COST OF CAPITAL
1. INTRODUCTION
Cost of capital provides useful guidelines in determining optimal capital structure of a firm.
It refers to the minimum rate of return of a firm which must earn on its investment so that the
market value of the company’s equity share may not fall.
Cost of capital is the rate of return the firm requires firm investment in order to increase the
value of the firm in the market place. The concept of cost is perceived in different
dimensions, A firm’s cost of capital is really the rate of return that it requires on the projects
available. A company grows by making investments that are expected to increase revenues
and profits. The company acquires the capital or funds necessary to make such investments
by borrowing or using funds from owners.
By applying this capital to investments with long - term benefits, the company is producing
value today, but how much value? The answer depends not only on the investments ’
expected future cash flows but also on the cost of the funds.
Borrowing is not costless. Neither is using owners’ funds.
The cost of this capital is an important ingredient both in investment decision making
by the company ’ s management and in the valuation of the company by investors. If a
company invests in projects that produce a return in excess of the cost of capital, the
company has created value; in contrast, if the company invests in projects whose returns are
less than the cost of capital, the company has actually destroyed value. Therefore, the
estimation of the cost of capital is a central issue in corporate financial management.
Cost of capital estimation is a challenging task. As we have already implied, the cost of
capital is not observable but rather must be estimated. Arriving at a cost of capital estimate
requires a host of assumptions and estimates. Another challenge is that the cost of capital that
is appropriately applied to a specific c investment depends on the characteristics of that
investment: The riskier the investment’s cash flows, the greater its cost of capital will be.
2. FINANCIAL GEARING
Financial gearing refers to the relative proportions of debt and equity that a company uses to
support its operations. This information can be used to evaluate the risk of failure of a
business. When there is a high proportion of debt to equity, a business is said to be highly
geared.
The formula used for financial gearing is:
(Short-term debt + Long-term debt + Capital leases)
Equity
As a simple illustration, in order to fund its expansion, XYZ Corporation cannot sell
additional shares to investors at a reasonable price; so instead, it obtains a $10,000,000 shortterm loan.
For instance, a company has $2,000,000 of equity;
so the debt-to-equity (D/E) ratio is
D/E = $10,000,000 (total liabilities)
$2,000,000 (shareholders' equity)
= 5x
Gearing is measured by a number of ratios—including:
• the D/E ratio,
• Shareholders' equity ratio,
• Debt-service coverage ratio (DSCR)
These ratios indicate the level of risk associated with a particular business. The appropriate
level of gearing for a company depends on its sector and the degree of leverage of its
corporate peers.
For example, a gearing ratio of 80% shows that a company’s debt levels are 80% of its
equity.
A gearing ratio of 80% might be very manageable for a utility company—as the business
functions as a monopoly with support from the Government.
But it may be excessive for a technology company, with intense competition in a rapidly
changing marketplace. The company would definitely be considered highly geared.
2.1. Why Choose a Capital Structure?
capital structure is a firm’s mix of debt and equity used to finance a firm’s assets.
A target capital structure is important as it determines the proportion of debt
and equity used to estimate a firm’s cost of capital.
The firm’s optimum debt/equity mix minimizes the firm’s cost of capital, which, in turn
helps, the firm to maximize shareholder wealth.
3. COST OF CAPITAL
The cost of capital is the rate of return that the suppliers of capital — bondholders and
owners — require as compensation for their contribution of capital. Another way of looking
at the cost of capital is that it is the opportunity cost of funds for the suppliers of capital: A
potential supplier of capital will not voluntarily invest in a company unless its return meets or
exceeds what the supplier could earn elsewhere in an investment of comparable risk.
A company typically has several alternatives for raising capital, including issuing equity, and
debt. Each source selected becomes a component of the company’s funding and has a cost
(required rate of return) that may be called a component cost of capital.
The cost of capital of a company is the required rate of return that investors demand for the
average - risk investment of a company. The most common way to estimate this required rate
of return is to calculate the marginal cost of each of the various sources of capital and then
calculate a weighted average of these costs.
This weighted average is referred to as the weighted average cost of capital ( WACC ).
The WACC is also referred to as the marginal cost of capital ( MCC ) because it is the cost
that a company incurs for additional capital.
The weights in this weighted average are the proportions of the various sources of capital that
the company uses to support its investment program.
