Chapter 1
Chapter 1
Chapter 1
INTRODUCTION
Cost of capital is an integral part of investment decision as it is used to
measure the worth of investment proposal provided by the business concern. It
is used as a discount rate in determining the present value of future cash flows
associated with capital projects. Cost of capital is also called as cut-off rate,
target rate, hurdle rate and required rate of return. When the firms are using
different sources of finance, the finance manager must take careful decision
with regard to the cost of capital; because it is closely associated with the value
of the firm and the earning capacity of the firm.
Meaning of Cost of Capital
Cost of capital is the rate of return that a firm must earn on its project
investment to maintain its market value and attract funds.
Cost of capital is the required rate of return on its investments which
belongs to equity, debt and retained earnings. If a firm fails to earn
return at the expected rate, the market value of the shares will fall and it
will result in the reduction of overall wealth of the shareholders.
Definitions
The following important definitions are commonly used to understand the
meaning and concept of the cost of capital.
According to the definition of John J. Hampton “ Cost of capital is the
rate of return the firm required from investment in order to increase the
value of the firm in the market place”.
According to the definition of Solomon Ezra, “Cost of capital is the
minimum required rate of earnings or the cut-off rate of capital
expenditure”.
According to the definition of James C. Van Horne, Cost of capital is “A
cut-off rate for the allocation of capital to investment of projects. It is the
rate of return on a project that will leave unchanged the market price of
the stock”.
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According to the definition of William and Donaldson, “Cost of capital
may be defined as the rate that must be earned on the net proceeds to
provide the cost elements of the burden at the time they are due”.
Assumption of Cost of Capital
Cost of capital is based on certain assumptions which are closely associated
while calculating and measuring the cost of capital. It is to be considered that
there are three basic concepts:
1. It is not a cost as such. It is merely a hurdle rate.
2. It is the minimum rate of return.
3. It consists of three important risks such as zero risk level, business risk and
financial risk.
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Importance to Other Financial Decisions
Apart from the above points, cost of capital is also used in some other areas
such as, market value of share, earning capacity of securities etc. Hence, it
plays a major part in the financial management.
COMPUTATION OF COST OF CAPITAL
Computation of cost of capital consists of two important parts:
1. Measurement of specific costs
2. Measurement of overall cost of capital
Measurement of Specific Cost of Capital
It refers to the cost of each specific sources of finance like:
1. Debt
2. Preferred stock
3. Common stock
4. Retained earnings
Two important points you should bear in mind about the specific cost of
capital. These are:
1. One is that it is computed on an after-tax basis. Meaning, if there would
be any tax implication on the individual source of capital, it should be
considered. In almost all circumstances, the tax implication is only on
debt sources of finance.
2. The second point is that the specific cost of capital is expressed as an
annual percentage or rate like 6%, 9%, or 10%. The cost of capital is not
stated in terms of birr.
1. The cost of debt
The cost of long-term debt, kd, is the after-tax cost today of raising long-term
funds through borrowing. For convenience, we typically assume that the funds
are raised through the sale of bonds.
This is the minimum rate of return required by suppliers of debt. The
relevant specific cost of debt is the after-tax cost of new debt.
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Generally, debt is the cheapest source of finance to a firm and, hence,
the cost of debt is the lowest specific cost of capital. There are two basic
explanations for this:
First, debt suppliers, generally, assume the lowest risk among all
suppliers of capital. They receive interest payments before
preferred and common dividends are paid. Since they assume the
smallest risk, their return is the lowest. Their lowest return would
be the lowest cost of capital to the firm.
Second, raising capital through debt sources entails interest
expense. The interest expense in turn reduces the firm’s income
which ultimately would cause tax payment to be reduced. So
raising money in the form of debt results in the smallest tax
burden, and finally, the firm’s cost of debt would be the lowest.
Debt sources of finance may take several forms like bonds, promissory notes,
bank loans.
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I = Annual interest payment
Pn = the par value of the bond
n = Length of the holding period of the bond in years.
Required: Calculate the after tax cost of Abyssinia’s new bond issue:
Solution:
Given:Pn
Given:Pn = Br. 1,000; I = Br. 120 (Br. 1,000 x 12%); n = 15; Pd = Br. 1,010; f =
Br. 30;
t = 40%; Kdt =?
