# Methods to Calculate Cost of Capital

The cost of capital is a significant factor in designing the capital structure of an undertaking, as basic reason of running of a business undertaking is to earn return at least equal to the cost of capital.

Commercial undertaking has no relevance if, it does not expect to earn its cost of capital. Thus cost of capital constitutes an important factor in various business decisions. For example, in analysing financial implications of capital structure proposals, cost of capital may be taken as the discounting rate.

Obviously, if a particular project gives an internal rate of return higher than its cost of capital, it should be an attractive opportunity.

Following are the cost of capital acquired from various sources :

A) Cost of debt :
The explicit cost of debt is the interest rate as per contract adjusted for tax and the cost of raising debt.
• Cost of irredeemable debentures :
Cost of debentures not redeemable during the life time of the company,

Kd = (I/NP) * (I - T)

Where,

Kd = Cost of debt after tax
I = Annual interest rate
NP = Net proceeds of debentures
T = Tax rate

However, debt has an implicit cost also, that arises due to the fact that if the debt content rises above the optimal level, investors would start considering the company to be too risky and, thus, their expectations from equity shares will rise. This rise, in the cost of equity shares is actually the implicit cost of debt.
• Cost of redeemable debentures :
If the debentures are redeemable after the expiry of a fixed period the cost of debentures would be :

Kd = I(1 - t) + [(RV - NP)]/N
[(RV + NP)/2]

Where,
I = Annual interest payment
NP = Net proceeds of debentures
RV = Redemption value of debentures
t = tax rate
N = Life of debentures

B) Cost of preference shares :
In case of preference shares, the dividend rate can be taken as its cost, as it is this amount that the company intends to pay against the preference shares.

As, in case of debt, the issue expenses or discount/premium on issue/redemption is also to be taken into account.
• Cost of irredeemable preference shares :
Cost of irredeemable preference shares = PD/PO

Where,
PD = Annual preference dividend
PO = Net proceeds of an issue of preference shares
• Cost of redeemable preference shares :
If the preference shares are redeemable after the expiry of a fixed period, the cost of preference shares would be.

Kp = PD + [(RV - NP)]/N
[(RV + NP)/2]
Where,
PD = Annual preference dividend
NP = Net proceeds of debentures
RV = Redemption value of debentures
N = Life of debentures

However, since dividend of preference shares is not allowed as deduction from income for income tax purposes, there is no question of tax advantage in the case of cost of preference shares.

It would, thus, be seen that both in case of debt and preference shares, cost of capital is calculated by reference to the obligations incurred and proceeds received. The net proceeds received must be taken into account in working cost of capital.

C) Cost of ordinary or equity shares :
Calculation of the cost of ordinary shares involves a complex procedure, because unlike debt and preference shares there is no fixed rate of interest or dividend against ordinary shares.

Hence, to assign a certain cost to equity share capital is not a question of mere calculation, it requires an understanding of many factors basically concerning the behaviour of investors and their expectations.

As, there can be different interpretations of investor's behaviour, there are many approaches regarding calculation of cost of equity shares. The 4 main approaches are :

1. D/P ratio (Dividend/Price) approach :

This emphasizes that dividend expected by an investor from a particular share determines its cost. An investor who invests in the ordinary shares of a particular company, does so in the expectation of a certain return. In other words, when an investor buys ordinary shares of a certain risk, he expects a certain return, The expected rate of return is the cost of ordinary share capital. Under this approach, thus, the cost of ordinary share capital is calculated on the basis of the present value of the expected future stream of dividends.
For example, the market price of the equity shares (face value Rs. 10) of a particular company is Rs. 15. If it has been paying a dividend of 20 % and is expected to maintain the same, its cost of equity shares at face value is 0.2 * 10/15 = 13.3%, since it is the maximum rate of dividend, at which the investor will buy share at the present value. However, it can also be argued that the cost of equity capital is 20 % for the company, as it is on this expectation that the market price of shares is maintained at Rs. 15.

Cost of equity shares of a company is that rate of dividend that maintains the present market price of shares. As the objective of financial management is to maximise the wealth of shareholders, it is rational to assume that the company must maintain the present market value of its share by paying 20 % dividend, which then is its cost of equity capital. Thus, the relationship between dividends and market price shows the expectation of the investors and thereby cost of equity capital.
This approach co-relates the basic factors of return and investment from view point of investor. However, it is too simple as it pre-supposes that an investor looks forward only to dividends as a return on his investment.

