**This article throws light upon the top four sources of finance. The sources are: 1. Cost of Debt 2. Cost of Preference Capital 3. Cost of Equity Share Capital 4. Cost of Retained Earnings.**

**Finance: Source # 1. Cost of Debt: ****i. Cost Perpetual/Irredeemable Debt****: **

The cost of debt is the rate of interest payable on debt.

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**For example, a company issues Rs. 1,00,000 10% debentures at par; the before-tax cost of this debt issue will also be 10% By way of a formula, before-tax cost of debt may be calculated as: **

(i) K_{db} = I/P

where, K _{db} = Before tax cost of debt

I = Interest

and P = Principal

In case the debt is raised at premium or discount, we should consider P as the amount of net proceeds received from the issue and not the face value of securities.

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**The formula may be changed to: **

(ii) K_{db} = I/NP (where, NP= Net Proceeds)

Further, when debt is used as a source of finance, the firm saves a considerable amount in payment of tax as interest is allowed as a deductible expense in computation of tax. Hence, the effective cost of debt is reduced.

**The After-tax cost of debt may be calculated with the help of following formula: **

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(iii) K_{da }= K_{db }(1-t) = I/NP (1-t)

where, K _{da} = After-tax cost of debt

t = Rate of tax.

**Illustration 1: **

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(a) X Ltd. issues Rs. 50,000 8% debentures at par. The tax rate applicable to the company is 50%. Compute the cost of debt capital.

(b) Y Ltd. issues Rs. 50,000 8% debentures at a premium of 10%. The tax rate applicable to the company is 60%. Compute cost of debt capital.

(c) A Ltd. issues Rs. 50,000 8% debentures at a discount of 5%. The tax rate is 50%, Compute the cost of debt capital.

(d) B Ltd. issues Rs. 1,00,000 9% debentures at a premium of 10%. The costs of floatation are 2%. The tax rate applicable is 60%. Compute cost of debt-capital.

**Solution: **

**ii. Cost of Redeemable Debt****: **

Usually, the debt is issued to be redeemed after a certain period during the life time of a firm. Such a debt is known as redeemable debt. The cost of redeemable debt capital may be computed by using yield to maturity, also called internal rate of return or trial and error method. The approximate cost of redeemable debt can also be computed by using the simple shortcut method.

**(a) Yield to Maturity or Trial and Error Method****: **

**(i) Before tax cost of redeemable debt****: **

where, V_{0} = Current value or the issue price of debt/debenture

V_{n} = Redeemable value of debt

I, I_{2} …I_{n} = Amount of annual interest in period 1, 2 …………………, and so on

n = Number of years to redemption

k_{d} = Yield to maturity or internal rate of return or cost of debt/debenture

The value of k_{d} (yield to maturity) can be found by trial and error method using present value tables.

**(ii) After tax cost of redeemable debt****: **

k_{da} = k_{db }(1-t)

Where, k_{db} = After tax cost of debt

k_{db} = Before tax cost of debt

t = Tax Rate

**Illustration 2: **

A five year Rs. 100 debenture of a firm can be sold for a net price of Rs. 95.90. The coupon rate of interest is 14 per cent per annum, and the debenture will be redeemed at 5 per cent premium on maturity. The firm’s tax rate is 35 per cent. Compute the yield to maturity and the after tax cost of debenture.

**The present value factors at 15% and 17% per p.a. are as given below: **

**Solution: **

**(b) Shortcut Method to Compute Cost of Redeemable Debt****: **

**In order to avoid the complex calculations of hit and trial method, we can compute the approximate cost of redeemable debt by using the following simple formula: **

(i) Before-tax cost of redeemable debt,

where, I = Annual Interest

n = Number of years in which debt is to be redeemed

RV = Redeemable value of debt

NP = Net proceeds of debentures

(ii) After-tax cost of redeemable debt

Where, I = Annual interest

t = Tax rate

n = Number of years in which debt is to be redeemed

RV = Redeemable value of debt

NP = Net proceeds of debentures

**Illustration 3: **

A company issues Rs. 10,00,000 10% redeemable debentures at a discount of 5%. The costs of floatation amount to Rs. 30,000. The debentures are redeemable after 5 years. Calculate before-tax and after-tax cost of debt assuming a tax rate of 50%.

**Solution: **

**Illustration 4: **

A 5-year Rs. 100 debenture of a firm can be sold for a net price of Rs. 96.50. The coupon rate of interest is 14 per cent per annum, and the debenture will be redeemed at 5 per cent premium on maturity. The firm’s tax rate is 40 per cent. Compute the after-tax cost of debenture.

