The COC Comprisesthree Components Which Are
COST OF CAPITAL
(1)INTRODUCTION
The main objective ofbusiness firm is the maximization of the wealth of the shareholders in the long run; hence, management should only invest in projects which give a return in excess of the cost of funds invested in the projects of the business. Cost of capital (COC) can be viewed from the point of views of both the investors and companies. The COC for investors is the return that investors require from their investment in a particular company. It is seen as an opportunity cost of finance because it is theminimum return that investors require and if they do not get this return, they will transfer some or all of their investment somewhere else. Companies must therefore make a sufficient return from their own capital investments to pay the returns required by their shareholders and holders of debt capital. The COC for investors therefore establishes a COC for companies. The COC for a company is the return that it must make on its investments so that it can afford to pay its investors the returns that they require and maintain the market value of its shares.
(2)Elements of cost of capital
The COC comprisesthree components which are:
(i)Risk-free rate of return –This is the return which would be required from an investment if it were completely free from risk. Typically, a risk-free yield would be the yield on government securities.
(ii)Premium for business risk – Economic, social, and political factors affect the firm’s operations, and henceits operating income (EBIT). These factors which are generally referred to as environmental factors or business environment are externally imposed, which means they cannot be controlled by the firm. Among the most important factors are fiscal and monetary policies of the government. The firm’s business environment is constantly changing, and thiscauses itsoperating income to vary as well.The variability of operating income which is caused by changes in the firm’s business environment is known as business risk. It is faced by all these who invest in the firm’s securities (shareholders and long-term creditors alike).
(iii)Premium for financial risk – This relates to the danger of high debt levels(high gearing). This type of risk varies directly with the debt – equity ratio, the higher the proportion of debt in the capital structure, the higher thefinancial risk. It is encountered only by ordinary shareholders of a firm and for an all –equity firm, the financial risk is zero.
∴ COC = RO + B + F
whereRO = return at zero risk level
B =premium for business risk
F = premium for financial risk which is related to the pattern of capital structure
(3)Importance of the cost of capital
The COC is very important in financial management and plays a crucial role in the following areas
(i)Capital budgeting decisions – the COC is used for discountingcash flows under NPV method for investment appraisals.
(ii)CapitalStructure Decisions - An optimal capital structure is that structure at which the value of the firm is maximum and COC is the lowest, so, COC is crucial in designing optimal capital structure
(iii)Evaluation of Financial Performance - COC is used to evaluate the financial performance of top management. The actualprofitability iscompared to the expected and actual COC of funds and if profit is greater than the cost of capital, theperformance may be said to be satisfactory.
(iv)Other Financial Decisions –COC is also useful in making such other financial decisions as dividend policy, capitalization of profits, making the rights issue, etc.
(4)Classification of COC
COC can be classified as follows:
(i)Historical cost & Future Costs: Historical costs are book costs relating to the past while future costs are estimated costs which act as guide for estimation of future costs.
(ii)Specific costs & composite costs:Specific cost is the cost of a specific source of capital, while composite cost is combined cost of various sources of capital. Composite cost which is also known as the weighted average cost of capital should be considered in capital budgeting decisions.
(iii)Explicit & Implicit cost:Explicit costof any source of finance is the discount rate which equates the present value of cash inflows with the PV of cash outflows. It is the IRR. Implicit cost, which is also known as the opportunity cost is the opportunity forgone in order to take up a particular project, e.g. the implicit cost of retained earnings is the rate of return available to shareholders by investing the funds elsewhere.
(iv)Average & Marginal Cost: An average cost is the combined cost or weightedaverage cost of various sources of capital. Marginal cost refers to the average cost of capital of new or additionalfunds required by a firm. It is the marginal cost which should be taken into consideration in investment decision.
(5)Problems in the Determination of COC
(i)Controversy regarding the relevance or otherwise of historic costs or future costs in decision making process
(ii)Whether to use book value or market value weights in determining WACC poses a problem
(iii)Computation of cost of equity depends on the expected rate of return by its investors which is very difficult to quantify in reality
(6)Computation of cost of capital
Computation of COC of a firm involves the following steps:
(i)Computation of cost of specific sources of a capital, namely equity, retained earnings, preferences capital, and debt.
(ii)Computation of a weighted average cost of capital (WACC).