Then apply the three steps:
i) NPd = Br. 1,010 – Br. 30 = Br. 980
Br . 1 ,000−Br . 980
Br . 120 +
15
= 12 .26 %
Br . 1 ,000+Br . 980
ii) Kd = 2
iii) Kdt = 12.26% (1 – 40%) = 7.36%
Therefore, the after – tax cost of Abyssinia’s new bond issue is 7.36%. That is,
Abyssinia should be able to earn a minimum of 7.36% to satisfy bondholders.
Otherwise, the firm’s value will decline.
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Class work
Ayenew Company’s financing plans for next year include the sale of long-term
bonds with a 10% coupon. The company believes it can sell the bonds at a
price that will provide a yield to maturity of 12% to investors. If its marginal tax
rate is 35%, what is Ayenew’s after-tax cost of debt?
2. The cost of preferred stock
Preferred stock represents a special type of ownership interest in the firm. It
gives preferred stockholders the right to receive their stated dividends before
any earnings can be distributed to common stockholders. Because preferred
stock is a form of ownership, the proceeds from its sale are expected to be held
for an infinite period of time.
The cost of preferred stock is the minimum rate of return a firm must
earn in order to satisfy the required rate of return of the firm’s preferred
stock investors.
It is also the minimum rate of return a firm’s preferred stock investors
require if they are to purchase the firm’s preferred stock.
When a firm raises capital by issuing new preferred stock, it is expected to pay
fixed amount of dividends to the preferred stockholders. So it is the dividend
payment that is the cost of the preferred stock to the firm stated as an annual
rate.
The cost of a new preferred stock issue can be computed by following two
steps:
i) Determine the net proceeds from the sale of each preferred stock.
NPpf = Ppf – f
Where:
NPpf = Net proceeds from the sale of each preferred stock
Ppf = Market price of the preferred stock
f = Flotation costs
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ii) Compute the cost of preferred stock issue
Kps = Dps
NPpf
Where:
Kps = the cost of preferred stock
DPs = the pre share annual dividend on the preferred stock
Example: Sefa Computer Systems Company has just issued preferred stock.
The stock has 12% annual dividend and Br. 100 par value and was sold at
102% of the par value. In addition, flotation costs of Br. 2.50 per share must be
paid. Calculate the cost of the preferred stock.
Solution:
Given: Pps = Br. 102 (Br. 100 x 102%); Dps = Br. 12 (Br 100 x 12%); f = Br.
2.50;
Kps =?
Then apply the two steps:
Class work
Sattelite Share Company plans to sale preferred stock with par value of Br. 50
per share. The issue is expected to pay quarterly dividends of Br. 1.25 per
share and to have flotation costs of 6% of the par value. The preferred stock
sells at 95% of its par.
Required: Calculate the cost of preferred stock to Satellite Share Company.
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3. The cost of common stock
The cost of common stock is the minimum rate of return that a firm must earn
for its common stockholders in order to maintain the value of the firm.
A firm does not make explicit commitment to pay dividends to common
stockholders. However, when common stockholders invest their money
in a corporation, they expect returns in the form of dividends. Therefore,
common stocks implicitly involve a return in terms of the dividends
expected by investors and hence, they carry cost.
The cost of common stock is the cost of raising one more dollar of
common equity capital, either internally (from earnings retained in the
firm) or externally (by issuing new shares of common stock). There are
costs associated with both internally and externally generated capital.
The cost of issuing common stock is difficult to estimate because of the
nature of the cash flow streams to common shareholders. Common
shareholders receive their return (on their investment in the stock) in
the form of dividends and the change in the price of the shares they
own.
The dividend stream is not fixed, as in the case of fixed-rate preferred
stock. How often and how much is paid as dividends is at the discretion
of the board of directors. Therefore, this stream is unknown so it is
difficult to determine its value.
The change in the price of shares is also difficult to estimate; the price of
the stock at any future point in time is influenced by investors’
expectations of cash flows further into the future beyond that point.
Nevertheless, two methods are commonly used to estimate the cost of
common stock:
the dividend valuation model (DVM) and
the capital asset pricing model(CAPM). Each method relies on
different assumptions regarding the cost of equity; each produces
different estimates of the cost of common equity.
