years and finally sold them in January, 1992 for Rs.300. The amount of dividend received by him in each of these 5 years were as follows:
1987 Rs. 14 1990 Rs. 14.50
1988 Rs. 14 1991 Rs. 14.50
1989 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 to calculate the internal rate of return. This rate of return can be calculated by "trial and error method" as explained earlier. 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 was Rs.240. The present value of cash inflows (as on January 1,1987) amounts to Rs.240.40. Thus, at 10%, the present value of the cash inflows over a period of 5 years is equal to the cash outflow in the year 1987. The cost of equity capital can, therefore, be taken as 10%.

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

(i) The company will fundamentally remain the same as regards risk,
(ii) The shareholders continue to expect the same rate of return for bearing this risk,
(iii) The shareholders reinvested opportunity rate is equal to the realized yield.

Cost of retained earnings

The companies do not generally distribute the entire profits earned by them by way of dividend among their shareholders. Some profits are retained by them for future expansion of the business. Many people feel that such retained earnings are absolutely cost free. This is not the correct approach because the amount retained by company, if it had been distributed among the shareholders by way of dividend, would have given them some earning. The company has deprived the shareholders of this earnings by Retaining a part of profit with it. Thus, the cost of retained earnings is the earning forgone by the shareholders. In other words, the opportunity cost of retained earnings may be taken as the cost of the retained earnings. It is equal to the income that the shareholders could have otherwise earned by placing these funds in alternative investments. For example, if the shareholders could have invested the funds in alternative channels, they could have got a return of 10%. This return of 10% has been forgone by them because of the company is not distributing the full profits to them. The cost of retained earnings may, therefore, be taken at 10%.

The above analysis can also be understood in the following manner. Suppose the earnings not retained by the company is passed on to the shareholders, and are invested by the shareholders in the new equity shares of the same company, the expectation of the shareholders from the new equity shares would be taken as the opportunity cost of the retained earnings. In other words, if earnings were paid as dividends and simultaneously an offer for the right shares was made, the shareholders would have subscribed to the right shares on the expectation of certain return. This expected return can be taken as the cost of retained earnings of the company.

Tax Adjusted Return

In the example given above, we have presumed that the shareholders will have with them the amount of retained earnings available when distributed by the company. In actual practice, it does not happen. The shareholders have to pay tax on the dividends received, incur brokerage cost for making investments, etc. The funds available with the shareholders are, therefore, less than what they would have been with the company, had they been retained by it. On account of this reason, the cost of retained earnings to the company would be always less than the cost of new equity shares issued by the company (see illustration).

The following adjustments are made for ascertaining the cost of retained earnings:

(i) Income tax adjustment: The dividends receivable by the shareholders are subject to income tax. Hence, the dividends actually received by them are not the amount of gross dividends but the amount of net dividend, i.e., gross dividends less income tax.
(ii) Brokerage cost adjustment: Usually, the shareholders have to incur some brokerage cost for investing the dividends received. Thus, the funds available with them for reinvesting will be reduced by this amount.

The opportunity cost of retained earnings to the shareholders is, therefore, the rate of return that they can obtain by investing the net dividends (i.e., after tax and brokerage) in alternative opportunity of equal quality.

Illustration 10: ABC Ltd. is earning a net profit of Rs.50,000 per annum. The shareholders required rate of return is 10%. It is expected that retained earnings, if distributed among the shareholders, can be invested by them in securities of similar type carrying return of 10% per annum. It is further expected that the shareholders will have to incur 2% of the net dividends received by them as brokerage cost for making new investments. The shareholders of the company are in 30% tax bracket.

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

Solution: In order to calculate the cost of retained earnings to the company, it is necessary to calculate the net amount available to the shareholders for investment and the likely return 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 of earning 10%, the amount of earning received by them on their investment will amount to Rs.3,430 (i.e. 10% of Rs.34,300).

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

3,430 X 100
Rs. 50,000 = 6.86%.