**Solution: **

**Illustration 5: **

**Assuming that a firm pays tax at 50% rate, compute the after tax cost of debt capital in the following cases: **

(i) A perpetual bond sold at par, coupon rate of interest being 7%;

(ii) A 10 year, 8% Rs. 1.000 per bond sold at Rs. 950 less 4% underwriting commission.

**Solution****: **

**iii. Cost of Debt Redeemable in ****Installments: **

Financial institutions generally require principal to be amortised in installments. A company may also issue a bond or debenture to be redeemed periodically. In such a case, principal amount is repaid each period instead of a lump sum at maturity and hence cash outflows each period include interest and principal. The amount of interest goes on decreasing each period as it is calculated on the outstanding amount of debt.

**The before-tax cost of such a debt can be calculated as below: **

**Illustration 6: **

A company is proposing to issue a 5-year debenture of Rs. 1000 at 14 per cent rate of interest per annum. The debenture amount will be amortised equally over its life. If the present value of the debenture for an investor is Rs. 1046.59, calculate the minimum required rate of return or the cost of debt.

**Solution: **

**iv. Cost of Existing Debt****: **

If a firm wants to compute the current cost of its existing debt, the current market yield of the debt should be taken into consideration.

**Suppose a firm has 10% debentures of Rs. 100 each outstanding on January 1, 2006 to be redeemed on December 31, 2012 and the new debentures could be issued at a net realisable price of Rs. 90 in the beginning of 2008, the current cost of existing debt may be computed as: **

**v. Cost of Zero Coupon Bonds****: **

Sometimes companies issue bonds or debentures at a discount from their eventual maturity value and having zero interest rate. No interest is payable on such debentures before their redemption and at the time of redemption the maturity value of the bond is to be paid to the investors.

**The cost of such debt can be calculated by finding the present values of cash flows as below: **

(i) Prepare the cash flow table using an arbitrary assumed discount rate to discount the cash flows to the present value.

(ii) Find out the net present value by deducting the present value of the outflows from the present value of the inflows.

(iii) If the net present value is positive, apply higher rate of discount.

(iv) If the higher discount rate still gives a positive net present value, increase the discount rate further until the NPV becomes negative.

(v) If the NPV is negative at this higher rate, the cost of debt must be between these two rates.

The following illustration explains the procedure of determining the cost of zero coupon bonds.

**Illustration 7: **

X Ltd. has issued redeemable zero coupon bonds of Rs. 100 each at a discount rate of Rs. 60 repayable at the end of fourth year. Calculate the cost of debt.

**Solution: **

**vi. Floating or Variable Rate Debt: **

The interest on floating rate debt changes depending upon the market rate of interest payable on gilt edged securities or the prime lending rate of the bank. For example, suppose a company raises debt from external sources on the terms of prime lending rate of the bank plus four per cent.

If the prime lending rate of the bank is 8% p.a., the company will have to pay interest at the rate of 12% p.a. Further, if the prime lending rate falls to 6% p.a., the company shall pay interest at only 10% p.a.

**Illustration 8: **

ABC Ltd. raised a debt of? 50 lakhs on the terms that interest shall be payable at prime lending rate of bank plus three percent. The prime lending rate of the bank is 7 per cent. Calculate the cost of debt assuming that the corporate rate of tax is 35%.

**Solution: **

**vii. Real or Inflation Adjusted Cost of Debt: **

In the days of inflation, the real cost of debt is much less than the nominal cost as the fixed amount is payable irrespective of the fall in the value of money because of price level changes. The real cost of debt can be calculated as below:

Real Cost of Debt = 1 + Nominal Cost of Debt/1 + Inflation Rate

**Illustration 9: **

Excel Ltd. has issued 5000 10% Debentures of Rs. 100 each. The rate of inflation is 6%. Calculate the real cost of debt.

**Solution: **

**Finance: ****Source # ****2. Cost of Preference Capital: **

A fixed rate of divided is payable on preference shares. Though dividend is payable at the discretion of the Board of directors and there is no legal binding to pay dividend, yet it does not mean that preference capital is cost free. The cost of preference capital is a function of dividend expected by its investors, i.e., its stated dividend.

In case dividends are not paid to preference shareholders, it will affect the fund raising capacity of the firm. Hence, dividends are usually paid regularly on preference shares except when there are no profits to pay dividends.

**The cost of preference capital which is perpetual can be calculated as: **

K_{P} = D/P

where K_{P} = Cost of Preference Capital

D = Annual Preference Dividend

P = Preference Share Capital (Proceeds.)