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1. Cost of Common Stock Using the Dividend Valuation Mode
The DVM states that the price of a share of stock is the present value of all its
future cash dividends, where the future dividends are discounted at the
required rate of return on equity, r.
If these dividends are constant forever (similar to the dividends of perpetual
preferred stock, as we just covered), the cost of common stock is derived from
the value of perpetuity.
Let D represent the constant dividend per share of common stock that is
expected next period and each period after that forever; P0, the current
price of a share of stock; and re, the cost of common stock. The current
price of a share of common stock is:
P0= D
re
We can solve for re:
re= D
P0
However, common stock dividends do not usually remain constant. It’s typical
for dividends to grow at a constant rate.
Let D0 indicate this or current period’s dividend. If dividends grow at a
constant rate, g, forever, the present value of the common stock is the
present value of all future dividends:
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Expressing this in summation notation:
If we refer to the next period’s dividend, D1, as this period’s dividend, D0,
compounded one period at the rate g,
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We see that the cost of common stock is the sum of next period’s dividend
yield, D1/P0, plus the growth rate of dividends:
Cost of common stock = Dividend yield + Growth rate of dividends
Example:1
Consider a firm expected to pay a constant dividend of br.2 per share per year,
forever. If the firm issues stock at br.20 a share.
Required: compute the firm’s cost of common stock is:
re= br.2
br.20
= 0.10 or 10% per year
But, if dividends are expected to be br.2 in the next period and grow at a rate of
3% per year, and the required rate of return is 10% per year, the expected price
per share (with D1 = br.2 and g = 3%) is:
P0 = br.2
0.10 – 0.03
= br. 28.57 which is more than br.8 above the price if there is no
expected growth in dividends.
Example 2: An issue of common stock is sold to investors for Br. 20 per share.
The issuing corporation incurs a selling expense of Br. 1 per share. The current
dividend is Br. 1.50 per share and it is expected to grow at 6% annual rate.
Compute the specific cost of this common stock issue.
Solution
Given: Po = Br. 20; Do = Br. 1.50; g = 6%; f = Br. 1; Ks = ?
Then apply the two steps:
Class work
The DVM reflects two ideas that make some sense about the relation
between the cost of equity and the dividend payments:
The greater the current dividend yield, the greater the cost of equity.
The greater the growth in dividends, the greater the cost of equity.
However, the DVM has some drawbacks:
How do you deal with dividends that do not grow at a constant rate? This
model does not accommodate non-constant growth easily.
What if the firm does not pay dividends now? In that case, D1 would be
zero and the expected price would be zero. But a zero price for stock does
not make any sense! And if dividends are expected in the future, but
there are no current dividends, what do you do?
What if the growth rate of dividends is greater than the required rate of
return? This implies a negative stock price, which isn’t possible.
What if the stock price is not readily available, say in the case of a
privately-held firm? This would require an estimate of the share price.
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Therefore, the DVM may be appropriate to use to determine the cost of equity
for companies with stable dividend policies, but it may not applicable for all
firms.
2. Cost of Common Stock Using the Capital Asset Pricing Model
The investor’s required rate of return is compensation for both the time value of
money and risk. To figure out how much compensation there should be for
risk, we first have to understand what risk we are talking about.
The capital asset pricing model (CAPM) assumes an investor holds a
diversified portfolio—a collection of investments whose returns do not
move in the same direction nor at the same time nor by the same
amount. The result is that the only risk left in the portfolio as a whole is
the risk related to movements in the market as a whole—market risk.
If we assume all shareholders’ hold diversified portfolios, the risk that is
relevant in valuing a particular investment is the market risk of that
investment. The greater the market risk, the greater the compensation—
meaning a higher yield—for bearing this risk. And the greater the yield,
the lower the present value of the asset because expected future cash
flows are discounted at a higher rate that reflects the higher risk.