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

The cost of retained earnings after making adjustment for income tax and brokerage cost payable by the shareholders can be determined according to the following formula:
kr = Ke(1-T) (1-B)
where
Kr = 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 the above illustration can be calculated according to the above formula, 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 making adjustment for tax liabilities, is a difficult process because personal income tax rates will differ from shareholder to shareholder. Thus, it will be necessary to find out the personal income-tax rates of the different shareholders of the company in case cost of retained earnings it to be calculated according to the above approach. In case of a widely held public company, there are a large number of shareholders of varying means and incomes. It is, therefore, almost impossible to determine a single tax rate that would correctly reflect the opportunity cost of retained earnings to every shareholder. Even computation of a weighted average tax would also not give satisfactory results. Some authorities have, therefore, recommended the use of another approach termed by them as external yield criterion. According to this approach the opportunity cost of retained earnings is the rate of return that can be earned by investing the funds in another enterprise by the firm. Thus, according to this approach, the cost of retained earnings is simply the return on direct investment of funds by the firm and not what the shareholders are able to obtain on their investments. The approach represents an economically justifiable opportunity cost that can be applied consistently. Moreover, the need for determining the marginal tax rate for investors will not arise in case the approach is follows.

The "External Yield Criterion", suggested above, has not yet been universally accepted. In the absence of a universally acceptable and practically feasible method for determining separately the cost of retained earnings, many accountants calculate the cost of retained earnings on the same pattern as that of equity shares. Moreover, when the cost of funds raised by equity shares, the need for determining the separate cost for retained earnings does not at all arise. Some calculate it on the Dividend Payout Basis.

Weighted average cost of capital

After calculating the cost of each component of capital, the average cost of capital is generally calculated on the basis of weighted average method. This may also be termed as overall 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 of funds: 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 the cost of capital on "after tax basis". This is because the return to the shareholders is an important figure in determining the cost of capital and they can get dividends only after the taxes have been paid.

2. Assigning weights to specific costs: This involves determination of the proportion of each source of funds in the total capital structure of the company. This may be done according to any of the following method.

(a) Marginal weights method: In case of this method weights are assigned to each source of funds, in the proportion of financial inputs the firm intends to employ. The method is based on the logic that our concern is with the new or incremental capital and not with capital raised in the past. In case the weights are applied in a ratio different than the ratio in which the new capital is to be raised, the weighted average cost of capital so calculated may be different from the actual cost of capital. This may lead to wrong capital investment decisions. However, the method of marginal weighting suffers from one major limitation. It does not consider the long-term implications of the firm's current financing. A firm should give due attention to long-term implications while designing the firm's financing strategy. For example, a firm may accept a project giving an aftertax return of 6% because it intends to raise the funds required by issue of debentures having an after-tax cost of 5%. In case next year the firm intends to raise funds by issue of equity shares having a cost of 9%, it will have to reject a project which gives a return of only 8%. Thus, marginal weighting method does not consider the fact that to-day's financing affects tomorrow's cost.

(b) Historical weights method: According to this method the relative proportions of various sources to the existing capital structure are used to assign weights. Thus, in case of this method the basis of weights is the proportion of funds already employed by the firm. This is based on the assumption that the firm's present capital structure is optimum 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 of capital will be different, depending upon whether book value weights are used or market value weights are used.

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

(i) The market values of the securities are closely approximate to the actual amount to be received from the sale of such securities.
(ii) The cost of each specific source of finance which constitutes the capital structure is calculated according to the prevailing market price.

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

(i) The market values of the securities may fluctuate considerably.
(ii) Market values are not readily available as compared to the book values. The book values can be taken from the published records of the firm.
(iii) The analysis of the capital structure of the company, in terms of debt-equity ratio, is based on the book values and not on the market-values.

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

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

Illustration 11: From the following capital structure of a company, 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. 10 shares)
Retained earnings
Preference share capital
Debentures Rs. 45,000

15,000
10,000
30,000 Rs. 90,000


10,000
30,000
The after-tax cost of different sources of finance is as follows:
Equity share capital: 14%; Retained earnings: 13%; Preference share capital: 10%; Debenture: 5%.

