Cost of Capital

 Concept of the Cost of Capital

 Computing a Firm’s Cost of Capital
 Cost of Individual Sources of Capital
 Optimal Capital Structure
 Marginal Cost of Capital
 Combining the MCC and IOS
Concept of the Cost of Capital
 When a firm invests money in a project, it should earn at least
as much as it cost the firm to acquire the funds. Therefore, the
cost of capital may be defined as the minimum acceptable rate
of return.
 The term “cost of capital” has also been referred to as the
firm’s required rate of return, the hurdle rate, and the
opportunity cost.
Computing a Firm’s Cost of Capital
 Weighted Cost of Capital:
 For a given amount of investment capital to be
raised, the cost of capital is a weighted average of
the after-tax costs of the individual sources of
financing.
 Example: Assume a firm wishes to raise Rs.10
million using 40% debt, 10% preferred stock, and 50%
common equity financing, the firm’s cost of capital is
worked out as:
Source of Financing After-Tax Cost Weight
Debt 8% .4
Preferred Stock 10% .1
Common Equity 14% .5
Weighted Average Cost of Capital:
.4(8%) + .1(10%) + .5(14%) = 11.2%
 Computing a Firm’s Cost of Capital
(Continued)

 Questions to be Addressed:
 1. What are the costs of the
individual sources of
capital?
 2. What set of weights (i.e., the
capital structure) is
appropriate?
 3. What is the relationship between
the cost of capital and the amount of
investment capital to be raised?
 Cost of Individual Sources of Capital
 Cost of Debt (kd)
 The cost of debt is the cost associated with raising one more dollar by issuing
debt. Suppose you borrow one dollar and promise to repay it in one year, plus
pay $0.10 to compensate the lender for the use of her money

k d  Y(1  T)
where : k d  after - tax cost of debt
Y  before - tax cost of debt
(i.e., interest rate on new debt,
or yield to maturity on a bond)
T = marginal tax rate

Note: Flotation costs on new debt (if any) have been ignored since the majority of debt is privately
placed and has no flotation cost. If, however, bonds are publicly placed and involve flotation costs,
an adjustment could be made to the before-tax cost of debt.
 Cost of common equity

 Two kinds of Common Equity

 Retained Earnings (internal common equity)

 Issuing new shares of common stock

 Cost of Internal Common Equity

 Management should retain earnings only if they earn as much as stockholder’s next best
investment opportunity.
 Cost of Internal Equity = opportunity cost of common stockholders’ funds.
 Cost of internal equity must equal common stockholders’ required rate of return.

 Methods to determine cost of equity are:

 Dividend Growth Model

 Cost of Individual Sources (Continued)
 Cost of Preferred Stock (kp)

 For preference shares, the dividend rate can be considered as its

cost, since it is this amount which the company wants to pay
against the preference shares.
 Like debentures, the issue expenses or the discount/premium on
issue/redemption are also to be taken into account.

The cost of preference shares:

(Kp) = DP / NP

 Where, DP = Preference dividend per share

 NP = Net proceeds from the issue of preference shares.

 Cost of Common Equity

 Cost of Common Equity:

The rate of return required by the firm’s common stockholders. An opportunity cost
concept (i.e., what rate of return could the stockholders earn if they invested the
funds in other alternatives of comparable risk.)

 Cost of Retained Earnings (ke):

 Generally, the companies do not distribute the entire profits by way of divided among their
shareholders. A part of such profits is retained for further expansion and development. It may
lead to growth in both cash flow earnings and in dividends.
 Retained earnings, like equity funds, have no accounting cost but do have an opportunity cost.
 The opportunity cost of retained earnings is the dividend foregone by the shareholders. In other
words, if the company retains cash flow, the equity shareholder foregoes the return he could
have obtained if these funds were paid out. He receives higher dividends in future.
 Those projects which expected that extra future dividends at least cover these foregone
opportunities should be financed by retained earnings.
 As such, the cost of equity reflects the return which shareholders would receive if cash flows
were paid out by way of dividends.
 Cost of equity (continued)

 Cost of New Common Stock (ke):

(Using the constant growth in dividends model)

Ke = D1/(Po) + g

 Where,

 g=growth rate that represents the capital gain yield

 D1= D0(1+g)
 Po= Current market price of share

This method is suitable for those entities where growth rate in dividend is relatively stable. But
this method ignores the capital appreciation in the value of shares. A company which
declares a higher amount of dividend out of given quantum of earnings will be placed at a
premium as compared to a company which earns the same amount of profits but utilizes a
major part of it in financing its expansion program
Earnings/Price Ratio Method:

This method takes into consideration the earnings per share (EPS) and the market price of share.
This method recognizes both dividend and retained earnings unlike the dividend approach which
just focused on dividend for computation of cost of equity capital.
Thus, the cost of equity share capital will be based upon the expected rate of earnings of a
company. The argument is that each investor expects a certain amount of earnings whether
distributed or not, from the company in whose shares he invests.
If the earnings are not distributed as dividends, it is kept in the retained earnings and it causes
future growth in the earnings of the company as well as the increase in market price of the share.

Thus, using the Earnings growth model the cost of equity share capital will be:

Ke = E / P (1 – f) + g

where E = Current earnings per share

P = current Market price per share, net of any brokerage.

Note: If it were not for flotation costs (f), the cost of newly issued common stock would be equal to the cost of retained earnings.
(They are both sources of common equity).
 Using the Capital Asset Pricing Model
(CAPM) to Estimate the Cost of Common
Equity
 Ke = Rf + β (RM – RF)

Where,

Ke = Cost of equity
Rf =Expected Return on risk free security
Rm= Expected Return from the market
Β= coefficient of systematic risk
Limitation of dividend and earning price method is that they do not consider the risk
directly. The market price of the share that is considered in the earlier models reflect
risk associated with a particular share. A less risky share will command a higher share
price and hence a lower cost of equity capital. The expected return of a security is
directly proportional to the degree of risk.

According to the CAPM approach, the return on security is determined by the degree
of risk to which the security is exposed. It shows that the expected return on a security
is equal to the risk-free return plus a risk premium, which is based on the beta of that
security.

A security is exposed to two types of risk:

c) Unsystematic Risk
d) Systematic Risk

Unsystematic Risk is an industry or firm-specific threat in each kind of investment. It is

also known as “Specific Risk”, “Diversifiable risk” or “Residual Risk”. These are risks
which are existing but are unplanned and can occur at any point in causing widespread
disruption. For e.g., if the staff of the airline industry goes on an indefinite strike, then
this will cause risk to the shares of the airline industry and fall in the prices of the stock
impacting this industry.
Systematic Risk does not have a specific definition but is inherent risk existing in the stock market.
These risks are applicable to all the sectors but can’t be controlled. If there is an announcement or
event which impacts the entire stock market, a consistent reaction will flow in which is a systematic
risk. For e.g. if Government Bonds is offering a yield of 5% in comparison to the stock market which
offers a minimum return of 10%. Suddenly, the government announces an additional tax burden of
1% on stock market transactions, this will be a systematic risk impacting all the stocks and may
make the Government bonds more attractive.

Following are a few events that are source of systematic risk:-

• Any major central bank action: reducing or raising policy rate, open market operations, etc.
• Bankruptcy of any institution critical to smooth functioning of financial market and economy.
• Wars, earth quakes, tsunamis, etc.
• Major fiscal policy changes such as new tax legislation, reduction or increase in tax rates and
incidence.
• Major trade war or currency war.
• Inflation or hyperinflation

Total Risk (σ) = Systematic Risk (β) + Unsystematic Risk

Total risk is measured using the standard deviation while systematic risk is estimated by
calculating beta coefficient.
Market Risk
Market risk is caused by the herd mentality of investors, i.e. the tendency of investors to
follow the direction of the market. Hence, market risk is the tendency of security prices to
move together. If the market is declining, then even the share prices of good performing
companies fall. Market risk constitutes almost two-thirds of total systematic risk.
Therefore, sometimes the systematic risk is also referred to as market risk. Market price
changes are the most prominent source of risk in securities.

Interest Rate Risk

Interest rate risk arises due to changes in market interest rates. In the stock market, this
primarily affects fixed income securities because bond prices are inversely related to the
market interest rate. In fact, interest rate risks include two opposite components: Price
Risk and Reinvestment Risk. Both of these risks work in opposite directions. Price risk is
associated with changes in the price of a security due to changes in interest rate.
Reinvestment risk is associated with reinvesting interest/ dividend income. If price risk is
negative (i.e., fall in price), reinvestment risk would be positive (i.e. increase in earnings on
reinvested money). Interest rate changes are the main source of risk for fixed income
securities such as bonds and debentures.
Purchasing Power Risk (or Inflation Risk)

Purchasing power risk arises due to inflation. Inflation is the persistent and sustained
increase in the general price level. Inflation erodes the purchasing power of money, i.e., the
same amount of money can buy fewer goods and services due to an increase in prices.
Therefore, if an investor’s income does not increase in times of rising inflation, then the
investor is actually getting lower income in real terms. Fixed income securities are subject to
a high level of purchasing power risk because income from such securities is fixed in nominal
terms. It is often said that equity shares are good hedges against inflation and hence subject
to lower purchasing power risk.