Therefore, the WACC, in its most general terms, is
where
EXAMPLE - Computing the Weighted Average Cost of Capital
Assume that ABC Corporation has the following capital structure: 30 percent debt,
10 percent preferred stock, and 60 percent common stock. ABC Corporation wishes
to maintain these proportions as it raises new funds. It’s before-tax cost of debt is
8 percent, its cost of preferred stock is 10 percent, and its cost of equity is 15 percent.
If the company’s marginal tax rate is 40 percent, what is ABC’s weighted average cost
of capital?
WACC = (0.3)(0.08)(1- 0.40) + (0.1)(0.1) + (0.6)(0.15)
= 11.44%
4. COSTS OF THE DIFFERENT SOURCES OF CAPITAL
Each source of capital has a different cost because of the differences among the sources, such
as seniority, contractual commitments, and potential value as a tax shield. We focus on the
costs of three primary sources of capital: debt, preferred equity, and common equity.
4.1. Cost of Debt
The cost of debt is the cost of debt financing to a company when it issues a bond or takes
out a bank loan.
Small businesses may use short-term debt only to purchase their assets. For example, they
may use supplier credit in the form of accounts payable. They could also just use short-term
business loans, either from a bank or some alternative source of financing.
Larger businesses may use intermediate or long-term business loans or may even issue bonds
to raise money for financing.
The cost of debt is the interest that is paid on the loan obtained.
4.1.1. Taxes and cost of debt
Interest payments on loans are tax deductible. Which means they provide tax savings. Interest
expense reduces the operating profit amount on which the tax amount is paid against.
EXAMPLE: Assume that a company obtained a loan =$100, interest rate = 10% and tax rate
= 40%. What is the cost of debt?
Calculation of net income assuming
interest is tax deductible
Calculation of net income assuming
interest is NOT tax deductible
Revenue
Less: operating expenses
interest
100
50
10
Revenue
Less: operating expenses
Operating profit
100
50
50
Operating profit
Less: Tax expense (40%)
Net Income
40
16
24
Less: Tax expense (40%)
Interest expense
Net Income
20
10
20
solution
After-tax cost of debt = before-tax cost of debt(1- tax rate)
= 0.10 (1 - 0.40)
= 0.6
= 6%
4.2.
Cost of Preferred Stock
The cost of preferred stock is the cost that a company has committed to pay preferred
stockholders as a preferred dividend when it issues preferred stock. Cost of preferred stock is
not tax deductible.
we use this formula for the cost preferred stock
Where
Therefore, the cost of preferred stock is the preferred stock ’ s dividend per share divided
by the current preferred stock ’ s price per share.
EXAMPLE 1 - Calculating the Cost of Preferred Equity
Alcoa, Inc. has one class of preferred stock outstanding, a $3.75 cumulative preferred
stock, for which there are 546,024 shares outstanding.If the price of this stock is
$72, what is the estimate of Alcoa’s cost of preferred equity?
Solution
The cost of Alcoa’s preferred stock = $3.75/$72.00
= 5.21%
EXAMPLE 2 – A company issues preferred stock with a par value = 100 and preferred
dividend = 5 per share. The current share price is 125 and the marginal tax rate is 30%. What
is the cost of preferred stock?
rp = 5/125
= 4%
4.3.
Cost of Common Equity
The cost of common equity, re, usually referred to simply as the cost of equity, is the rate of
return required by a company’s common shareholders. A company may increase common
equity through the reinvestment of earnings — that is, retained earnings — or through the
issuance of new shares of stock.
Commonly used approaches for estimating the cost of equity are the Capital Asset Pricing
Model and Dividend Discount Model Approach.
4.3.1. Capital Asset Pricing Model (CAPM).
The Capital Asset Pricing Model (CAPM) is an equilibrium model that measures the
relationship between risk and expected return of an asset based on the asset’s sensitivity to
movements in the overall stock market.
Capital Asset Pricing Model Approach In the capital asset pricing model (CAPM) approach,
we use the basic relationship from the capital asset pricing model theory that the expected
return on a stock, E( Ri ), is the sum of the risk - free rate of interest, RF , and a premium for
bearing the stock’s market risk, bi (RM - RF):
where
bi = return sensitivity of stock i to changes in the market return
E(RM) = expected return on the market
E(RM) - RF = expected market risk premium
Where:
Risk-free return (RF)
A risk - free asset is defined here as an asset that has no default risk. A common proxy for
the risk - free rate is the yield on a default - free government debt instrument. In general, the
selection of the appropriate risk - free rate should be guided by the duration of projected cash
flows. If we are evaluating a project with an estimated useful life of 10 years, we may want to
use the rate on the 10 - year Treasury bond.