The expected stream of dividends is of importance to an investor but, he looks forward to capital appreciation also in the value of shares. It may lead us to ignore the growth in capital value of the share. Under, this approach, a company which declares a higher amount of dividend out of a given quantum of earnings will be placed at a premium as compared to a company which earns the same amount of profits but utilises a major part of the same in financing its expansion programmes.

Thus, D/P approach may not be adequate to deal with the problem of determining the cost of ordinary share capital.

2. E/P (Earnings/Price) ratio approach :

The advocates of this approach co-relates the earnings of the company with the market price of its shares. As per it, the cost of ordinary share capital would be based on the expected rate of earnings of a company.

The argument is that each investor expects a certain amount of earnings, whether distributed or not from the company in whose shares he invests, thus, an investor expects that the company in which he is going to subscribe for share should have at least 20 % of earning, the cost of ordinary share capital can be construed on this basis.

Suppose, a company is expected to earn 30 % the investor will be prepared to pay Rs 150 (30/20 * 100) for each of Rs. 100 share. This approach is similar to the dividend price approach, only it seeks to nullify the effect of changes in dividend policy.

This approach also does not seem to be a complete answer to the problem of determining the cost of ordinary share as it ignores the factor of capital appreciation or depreciation in the market value of shares.

3. D/P + growth approach :

The dividend/price + growth approach emphasises what an investor actually expects to receive from his investment in a particular company's ordinary share in terms of dividend plus the rate of growth in dividend/earnings.

This growth rate in dividend (g) is taken to be good to the compound growth rate in earnings per share.

Ke = [D1/P0] + g

Where,
Ke = Cost of capital
D1= Dividend for the period 1
P0 = Price for the period 0
g = Growth rate

D/P + g approach seems to answer the problem of expectations of investor satisfactorily, however, it poses one problem that is how to quantify expectation of investor relating to dividend and growth in dividend.

4. Realised yield approach :

It is suggested that many authors that the yield actually realised for a period of time by investors in a particular company may be used as an indicator of cost of capital.

In other words, this approach takes into consideration the basic factor of the D/P + g approach but, instead of using the expected values of the dividends and capital appreciation, past yields are used to denote the cost of capital. This approach is based upon the assumption that the past behaviour would be repeated in future and thus, they may be used to measure the cost of ordinary capital.

Which approach to use ? In case of companies with stable income and stable dividend policies the D/P approach may be a good way of measuring the cost of ordinary share capital.

In case of companies whose earnings accrue in cycles, it would be better if the E/P approach is used, but representative figures should be taken into account to include complete cycle. In case of growth companies, where expectations of growth are more important, cost of ordinary share capital may be determined as the basis of the D/P + g approach.

In the case of companies enjoying a steady growth rate and a steady rate of dividend, the realised value approach may be useful. The basic factor behind determination of cost of ordinary share capital is to measure expectation of investors from ordinary shares of that particular company.

Thus, the whole question of determining the cost of ordinary shares hinges upon the factors which go into the expectations of a particular group of investors in the company of a particular risk class.

D) Cost of reserves :

The profits retained by a company and used in the expansion of business also entail cost. Many people tend to feel that reserves have no cost. However, it is not easy to realised that by depriving the shareholders of a part of the earnings, a cost is automatically incurred on reserves.

This may be termed as the opportunity cost of retained earnings. Suppose, these earnings are not retained and are passed on to shareholders, suppose further that shareholders invest the same in new ordinary shares.

This expectation of the investors from new ordinary shares should be the opportunity cost of reserves. In other words, if earnings were paid out as dividends and simultaneously an offer for right shares was made shareholders would have subscribed to the right share on the expectation of a certain return.

This return may be taken as the indicator of the cost of reserves. People do not calculate the cost of capital of retained earnings as above. They take cost of retained earnings as the same as that of equity shares. However, if the cost of equity shares is determined on the basis of realized value approach or D/P + g approach, the question of working out a separate cost of reserves is not relevant since cost of reserves is automatically included in the cost of equity share capital.

E) Cost of depreciation funds :

Depreciation funds, cannot be construed as not having any cost. Logically speaking, they should be treated on the same footing as reserves when it comes to their use, though while calculating the cost of capital these funds may not be considered.