Further, if preference shares are issued at Premium or Discount or when costs of floatation are incurred to issue preference shares, the nominal or par value of preference share capital has to be adjusted to find out the net proceeds from the issue of preference shares.

**In such a case, the cost of preference capital can be computed with the following formula: **

K_{P} = D/NP

It may be noted that as dividends are not allowed to be deducted in computation of tax, no adjustment is required for taxes.

Sometimes Redeemable Preference Shares are issued which can be redeemed or cancelled on maturity date.

**The cost of redeemable preference share capital can be calculated as: **

where, K_{pr} = Cost of Redeemable Preference Shares

D = Annual Preference Dividend

MV = Maturity Value of Preference Shares

NP = Net Proceeds of Preference Shares.

**Illustration 10: **

A company issues 10,000 10% Preference Shares of Rs. 100 each. Cost of issue is Rs. 2 per share. Calculate cost of preference capital if these shares are issued (a) at par, (b) at a premium of 10%, and (c) at a discount of 5%.

**Solution: **

**Illustration 11: **

A company issues 10,000 10% Preference Shares of Rs. 100 each redeemable after 10 years at a premium of 5%. The cost of issue is Rs. 2 per share. Calculate the cost of preference capital.

**Solution: **

**Illustration 12: **

A company issues 1,000 7% Preference Shares of Rs. 100 each at a premium of 10% redeemable after 5 years at par. Compute the cost of preference capital.

**Solution: **

**Finance: ****Source # ****3. Cost of Equity Share Capital****: **

The cost of equity is the ‘maximum rate of return that the company must earn on equity financed portion of its investments in order to leave unchanged the market price of its stock.’ The cost of equity capital is a function of the expected return by its investors.

The cost of equity is not the out-of-pocket cost of using equity capital as the equity shareholders are not paid dividend at a fixed rate every year. Moreover, payment of dividend is not a legal binding. It may or may not be paid.

But it does not mean that equity share capital is a cost free capital. Shareholders invest money in equity shares on the expectation of getting dividend and the company must earn this minimum rate so that the market price of the shares remains unchanged. Whenever a company wants to raise additional funds by the issue of new equity shares, the expectations of the shareholders have to evaluate.

**The cost of equity share capital can be computed in the following ways: **

**(a) Dividend Yield Method or Dividend/Price Ratio Method: **

According to this method, the cost of equity capital is the ‘discount rate that equates the present value of expected future dividends per share with the net proceeds (or current market price) of a share’.

**Symbolically:**

K_{e} = D/NP or D/MP

where, Ke = Cost of Equity Capital

D = Expected dividend per share

NP = Net proceeds per share and

MP = Market Price per share.

The basic assumptions underlying this method are that the investors give prime importance to dividends and risk in the firm remains unchanged.

**The dividend price ratio method does not seem to consider the growth in dividend:**

(i) It does not consider future earnings or retained earnings, and

(ii) It does not take into account the capital gains.

This method of computing cost of equity capital is suitable only when the company has stable earnings and stable dividend policy over a period of time.

**Illustration 13: **

A company issues 1000 equity shares of Rs. 100 each at a premium of 10%. The company has been paying 20% dividend to equity shareholders for the past five years and expects to maintain the same in the future also. Compute the cost of equity capital. Will it make any difference if the market price of equity share is Rs. 160?

**Solution: **

**(b) Dividend Yield Plus Growth in Dividend Method: **

When the dividends of the firm are expected to grow at a constant rate and the dividend-pay-out ratio is constant this method may be used to compute the cost of equity capital. According to this method the cost of equity capital is based on the dividends and the growth rate.

Further, in case cost of existing equity share capital is to be calculated, the NP should be changed with MP (market price per share) in the above equation.

K_{e} = D_{1}/MP + G

**Illustration 14: **

(a) A company plans to issue 1000 new shares of Rs. 100 each at par. The floatation costs are expected to be 5% of the share price. The company pays a dividend of Rs. 10 per share initially and the growth in dividends is expected to be 5%. Compute the cost of new issue of equity shares.

(b) If the current market price of an equity share is Rs. 150, calculate the cost of existing equity share capital.

**Solution: **

**Illustration 15: **

The shares of a company are selling at Rs. 40 per share and it had paid a dividend of Rs. 4 per share last year. The investor’s market expects a growth rate of 5 per cent per year.

(a) Compute the company’s equity cost of capital;

(b) If the anticipated growth rate is 7 per cent per annum, calculate the indicated market price per share.

**Solution: **

**Alternatively: **

K_{e} = D_{1}/MP + g

Or, MP = D_{1}/K_{e} – g

= 4.28/0.155 – 0.07 = Rs. 50.35

**(c) Earning Yield Method/Earning Price Ratio: **

According to this method, the cost of equity capital is the discount rate that equates the present values of expected future earnings per share with the net proceeds (or, current market price) of a share.