The cost of common stock is the sum of the investor’s compensation for
the time value of money and the investor’s compensation for the market
risk of the stock:
Cost of common stock = Compensation for the time value of
money +Compensation for market risk
Let’s represent the compensation for the time value of money as the
expected risk-free rate of interest, rf. The risk-free rate of interest is the
rate that is earned on an asset that has no risk. If a particular common
stock has market risk that is the same as the risk of the market as a
whole, then the compensation for that stock’s market risk is the
marketrisk premium. The market’s risk premium is the difference
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between the expected return on the market, rm, and the expected risk-
free rate, rf:
Market risk premium = rm– rf
Because we know the compensation for the time value of money, rf, and now
we know the compensation for market risk, we see that the cost of common
stock, re, is:
re = rf+ B(rm– rf)
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The term (rm– rf) represents the risk premium required by investors for
bearing the risk of owning the market portfolio.
The multiplier, β, fine tunes this market risk premium to compensate for
the market portfolio associated with the individual firm. β, commonly
referred to as beta, is a measure of the sensitivity of the returns on a
particular security (or group of securities) to changes in the returns on
the market—a measure of market risk.
A common stock having a β greater than 1.0 has more risk than the average
security in the market. A common stock having a β less than 1.0 has less risk
than the average security in the market.
Suppose a firm’s stock has a β of 2.0. This means its market risk is
twice the risk of the average security in the market. If the expected
riskfree rate of interest is 6% and the expected return on the market is
10%, the cost of common stock, re, is:
re= 0.06 + 2.0(0.10 – 0.06) = 0.14 or 14%
In this example, the market risk premium is (10% – 6%) = 4%. A market
risk premium of 4% means that if you own a portfolio with the same risk
as the market as a whole (that is, with a beta of 1.0), you would expect to
receive a 10% return comprising: 6% to compensate you for the price of
time and 4% to compensate you for the price of market risk.
If you invest in a security with a β of 2.0, you would expect a return of
14% comprising: 6% to compensate you for the price of time and 2.0
times 4% = 8% to compensate you for the price of that security’s
particular risk.
The CAPM is based on two ideas that make sense: Investors are risk averse
and they hold diversified portfolios. But the CAPM is not without its
drawbacks:
First, the estimates rely heavily on historical values returns on the stock
and returns on the market. These historical values may not be
representative of the future, which is what we are trying to gauge. Also,
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the sensitivity of a firm’s stock returns may change over time; for
example, when the firm changes its capital structure.
Second, if the firm’s stock is not publicly-traded, there are no data
sources even for historical values.
As you know, dividends are paid out of a firm’s earnings. Their payment,
madein cash to common stockholders, reduces the firm’s retained earnings.
Let’s say a firm needs common stock equity financing of a certain amount; it
has two choices relative to retained earnings:
It can issue additional common stock in that amount and still pay
dividends to stockholders out of retained earnings. Or
it can increase common stock equity by retaining the earnings (not
paying the cash dividends) in the needed amount. In a strict accounting
sense, the retention of earnings increases common stock equity in the
same way that the sale of additional shares of common stock does.
It is not necessary to adjust the cost of retained earnings for flotation costs,
because by retaining earnings, the firm “raises” equity capital without
incurring these costs.
Retained earnings represent profits available for common stockholders
that the corporation chooses to reinvest in itself rather than payout as
dividends.
Retained earnings are not securities like stocks and bonds and hence do
not have market price that can be used to compute costs of capital.
The cost of retained earnings is the rate of return a corporation’s
common stockholders expect the corporation to earn on their reinvested
earnings, at least equal to the rate earned on the outstanding common
stock. Therefore, the specific cost of capital of retained earnings is
equated with the specific cost of common stock. However, flotation costs
are not involved in the case of retained earnings.
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Computing the cost of retained earnings involves just a single procedure of
applying the following formula:
Kr = D1 + g
Po
Where:
Kr = the cost of retained earnings
D1 = the expected dividends payment at the end of next year
Po = the current market price of the firm’s common stock
g = the expected annual dividend growth rate.
Example: Zeila Auto Spare Parts Manufacturing Company expects to pay a
common stock dividend of Br. 2.50 per share during the next 12 months. The
firm’s current common stock price is Br. 50 per share and the expected
dividend growth rate is 7%. A flotation cost of Br. 3 is involved to sale a share
of common stock.
Required: Compute the cost of retained earnings
Solution
Given: Po = Br. 50; D1 = Br. 2.50; g = 7%; Kr = ?
