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
DIV
Ke =
MV ex div
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 =
DIV (I+g)
Mv
+ g
Where g = growth rate which can be computed as follows
g=
n−1
Latest Dividend
√Earlier Dividend (base yr) – 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.
Future Price (Pn )
Ke =
Mv
(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 =
DIV
Mv +floatation cost
+ 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
=
DIV ( I + g )
Mv
+ 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
=
Ke
=
EPS
Net proceeds
EPS
Market price
(for new share)
(for existing equity)
(h) Capital Asset Pricing Model (CAPM) Technique
E(R1 ) = (R F ) + [E(Rm ) − Rf ] β𝑖
where R1 = Required or expected return on stock is
Rf = Risk-free rate
Rm = expected return on the market portfolio
β𝑖 = Systematic risk of stock on company 𝑖
(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
Latest Dividend
g = √Earlier Dividend – 1
4
= √1.749 – 1
=
= 0.149
5−1
262,300
√150,000
- 1
= 0.15
= 15%
Or
∴
Ke
DIV ( 1 + g )
=
=
Mv
262,350 1+0.15
1,000,000 x 3.35
+ g
+ 0.15
= 0.24
= 24%
EXAMPLE 2: The following are the data in respect of “stupid simple” Plc:
Market price per share
Dividend per share
Growth rate
N7
N0.50
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
=
=
=
DIV (1+g)
Mv−floatation cost
0.50
1+0.06
7−(0.25+0.50)
0.53
6.25
= 0.1448
+g
+ 0.06
+ 0.06
i.e 14.5%
(b) Determination of Ke of Retained Earnings
Ke
=
=
=
DIV (1+g)
Mv−floatation cost
0.50 ( 1+0.06)
7
0.53
= 0.1357
7
+g
+ 0.06
+ 0.06
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
41
g=
√
30
26
–1
= 0.049 i.e., 4.9%
Ke
=
=
DIV (1+g)
Mv
30 (1+0.049)
2.35−0.30
+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 =
DIV (1+g)
Mv
+g =
0.10 (1+0.07)
1.20
+ 0.07
= 0.159 i.e., 15.9%
(ii)
CAPM
R1 = R f +[(Rm − Rf )β𝑖]
= 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 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
K iP =
DIVi P
MVi P
where DIViP = future fixed dividend payment
MVi P = 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 + [
P1
P1 + P2
(R 2 − R 1 )]
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
K iP =
DIVi P
MVi P
=
8% x N1
80
=
8
80
= 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
K iP =
DIVi P
MVi P
10% x N100 x 10,000,000
=
9,800,500
=
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 MV
N98
Outflow
1-4
Annual Dividend (5% x N100) N5
4
Redeemable value
N100
Inflow
Inflow
Yr
0
Variables
Current MV
CF
N98
DCF
@8%
1.0000
PV
(98)
DCF
@5%
1.000
PV
(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)
IRR = R1 + [
P1
P1 + P2
(R 2 − R 1 )]
2.00
= 5% +
2
2+7.94
(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
=
INT
MVex int
b (ii) with tax
Kd
=
INT (I−t)
MVex−int
x
100
1
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 =
Nominal cost of debt
Inflation rate
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
=
INT (I−t)
MV ex−int
=
15% x 10,000,000 (1−0.35)
10,500,000
975,000
10,500,000
= 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 MV
N100
Outflow
1-5
Interest net of tax
N10
Inflow
5
Redemption value
N105
(1-0.45)=5.5
Inflow
Yr
0
Variables
Current MV
CF
N100
DCF
7%
1.0000
PV
(100)
DCF
6%
1.0000
PV
(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 =
VEKE
Vcoy
+
VD KD
Vcoy
+
Vp Kp
Vcoy
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)
DIV ( I + g )
Ke =
Mv
6(1+0.05)
=
24
+ g
+ 0.05
= 31.25%
(ii)
Kp =
DIVp
MVp
=
14% x N10
95% x N10
=
1.4
9.5
x
100
1
= 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
=
2,707,200
14,000,000
x
100
1
= 19.33%
Method 2
(1)
Nature
(2)
(3)
(4)
Nominal
Ratio (%)
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
WACC =19.33
COC (%)
(3x4)
WACC
19.33