**Symbolically: **

K_{e} = Earnings per share/Net Proceeds

= EPS/NP

where, the cost of existing capital is to be calculated:

K_{e} = Earnings per share/Market Price per share

= EPS/MP

**This method of computing cost of equity capital may be employed in the following cases: **

(i) When the earnings per share are expected to remain constant.

(ii) When the dividend pay-out- ratio is 100 per cent or when the retention ratio is zero, i.e., all the available profits are distributed as dividends.

(iii) When a firm is expected to earn an amount on new equity shares capital, which is equal to the current rate of earnings.

(iv) The market price of the share is influenced only by earnings per share.

**Illustration 16: **

A firm is considering an expenditure of Rs. 60 lakhs for expanding its operations. The relevant information is as follows:

Compute the cost of existing equity share capital and of new equity capital assuming that new shares will be issued at a price of Rs. 52 per share and the costs of new issue will be Rs. 2 per share.

**Solution:**

**(d) Realised Yield Method: **

One of the serious limitations of using dividend yield method or earnings yield method is the problem of estimating the expectations of the investors regarding future dividends and earnings. It is not possible to estimate future dividends and earnings correctly; both of these depend upon so many uncertain factors.

To remove this drawback, realised yield method, which takes into account the actual average rate of return realised in the past, may be applied to compute the cost of equity share capital. To calculate the average rate of return realised, dividend received in the past along with the gain realised at the time of sale of shares should be considered. The cost of equity capital is said to be the realised rate of return by the shareholders.

**This method of computing cost of equity share capital is based upon the following assumptions: **

(a) The firm will remain in the same risk class over the period;

(b) The shareholders’ expectations are based upon the past realised yield;

(c) The investors get the same rate of return as the realised yield even if they invest elsewhere;

(d) The market price of shares does not change significantly.

**Finance: ****Source # ****4. Cost of Retained Earnings****: **

It is sometimes argued that retained earnings do not involve any cost because a firm is not required to pay dividends on retained earnings. However, the shareholders expect a return on retained profits. Retained earnings accrue to a firm only because of some sacrifice made by the shareholders in not receiving the dividends out of the available profits.

The cost of retained earnings may be considered as the rate of return which the existing shareholders can obtain by investing the after-tax dividends in alternative opportunity of equal qualities. It is, thus, the opportunity cost of dividends foregone by the shareholders.

**Cost of retained earnings can be computed with the help of following formula: **

K_{r} = D_{1}/NP + G or D_{1}/MP + G

where, K_{r} = Cost of retained earnings

D = Expected dividend at the end of the year

NP = Net proceeds of share issue

G = Rate of growth.

MP = Market price per share

Further, it is important to note that shareholders, usually, cannot obtain the entire amount of retained profits by way of dividends even if there is 100 per cent payout ratio. It is so because the shareholders are required to pay tax on their dividend income. So, some adjustment has to be made for tax.

However, tax adjustment in determining the cost of retained earnings is a difficult problem because all shareholders do not fall under the same tax bracket. Moreover, if the shareholders wish to invest their after-tax dividend income in alternative securities, they may have to incur some costs of purchasing the securities, such as brokerage.

Hence, the effective rate of return realised by the shareholders from the new investment will be somewhat lesser than their present return from the firm.

**To make adjustment in the cost of retained earnings for tax and costs of purchasing new securities, the following formula may be adopted: **

**Illustration 17: **

A firm’s K_{e} (return available to shareholders) is 15%, the average tax rate of shareholders is 40% and it is expected that 2% is brokerage cost that shareholders will have to pay while investing their dividends in alternative securities. What is the cost of retained earnings?

**Solution: **

**Supernormal Growth****: **

It dividends of a firm are expected to grow at a supernormal growth rate during the periods when it is experiencing very high demand for its products and then, the dividends grow at a normal rate when the demand reaches the normal level, the constant growth equation [P0 (or MP) = D0 (1+g)/K_{e }– g] can be suitably modified to calculate the cost of equity.

**In case, the dividends of a firm are expected to grow at a supernormal growth rate, g _{s}, for n years and then grow at a normal growth rate, g_{n}, till infinity; the cost of equity share can be calculated as: **

**Illustration 18: **

The equity share of a company is currently selling at Rs. 305.08 and it is currently paying a dividend of Rs. 4.24 per share. The dividend is expected to grow at a 18 per cent annual rate for five years and then at 12 per cent forever. Calculate the cost of equity capital.

**Solution: **