The COC Comprisesthree Components Which Are

COST OF CAPITAL

(1) INTRODUCTION

The main objective of business 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 the minimum 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 comprises three 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 hence its 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 this causes its operating 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 the financial

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

where RO = 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 discounting cash flows

under NPV method for investment appraisals.

(ii) Capital Structure 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 actual profitability is

compared to the expected and actual COC of funds and if profit is greater than

the cost of capital, the performance 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 cost of 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

weighted average cost of various sources of capital. Marginal cost refers to the

average cost of capital of new or additional funds 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 who normally expect some dividend from the company 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 shareholders and could thus be determined 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 = where Ke = 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.

(e) Cost of New Ordinary Shares When it is proposed to raise new issues of ordinary shares, floatation cost

should be deducted 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 are profits 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 similar public 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 financial

risk 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 so because 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

company must 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 flow of the project 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-tax profits earned.

EXAMPLE 1

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 financed entirely 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

∴ Ke = + g

= + 0.15

= 0.24

EXAMPLE 2: The following are the data in respect of “stupid simple” Plc: Market price per share N7 Dividend 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

= 0.1448 i.e 14.5%

(b) Determination of Ke of Retained Earnings

Ke = + g

= + 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‘s earnings and dividends per share during the past 4years are as follows:

Year ended 31st December EPS OPS 2009 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 DPS N0.10

Expected average annual growth rate of dividends 7% beta coefficient for the firm’s shares 0.5

Expected rate of return on risk-free securities 8% Expected return on the market portfolio 12%

Required

Calculate the using (i) dividend growth modal & (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%

Cost of Preference Capital

(a) Introduction: cost of preference share capital is the rate of return that must be

earned 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-term debt 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

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 the minimum 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: Anihuntodun Plc 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 10,000,000 irredeemable preference share when the market is N9,800,500

Required

Calculate the cost of irredeemable preference share Solution

= 10.20%

EXAMPLE 7: Bonitiri Plc has just issued 4years 5% redeemable preference share

N1,100,000. The current market price of the debenture is N98 ex-div

Required Calculate the cost of redeemable preference share Solution Yr Variables Cash flow Remarks 0 Current N98 Outflow MV 1-4 Annual N5 Inflow Dividend (5% x N100) 4 Redeemab N100 Inflow le value

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 capital structure 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

shareholders and preference shareholders is an appropriation of 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 rate

that equates the current market value ex-interest with the present value of

associated future cash flow.

In calculating the cost of debt, the cost of capital must be adjusted 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 usually raise 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 interest

that vary from customer to customer. The variable portion will act like a risk premium. In case of established and 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 has floating 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 not compensated 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 the tax 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 Remarks 0 Current N100 Outflow MV 1-5 Interest net N10 (1- Inflow of tax 0.45)=5.5 5 Redemption N105 Inflow value

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 of return jointly required by all providers of capital. The cost of individual capital is separately calculated and the weighted average 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 = + +

Where VE = Current market value of equity

KE = cost of equity capital

VD = value of debt ex-unit

KD = Cost of irremediable debt

Vp = value of preference share ex-div

Kp = cost of preference shares

Vcoy = value of company

Example 10: Oko won lode Chemicals Ltd has paid up equity capital 600,000 equity shares of N10 each. The current market price of shares is N24. During the current year, the company has declared a dividend of N6 per share. The company has also previously issued 14% preference shares of N10 each aggregating N3,000,000 and 13% 50,000 debentures of N100 each. The company’s corporate tax rate is 40%, the growth in dividends on equity shares is expected at 5%. In case of preference shares the company has received only 95% of the fix value of shares after deducting issue expenses.

Required

Calculate the WACC of the company

Solution

(i) Ke= + g = + 0.05

= 31.25%

(ii) Kp = = = x

= 14.74%

(iii) KD = INT (I-t) = 13% (1-0.40)

= 0.078

= 7.8%

Method 1

Nature Nominal value COC (5) WACC Equity 6,000,000 31.25 1,875,000 14% Preference 3,000,000 14.74 442,200 15% Debenture 5,000,000 7.8 390,000 14,000,000 2,707,200

WACC = x

= 19.33%

Method 2

(1) (2) (3) (4) (3x4) Nature Nominal Ratio (%) COC (%) WACC Equity 6,000,000 42.86 31.25% 13.39 14% Preference 3,000,000 21.43 14.74 3.16 15% Debenture 5,000,000 35.71 7.8 2.78 14,000,000 100.00 19.33

WACC =19.33