Market Risk Premium E(RM) - RF
Market Risk Premium is the expected return an investor receives (or expects to receive in the
future) from holding a risk-laden portfolio instead of risk-free assets. The premium rate
allows the investor to take a decision if the investment in the securities should take place and
if yes, the rate that he will earn beyond the risk-free return offered by government securities.
Beta (βi)
The Beta is a measure of the volatility of a stock with respect to the market in general. The
fluctuations that will be caused in the stock due to a change in market conditions is denoted
by Beta. For example, if the Beta of a stock is 1.2, it would cause a 120% change due to any
change in the general market. The opposite is the case for Beta less than 1. For Beta which is
equal to 1, the stock is in sync with the changes in the market.
EXAMPLE 4.1 - Using the CAPM to Estimate the Cost of Equity
Valence Industries wants to know its cost of equity. Its chief financial officer (CFO)
believes the risk-free rate is 5 percent, equity risk premium is 7 percent, and Valence’s
equity beta is 1.5. What is Valence’s cost of equity using the CAPM approach?
solution
Cost of common stock = 5% + 1.5(7%)
=15.5%
EXAMPLE 4.2
In a developing market, the risk free rate is 10% and the expected return on the
market is 16%. The equity beta for a given company is 2. What is the cost of equity?
Solution
re = 10% + 2( 16% - 10%)
=22%
4.3.2
Dividend Discount Model Approach
the dividend discount model in general states that the intrinsic value of a share of stock is the
present value of the share’s expected future dividends.
Cost of equity is the same as cost of retained earnings.
The Dividend Discount Model is also called the Gordon growth model.
the price of a stock is:
** D1 = D0 (1+g)
We can then rewrite this equation and estimate the cost of equity:
Therefore, to estimate re , we need to estimate the dividend in the next period and the
assumed constant dividend growth rate. The current stock price, P0 , is known, and the
dividend of the next period , D1 , can be predicted if the company has a stable dividend
policy.
The challenge is estimating the growth rate, g. g can be estimated by:
i.
ii.
taking an average of historical dividends previously paid out.
Using the growth rate formula: g = (retention rate)(return on equity)
= (1 – payout rate)(ROE)
EXAMPLE 1
Hisense prices shares at $40/share. It paid a dividend of $3 last year and it expects dividends
to grow at 7% each year. Calculate the cost of equity.
Solution
**D1 = D0 (1+g)
RE = D0 (1+g) + g
P0
RE =$3(1+7%) + 7%
$40
RE = 0.15025
= 15.03%
In this case, investors expect 15.03% when they give us money. So the 15.03% is a cost to
the company. So when we want to go into projects, our return should be greater than 15.03%.
because if it is not greater than 15.03%, then we are going to be paying out this cost to our
shareholders and it is going to be nothing for the business.
EXAMPLE 2
You have gathered the following information about a company and the market.
• Current share price = 30
• Most dividend paid = 2
• Expected dividend payout rate = 40%
• Expected ROE = 15%
• Equity beta = 1.5
• Expected return on market = 15%
• Risk free rate = 8%
What is the cost of equity?
RE = D0 (1+g) + g
P0
g = (1 – payout rate)(ROE)
= 0.6 * 0.15
= 0.09
RE = 2(1.09) + 0.09
30
= 0.1627
=16.27%
5. WEIGHTED AVERAGE COST OF CAPITAL
Once you have calculated the cost of capital for all the sources of debt and equity and
gathered the other information needed, you can calculate the WACC.
When a business raises money by selling shares or receiving cash from investors, it is
considered to be equity. Raising money by borrowing from a bank or issuing bonds qualifies
as debt. Each of these methods has its own cost, which can be stated in terms of an interest
rate.
WACC refers to the calculation of a firm’s cost of capital in which each category of capital is
proportionately weighted.
EXAMPLE 5.1
A company has the following information about the capital structure and before-tax
component costs for a company. The company’s marginal tax rate is 40%. What is the cost of
capital?
Capital component
Debt
Preferred stock
Common stock
solution
Book value
$100
$20
$100
Market value
$90
$20
$300
Component cost
8%
10%
14%
Total weight = 90+20+300 = 410
=90*0.08 (1- 0.4) + 20*0.1 + 300*0.14
410
410
410
=0.1178
=11.78%