Exchange Rate Risk

In a globalized economy, most of the companies have exposure to foreign currency. Exchange
rate risk is the uncertainty associated with changes in the value of foreign currencies.
Therefore, this type of risk affects only the securities of companies with foreign exchange
transactions or exposures such as export companies, MNCs, or companies that use imported
raw material or products.
 Beta Coefficient
(Measure of Market Risk)
 The extent to which the returns on a given asset move
with the overall market

Change in the Asset's Returns

β
Change in the M arket's Returns

Higher betas mean greater risk. For example, a beta of 2.0 indicates that an asset’s
return should increase 2% for every 1% increase in the market. Conversely, the
asset’s return should decrease 2% for every 1% decrease in the market.
The Beta of a stock or portfolio measures the volatility of the instrument compared to the overall market
volatility. It is used as a proxy for the systematic risk of the stock, and it can be used to measure how risky
a stock is relative to the market risk. When used as a proxy to measure systematic risk, the β value of a
portfolio can have the following interpretation.

• When β = 0 it suggests the portfolio/stock is uncorrelated with the market return.

• When β < 0 it suggests the portfolio/stock has an inverse correlation with the market return.
• When 0 < β < 1 it suggests the portfolio/stock return is positively correlated with the market return
however with smaller volatility.
• When β = 1 it suggests that the portfolio return has a perfect correlation with the market portfolio
return.
• When β > 1 it suggests that the portfolio has a positive correlation with the market, but would have
price movements of greater magnitude
 The CAPM

ke
18
16
14
12
10
8
6
4
Rf 2 The Market
0
0 0.5 1 1.5 2

b
 Optimal Capital Structure

 What is the appropriate combination of debt and equity? If a

firm were 100% equity financed (debt ratio = 0), financial
risk would be zero (only business risk would exist), and the
weighted average cost of capital (ka) would be equal to the
cost of equity (ke). Initially, the use of debt may reduce (ka)
as a lower cost of debt is combined with a higher cost of
equity. Beyond some point, however, as added financial risk
drives up both the cost of debt and the cost of equity, (k a)
will increase.
 Problem: At what level of financial leverage will (ka) be
minimized?
Cost of Capital
30

25 ke

20

15 ka

10 kd

0
0 0.2 0.4 0.6 0.8

Debt/Asset Ratio
 Marginal Cost of Capital (MCC)
 MCC is the cost of obtaining an additional dollar of new capital. If, during
a given period of time, a firm tries to raise more and more capital, a
higher cost of capital may result. Whenever any of the costs of the
individual sources increase, the weighted average cost of capital (ka)
must be recalculated to reflect the cost of obtaining additional capital
(MCC).
 Marginal Cost of Capital (MCC)
(Continued)

 To develop a MCC schedule, all break points

must be determined, and at each point ka
must be recalculated.
 A break point is a level of financing at
which ka increases because one of the
individual costs increased.
 In the example that follows only retained
earnings break points will be illustrated. In
practice, however, changes in the costs of
all components (e.g., debt, preferred stock)
must be taken into account.
MCC Schedule
A ddition to Retained Earnings
Break P oint 
W eight of Common Equity
MCC
15 Break Point

10

5 ka 2
ka 1
0
0 10 20 30

Amount of New Capital

($ millions)
Combining the MCC and Investment
Opportunities Schedule (IOS)

 A firm should continue to invest

funds as long as the rates of return
received on the investments exceed
the firm’s cost of acquiring the
investment capital. In the following
graph the firm should accept
projects A and B, and reject project
C. The point of intersection
determines the firm’s optimal capital
budget, and the firm’s cost of capital
for its average risk projects.
 MCC and IOS Schedules

Percent
20 A
18 B
16
14
12 MCC
10
8
C
6
4 IOS
2
0
0 10 20 30

Amount of New Capital ($ millions)