(7)Cost of Equity Capital
(a)Introduction - cost of equity is the expected rate of return by the equity shareholders whonormally expect some dividend from thecompany while making investment in shares. Thus, the rate of return expected by them becomes the cost of equity. Conceptually, cost of equity share capital may be defined as the minimum rate of return that a firm must earn on the equity part of total investment in a project in order to leave uncharged the market price of such shares. The cost of equity is measured in reference to the dividend forgone by the shareholdersand could thus bedetermined by means of the dividend valuation model. The following are the different ways by which cost of equity can be measured.
(b)Constant Dividend with zero growth
Ke=
whereKe = cost of equity
Div = Dividend
MVex div = market value excluding dividend which can be calculated as cumulative dividend less dividend to be paid shortly.
(c)Dividend Growth at a constant rate
Ke= + g
Where g = growth rate which can be computed as follows
g = – 1
OR
g = ROCE x b
ROCE = return on capital employed
b = retention rate (i.e. rate of ploughing back profit)
(d)Zero Dividend
When the firm is NOT paying any dividend but re-investing all its earnings, the only form of benefit expected by the investors is CAPITAL GAIN which they will get when they sell their shares at a later date. The cost of equity is therefore the rate that equates the PV of this future price to the current price.
Ke=
(e)Cost of New Ordinary Shares
When it is proposed to raise new issues of ordinary shares, floatation cost should bededucted from the market value. Examples of floatation cost include printing and advertising cost, underwriting commission, etc.
Ke= + g
(f)Cost of Retained Earnings
Retained earnings areprofits re-invested in the business instead of being paid out as dividend. They belong to the ordinary shareholders and as such, the cost of retained earnings is essentially the same as the cost of other equity capital.
Ke= + g
(g)Earnings yield method
The cost of equity is the discount rate that capitalizes a stream of future earnings to evaluate the shareholdings. It is computed by taking earnings per share (EPS) into consideration. It is calculated thus:
Ke= (for new share)
Ke= (for existing equity)
(h)Capital Asset Pricing Model (CAPM) Technique
E = +β
where R1 = Required or expected return on stock is
Rf = Risk-free rate
Rm = expected return on the market portfolio
β= Systematic risk of stock on company
(i)Cost of Equity in an un-quoted company
Unquoted companies’ shares do not have a quoted market price thus making it difficult to calculate the cost of equity. An approach to calculating cost of equity for unquoted companies is to use the following procedure:
-Select a proxy similarpublic quoted company especially a company in the same industry as the un-quoted company.
-Estimate the cost of equity for the public quoted company.
-Add a further premium to the cost of equity for additional business and financialrisk because the company is not quoted.
(j)Cost of Equity capital: Gross or Net Dividend Yield
The cost of equity should be calculated on the basis of net dividend rather than gross dividend.
This is sobecause of the following:
- The net dividend is the appropriate choice because the COC is used as the discount rate for the evaluation of a capital project by a company and the companymust have sufficient profit from its investment to pay shareholders the net dividend they require out of after – tax profits.
- The taxation on profits is allowed for in the cash flow of each project. The discount rate is therefore applied to the cash flowof theproject after tax. If a company were to make a payment of dividends out of profits, the amount available would be the net dividend, related to the after-taxprofits earned.
EXAMPLE1
The dividends and earnings of Sebotimo Plc over the last 10years have been as follows:
Year / Dividends (N) / Earnings (N)2001 / 150,000 / 400,000
2002 / 192,000 / 510,000
2003 / 206,000 / 550,000
2004 / 245,000 / 650,000
2005 / 262,350 / 700,000
The company is financedentirely by equity and there are 1,000,000 shares in issue, each with a market value of N3.35 ex div
Required
Calculate the cost of capital
Solution
g = – 1 = - 1
= – 1= 0.149 = 0.15
= 15%
Or
∴Ke= + g
= + 0.15
= 0.24
= 24%
EXAMPLE 2:The following are the data in respect of “stupid simple” Plc:
Market price per share / N7Dividend per share / N0.50
Growth rate / 6%
Issue cost / N0.25
Underwriting of new issue / N0.50
Required
You are required to calculate
(i)Cost of equity
(ii)Cost of retained earnings
Solution
(a)Determination of Ke of new ordinary shares
Ke= + g
= + 0.06
= + 0.06
= 0.1448 i.e 14.5%
(b)Determination of Ke of Retained Earnings
Ke= + g
= + 0.06
= + 0.06
= 0.1357 i.e 13.6%
EXAMPLE 3: “Omo-Jeje” Plc has issued 10 million ordinary shares of N1. Details of the company‘searnings and dividends per share during the past 4years are as follows:
Year ended 31st December / EPS / OPS2009 / 35k / 26k
2010 / 33k / 27k
2011 / 43k / 29k
2012 (estimated) / 42k / 30k
The current (December, 2012)market value of each ordinary share of the company is N2.35 cum dividend. The 2012 dividend of 30k per share is due to be paid in January 2013.