Then apply the formula:
Kr = D1+ g = Br. 2.50 + 7% = 12%
Po Br. 50
Class work
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Weighted average cost of capital (wacc)
In the above we have seen how to compute the cost of capital for each
individual source of capital. The specific cost of capital is used in
evaluating an investment proposal to be financed by a particular capital
source. Practically, however, investments are financed by two or more
sources of capital. In such a situation, we cannot make use of the
individual cost of capital. Rather we should use the average cost of
capital employed by the firm.
The firm’s capital structure is composed of debt, preferred stock,
common stock, and retained earnings. Each capital source accounts to
some portion of the total finance. But the percentage contribution of one
source is usually different from another. So we must compute the
weighted average cost of capital rather than the simple average.
The weighted average cost of capital (WACC) is the weighted average of
the individual costs of debt, preferred stock and common equity
(common stock and retained earnings). It is also called the composite
cost of capital.
The computation of the overall cost of capital (Ko) involves the following
steps.
(a) Assigning weights to specific costs.
(b) Multiplying the cost of each of the sources by the appropriate weights.
(c) Dividing the total weighted cost by the total weights.
If the weights of the component capital sources are all given, the
weighted average cost of capital can be computed as:
WACC = WdKdt + WpsKps + WceKs
Where:
WACC = the weighted average cost of capital
Wd = The weight of debt
Wps = the weight of preferred stock
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Wce = the weight of common equity
Kdt = the after – tax cost of debt
Kps = the cost of preferred stock
Ks = the cost of common equity
The WACC is found by weighting the cost of each specific type of capital
by its proportion in the firm’s capital structure. Weights of the individual
capital sources can be calculated based on their book value or market
value.
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= 0.5 (5.3%) + 0.04 (12.0%) + 0.46 (16.0%)
= 2.65% + 0.48% + 7.36%
= 10.49%
The minimum rate of return on all projects should be 10.49%. Meaning, Muna
should accept all projects so long as they earn a return greater than or equal to
10.49%
If the market value weights are used, Muna should accept all projects with a
minimum rate of return of 11.52%
Class work
On January 1, 2002, the total assets of Zway Share Company were Br. 54
million. There was no short-term debt. The firm’s optimal capital structure is
given below.
Long-term debt Br. 27,000,000
Common equity 27,000,000
Total liabilities and equity Br. 54,000,000
New bonds will have a 10% coupon rate and will be sold at Par. Common stock
currently has a market price of Br. 60 and can be sold with a flotation cost of
Br. 6 per share. Dividend yield is estimated to be 4% and the expected dividend
growth rate is 8%
Required: Calculate:
1) the cost of debt assuming s 40% marginal corporate tax rate
2) the cost of common equity (50% common stock and 50% retained
earnings)
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3) the weighted average cost of capital
As a firm tries to have more new capital, the cost of each birr will rise at some
point. Thus, the marginal cost of capital (MCC) is the cost of obtaining
additional new capital. Technically speaking, the MCC is the weighted average
cost of the last birr of new capital obtained. So the concept of marginal cost of
capital is discussed in the context of the weighted average cost of capital.
The first point, therefore, in computing the MCC is to determine the breaking
points where the cost of capital will increase.
Example:
If the firm issues br. 1,500,000 of new debt, the first br. 1,000,000 costs 5%
per year and the next br. 500,000 costs 6% per year.
Suppose the firm raises capital in the proportions of 40% debt and 60% equity
and raises br. 2,000,000 of new capital comprising br. 800,000 debts and br.
1,200,000 common stock. Looking at the schedules, we see the cost of debt is
5% up to the first br. 1,000,000 of debt. However, the cost of equity changes
once we have raised br. 1,000,000: The first br. 1,000,000 of equity costs 9%
and the additional br. 200,000 costs 10%.
The cost of capital of the first br. 2,000,000 of new capital is:
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Br.2,000,000
br.2,000,000
br.2,000,000
The average cost of raising a birr of capital for the first br.2,000,000 of capital
is 7.5%.
The marginal cost of capital for the first br.1,800,000 is:
Marginal cost of capital for the first br.1,800,000
Br.720,000 * 0.05 + Br. 1,000,000 * 0.09 + 80,000 = 7.4 % per year.