Solution
(a) COMPUTATON OF WEIGHTED AVERAGE COST OF CAPITAL
(BOOK VALUE WEIGHTS)
Source (i) Amount (Rs.) (2) Proportion (3) After tax (4) Weighted Cost (Rs.) (5) = (3) x (4)
Equity Share Capital 45,000 .45 14% 6.30%
Retained Earnings 15,000 .15 13% 1.95%
Preference Share
Capital 10,000 .10 10% 1.00%
Debentures 30,000 .30 5% 1 .50%
Weighted average cost of capital (K0) 10.75%
Alternatively, the weighted average cost of capital can also be found as follows:

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


Source (i) Amount (Rs.) (2) After tax cost (Rs.)(3) Total after tax cost (4)=(2)x
(3)
Equity Share Capital
Retained Earnings
Preference Share Capital
Debentures
Total 45,000
15,000
10,000
30,000
1,00,000 14%
10%
10%
5% 6,300
1,950
1,000
1,500
10,750

Weighted average cost of capital (K0)
10,750 X 1000
= Rs. 1,00,000 = 10.75%.



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

Source (i) Amount (Rs.) (2) Proportion (3) After tax (4) Weighted Cost (Rs.) (5) = (3) x (4)
Equity Share Capital 90,000 0.692 14% 9.688
Retained Earnings - - - -
Preference Share
Capital 10,000 0.77 10% 0.770
Debentures 30,000 0.231 5% 1.155
Weighted average cost of capital (K0) 11.613%

Illustration 12: Excel Industrial Ltd., has assets of 1,60,000 which has been financed with Rs. 52,000 of debt and Rs.90,000 of equity and a general reserve of Rs.18,000. The firm's total profits after interest and taxes for the year ended 31st March, 1998, were Rs. 13,500. It pays 8% interest on debentures at Rs. 100 share is selling at a market price of Rs.120 per share. What is the weighted average cost of capital?

Solution
From the facts given in the question, the following balance sheet may be drawn:

BALANCE SHEET
Liabilities Rs. Assets Rs.
900 Equity shares of
Rs. 100 each
Reserves
8% Borrowed funds 90,000

18,000
52,000
1,60,000 Total Assets 1,60,000


_______
1,60,000

Calculation of earnings per share:
1. Earnings after interest and tax
available for equity share holders Rs. 13,500
2. Number of equity shares outstanding
of Rs. 100 each Rs. 900
3. Earning per share (EPS) (1) / (2) Rs. 15

Determination of specific costs:

(i) Cost of debt (Kd):
Kd = 8%(1-T)
= 8% (1-0.5) = 4%

(ii) Cost of equity (Ke):

Cost of equity share capital has been calculated on the basis of the earnings approach. It has been assumed that the future earnings per share would be equal to the present earning per share.

_____EPS__________ X 100
ke = Present market price of the share

Rs. 15 X 100
ke = Rs.120 = 12.5%.

(iii) Weighted average cost of capital (K0):

Weighted average cost of capital may be calculated by using the market value weights as they are more appealing than book value weights. Since the market value of debt has not been given, it has been assumed that its book value and market value are the same:

STATEMENT OF WEIGHTED AVERAGE COST
OF CAPITAL

Source of Capital Market Value (MV) Specific Costs (k) Total Costs (MV)x (K)
Debt
Equity Rs. 52,000
1,08,000
1,60,000 4.0%
12.5% Rs. 2,080
13,000
Rs. 15,580
Rs. 15,580 X 100
Ke = Rs. 1,60,000 = 9.74% approx.


Alternatively, the weighted average cost of capital can be ascertained on the basis of book value weights. In the absence of information regarding the cost of retained earnings, it will be appropriate to take cost of equity capital as also the cost of retained earnings. In the present case, the book value of equity share capital together with retained earnings amount to Rs. 1,08,000 (i.e., Rs.90,000 + 18,000). Hence, the weighted average cost of capital, calculated on the basis of book value weights will be same as calculated on the basis of market value weights.

Illustration 20: Your company' share is quoted in the market at Rs.20 currently. The company pays a dividend of Re. 1 per share and the investor expects a growth rate of 5 per cent per year. Compute:
(a) the company's cost of equity capital.
(b) If the anticipated growth rate is 6% p.a., calculate the indicated market price per share.
(c) If the company's cost of capital is 8% and the anticipated growth rate is 5% p.a., calculate the indicated market price 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

Re.l X 100 + 5%
Company's cost of equity capital = Rs. 20
= 10%

Dividend
(b) Market price = Cost of Equity -Growth Rate %
Re 1
Company's cost of equity capital = 10% - 6%
Re. 1
= 4% = Rs. 25

(c) Market price =
Re.l Re. 1
8%-5% = 3% = Rs. 33.33