Required
g = – 1
= 0.049 i.e., 4.9%
Ke= + g
= + 0.049
= 0.2025 i.e., 20%
EXAMPLE 4: The following data relates to ‘lazy-people” Plc
Current price per share on the stock Exchange N1.20
Current annual gross DPSN0.10
Expected average annual growth rate of dividends7%
beta coefficient for the firm’s shares0.5
Expected rate of return on risk-free securities8%
Expected return on the market portfolio12%
Required
Calculate the using (i) dividend growthmodal & (ii) CAPM
Solution
(i)Dividend growth modal
Ke= + g = + 0.07
= 0.159 i.e., 15.9%
(ii)CAPM
+
= 8% + (12% - 8%) 0.5
= 8% + 2%
= 10%
Cost of Preference Capital
(a)Introduction: cost of preference share capital is the rate of return that must beearned on preference capital financed investments, to keep unchanged the earnings available to the equity shareholders. A preference share is also a fixed interest source of funds like the long-termdebt and owners are expected to receive fixed dividend payment. The only difference between a debt and preference share is that dividend payments on preference shares are NOT allowable for tax purposes. The cost of preference shares will depend on whether it is redeemable or irredeemable.
(b)Irredeemable Preference shares (undated preference shares)
These are the preference share capital that cannot be redeemed in a short term. They stand in the equity portion of the balance sheet for a long term. It is sometimes called undated preference share capital because it has no fixed date for redemption. Dividend is fixed; no opportunity for growth in Dividend and it does not attract Tax
P =
where DIViP = future fixed dividend payment
= market value of irredeemable preference share
KiP = Cost of irredeemable preference share
(c)Redeemable Preference Shares –Redeemable preference share is the fixed preference share capital that can be redeemed at expiration. There is also no growth in dividend and the fixed dividend does not attract tax. The cost of the redeemable preference share is then theminimum rate of return required by the provider of redeemable preference shares. It is the discount rate that equates the current market value ex-div to the PV of associated future cash flows. The associated future cash flow are (i) the dividend from year 1 to the year of redemption, and (ii) the redemption value in the year of redemption.
The discount rate is calculated by the Interpolation method (trial and error) in a manner similar to the calculation of IRR. In carrying out the calculation, the following are the requirements.
(i)The current market value ex div is treated as cost outflow in year O
(ii)The annual dividend is treated as cash inflow from year 1 to year of redemption
(iii)The redeemable value is treated as cash inflow in the year of redemption
IRR = R1 +
EXAMPLE 5: AnihuntodunPlc has 8% preference shares which have a nominal value of N1 and a market value of 80k.