Br.1,800,000 Br. 1,800,000 r.1,800,000
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Amount of new debt Marginal cost of debt per year
Up to br. 1,000,000 5%
Br.1,000,000 to br.2,000,000 6%
Br. 2,000,000 to br.3,000,000 7%
Br.3,000,000 to br.4,000,000 8%
Br. 4,000,000 to br.5,000,000 9%
Equity
Amount of new equity Marginal costs of common stock per
year
Up to br. 1,000,0000 9%
Br.1,000,000 to br.3,000,000 10%
Br.3,000,000 to br. 5,000,000 11%
Br.5,000,000 to br.8,000,000 12%
And the marginal cost of capital for the next br.200,000 is:
Br.80,000 *0.05 + br.120,000 *0.10 = 8% per year.
Br. 200,000 br.200,000
If we raise one more birr of capital beyond the br. 2,000,000, but not more
than br. 1,000,000 in total debt nor more than br. 3,000,000 in total equity,
then it costs 5% for the additional debt and 10% for the additional equity:
Weighted average cost of capital beyond br. 2,000,000 but less than br.
4,000,000
= 0.40(0.05) + 0.60(0.10)
= 0.08 or 8% per year
Each time the marginal cost of either the equity or the debt changes, the
marginal cost of capital changes. These changes are referred to as break-
points.
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The set of marginal costs of capital for different levels of capital raised
makes up the marginal cost of capital schedule.
We can figure out where these break-points occur by looking at:
The marginal cost of debt schedule.
The marginal cost of stock schedule.
The capital structure proportions.
Let’s first look at the marginal cost of debt schedule. The marginal cost of
capital breaks when the marginal cost of debt changes from 5% to 6%—once
we have used up the first br. 1,000,000 of debt capital. Because our total
capital structure consists of 40% debt:
0.40(Total capital raised) = br. 1,000,000
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We can generalize the calculation of the break-point in the marginal cost of
capital schedule as:
Break-point in marginal cost of capital
= Break-point in marginal
cost of capital from source
Proportion of capital from source
Example: The target capital structure of Shala Corporation and other pertinent
data are given below.
Long-term debt ------------------ 40%; cost of preferred stock (Kps) = 12.06%
Preferred stock -------------------10% cost of retained earnings (Kr) = 14%
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Common equity ----------------- 50% cost of common stock (Ks) = 15%
Shala Corporation has Br. 900,000 available retained earnings. But when the
firm fully utilizes its retained earnings, it must use the more expensive new
common stock financing to meet its equity needs. In addition, the firm expects
that it can borrow up to Br. 1,200,000 of debt at 7.3% after-tax cost. Additional
debt will have an after-tax cost of 9.1%.
Required
1) What is the breaking point associated with the
a. Exhausting of retained earnings?
b. Increment of debt between Br. 0 to Br. 1,200,000?
2) Determine the ranges of total new financing where the WACC will rise
3) Calculate the WACC for each range of finance.
Solutions
1) a. Breaking point (BP) common equity = Br. 900,000 = Br. 1,800,000
50%
b. Breaking point (BP) long-term debt = Br. 1,200,000 = Br. 3,000,000
40%
The breaking points computed above can be interpreted as:
Shala can meet its equity needs using retained earnings until its total finance
need is Br. 1,800,000. But when total capital required is more than Br.
1,800,000, its equity needs should be met with common stock. Similarly, until
the firm’s total finance need reaches Br. 3,000,000, shala can raise any debt at
7.3% cost. Any further finance need beyond Br. 3,000,000 will cause the cost
of debt to rise to 9.1%.
2) There are three ranges of finance that could be identified on the basis of the
breaking points:
1st Range: Br. 0 to Br. 1,800,000,
2nd Range: Br. 1,800,000 to Br. 3,000,000, and
3rd Range: Br. 3,000,000 and above
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3) WACC (1st range) = 0.40 (7.3%) + 0.10 (12.06%) + 0.50 (14%)
= 2.92% + 1.21% + 7.00%
= 11.13%
WACC (2nd range) = 0.40 (7.3%) + 0.10 (12.06%) + 0.50 (15%)
= 2.92% + 1.21% + 7.50%
= 11.63%
WACC (3rd range) = 0.40 (9.1%) + 0.10 (12.06%) + 0.50 (15%)
= 3.64% + 1.21% + 7.50%
= 12.35%
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