Required
Determine the cost of preference capital
Solution
P = = = = 10%
EXAMPLE 6: A company issued 10%, N100 10,000,000irredeemable preference share when the market is N9,800,500
Required
Calculate the cost of irredeemable preference share
Solution
P =
=
= 10.20%
EXAMPLE 7: Bonitiri Plc has just issued 4years 5% redeemable preferenceshare N1,100,000. The current market price of the debenture is N98 ex-div
Required
Calculate the cost of redeemablepreference share
Solution
Yr / Variables / Cash flow / Remarks0 / Current MV / N98 / Outflow
1-4 / Annual Dividend (5% x N100) / N5 / Inflow
4 / Redeemable value / N100 / Inflow
DCF / DCF
Yr / Variables / CF / @8% / PV / @5% / PV
0 / Current MV / N98 / 1.0000 / (98) / 1.000 / (98)
1-4 / Annual DIV / N5 / 3.3121 / 16.56 / 3.5460 / 17.73
4 / Redeemable value / N100 / 0.7350 / 73.50 / 0.8227 / 82.27
(7.94) / 2.00
IRR = R1 +
= 5% + (8-5) %
= 5% + [0.2012 (3)%]
= 5% + 0.603603729
= 5.604%
Cost of Debt Capital
(a)Introduction:The capitalstructure of a firm normally includes the debt component also. Debt may be in the form of Debentures, Bonds, Term Loans from financial institutions, etc. The debt is carried at a fixed rate of interest irrespective of the profitability of the company. Since the coupon rate is fixed, the firm increases its earnings through debt financing. Then after payment of fixed interest charges, more surplus is available for equity shareholders, and hence EPS will increase. It is very important to know that dividends payable to equity shareholdersand preference shareholders is an appropriationof profit, whereas the interest payable on debt is a charge against profit. Therefore, any payment towards interest will reduce the profit and ultimately the company’s tax liability would decrease. This phenomenon is known as the “tax shield”. The tax should is viewed as a benefit which accrues to a company which is geared
(b)Irredeemable Debenture:- Irredeemable debenture is one in which there is no specific redemption date
b(1)without tax
Kd=
b (ii) with tax
Kd= x
where Kd = cost of irredeemable debt
INT =annual interest
t = company income tax rate
MV = value of debt ex-interest
(c)Redeemable Debenture:The cost of redeemable debenture is the minimum rate of return required by providers of redeemable debentures. It is the discount ratethat equates the currentmarket value ex-interest with the present value of associated future cash flow.
In calculating the cost of debt, the cost of capital must beadjusted to take into account income tax advantage of debts, this is because the interest on debt capital is an allowable deduction for the purpose of taxation. The cost of redeemable debenture is found by determining the IRR.
(d)Cost of floating rate debt:Companies usuallyraise debt on a rate of interest that varies from time to time. In floating debt rate, a certain percentage of interest will be of fixed nature over and above the fixed rate of interest, the lender will charge extra rate of interest depending on the money market and economic policies of the country. Banks are lending at prime lending rate plus variable portion of interestthat vary from customer to customer. The variable portion will act like a risk premium. In case of establishedand financially sound companies, the variable rate will be lesser and in case risk is attached to the lending, the variable rate will be more.
Thus, if a firm hasfloating rate debt, then the cost of an equivalent fixed interest debt should be substituted. “Equivalent” usually mean fixed interest debt with a similar term to maturity in a firm of similar standing, although if the cost of capital is to be used for project appraisal purposes, there is an argument for using debt of the same duration as the project under consideration.
(e)Nominal and Real cost of Debt:The real cost of debt will be less than the nominal cost as investors are notcompensated for the real drop in value of their funds. Thus, the real cost of debt is lesser than the cost of debt. The formula for the calculation of the real cost of debt is as follows:
Real cost of debt =
EXAMPLE 8: Ayomi Nig Plc issued 15%, N10,000,000 irredeemable debentures. Assuming thetax rate of 35% and the current market value of the debt is N10,500,000
Required
Determine the cost of Debt
Solution
Kd= =
= 9.286%
EXAMPLE 9: ABC Plc is financed by N15m 10% redeemable debentures currently quoted at N100 each. The debentures would be redeemed in 5 years time at N105. Corporation tax is 45%.
Required
Determine the cost of debt
Solution
Yr / Variables / Cash flow / Remarks0 / Current MV / N100 / Outflow
1-5 / Interest net of tax / N10 (1-0.45)=5.5 / Inflow
5 / Redemption value / N105 / Inflow
DCF / DCF
Yr / Variables / CF / 7% / PV / 6% / PV
0 / Current MV / N100 / 1.0000 / (100) / 1.0000 / (100)
1-5 / Interest net of tax / N5.5 / 4.1002 / 22.5511 / 4.2124 / 23.168
5 / Redemption value / N105 / 0.7130 / 74.8650 / 0.7473 / 78.467
(2.5839) / 1.635
IRR = 6.3875%
(10) Weighted average cost of Capital (WACC)
(a) Introduction: This represent the minimum rate ofreturn jointlyrequired by all providers of capital. The cost of individual capital is separately calculated and the weightedaverage determined. The weights normally attached are the respectively market values. When reference is made to cost of capital, it should be taken as the weighted average cost of capital.
The formula is:
WACC = + +