C O N T E N T
INTRODUCTION ………………………………………………………………………. 2
PART ONE – REQUIRED RETURN ON IN VESTMENT
INTRODUCTION ……………………………………………………………………….. 2
a. SYSTEMATIC AND UNSYSTEMATIC RISK……………………………………. 3
b. CAPITAL ASSET PRICING MODEL – BETA ………….………………………… 5
c. INFORMATION THAT BETA GIVE TO A FINANCIAL MANAGER ……………….. 7
SUMMARY………………………………………………………………………………. 9
PART TWO – CAPITAL INVESTMENT DECISION
INTRODUCTION ………………………………………………………………………… 10
a. TIME VALUE OF MONEY…………………………………………………………. 10
b. CHOOSING AN APPROPRIATE DISCOUNT RATE……………………………… 11
c. NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR)……. 13
d. COMPARE AND CONTRAST OF NPV AND IRR ………………………………… 14
SUMMARY ……………………………………………………………………………… 16
CONCLUSION …………………………………………………………………………… 17
REFERENCES ……………………………………………………………………………. 17
I N T R O D U C T I O N
A major objective of companies is to help create and improve shareholder value through
better risk-based decision making and capital allocation. Integration of the key functions
of managing risk, capital and value is essential in order to deliver shareholder value, as these
three elements are inextricably linked. The level of risk exposure determines capital needs;
however, capital utilization has a cost and reduces value creation; also the nature of the risk
determines the “price of risk”, which is a key driver of value creation. (Peter Needleman,
2004) Creating Value for investors means delivering consistently high returns on their
capital. This generally requires both strong revenue growth and attractive profit margins.
This paper looks at concepts of required return on investment and capital investment
decision. Part one of this paper discuss risk and the capital assets pricing model (CAPM)
and part two examines the time value of money and understands the investment appraisal
technique such as net present value (NPV) and internal rate of return (IRR).
PART ONE – REQUIRED RETURN ON INVESTMENT
INTRODUCTION
Capital is scarce and investors will seek out investment opportunities that will allow them to
optimize the return versus risk. Risk is often defined as the unexpected variability or
volatility of returns, and thus includes both potential worse than expected as well as better
than expected returns. The capital asset pricing model (CAPM) is in finance to determine
a theoretically appropriate required rate of return of an asset or portfolio. The CAPM
formula takes into account the asset’s sensitivity to systematic risk, as well as the expected
return of the market and the expected return of a theoretical risk-free asset. This part of
paper distinguishes systematic and unsystematic risk; examine beta of the CAPM and its
limitation, as well as discussing the information that beta give to a financial manager.
SYSTEMATIC AND UNSYSTEMATIC RISK (SECTION A)
The investors require two types of return on their investments. First is the expected return
which is to compensate the price of time. It reflected in the going market interest rate on
low- or no-risk securities. Second is the unexpected or risky return which is to compensate
the price of risk or risk premium of the particular activity which they have invested. Risk
in finance is the chance that an investment’s actual return will be different from expected.
The risk of a portfolio comprises systematic risk and unsystematic risk.
Systematic risk or relevant risk is risk that influences a large number of assets, each to a
greater or lesser degree. It is inherent in the market or system, this is also called market
risk. Systematic risk related to macroeconomic factors or market-wide events likes
recession, high inflation, change of interest rates and wars. This type of events affects
entire market and cannot be avoided through diversification. It is also called
undiversifiable risk. Systematic risk can be mitigated only by being hedged. It measures
by beta, the stock’s correlation to an overall market. For example, the Standard & Poor’s
500 Index is the proxy for the market.
Unsystematic risk is risk that influences a single company or a small group of companies.
It is also called unique or specific risk. It is related to events that affect a very specific
group of securities or an individual security. Examples include strikes, plant accidents,
takeovers, and CEO’s resignation of a single firm. Unsystematic risk could be essentially
eliminated by diversification, so a portfolio with many assets has almost no unsystematic
risk. For instance, by holding a large portfolio of stocks, the random unsystematic ups and
downs of one stock will be tempered by offsetting unsystematic downs and ups of other
stocks because of their positive or negative companies-specific events. Unsystematic risk
is also called diversifiable risk.
C
Total Risk (U)
Diversifiable
Unsystematic
or specific risk ε
D
Systematic or
Market Risk m Undiversifiable
Risk of
Portfolio
(standard
deviation
of return)
A
0
Number of securities in portfolio
B
Total Risk (U) comprises
systematic risk (m) and
unsystematic risk (ε) and are
measured on standard deviation:
R = Rf + U
Becomes
R = Rf + m +ε
Where
R is required rate of return
Rf is the risk free return (return on
time)
As number of securities increases,
the total risk declines along CD
until it reaches an effective
minimum AB, it is called
diversification. The remaining
risk is market risk which cannot
be diversifiable.
Figure 1: Systematic and Unsystematic Risk
Source: Master of Business Admin Text Book, 2608/9 Finance and Growth Strategies (6.13)
The behavior of systematic and unsystematic risk is shown in Figure 1. The Systematic
risk is often regarded as the only relevant risk. The systematic risk principle states that
the reward for bearing risk depends only on the systematic risk of an investment. Since
investors can avoid bearing unsystematic risk by simply holding a diversified portfolio.
Market Risk cannot be removed (except by diversifying into the security markets of other
countries). So, no matter how much total risk an asset has, only the systematic portion is
relevant in determining the expected return (and the risk premium) on that asset.
CAPITAL ASSET PRICING MODEL – BETA (SECTION B)
The capital assets pricing model
1 (CAPM) is a model that describes the relationship
between risk and expected return and that is used in the pricing of risky securities. The
CAPM says that the expected return of a security or a portfolio equals the rate on risk-free
security plus a risk premium.
Ke = R
f +βj (ERm - Rf)
* Ke is the required rate of return
* R
f is the risk-free return
* β
j is the security beta
* ER
m is the expected return on the overall market
* β
j (ERm - Rf) is the risk premium
The Beta coefficient is a key parameter in the CAPM and a risk metric employed primarily
in the equity markets. Beta is a measure of systematic risk of a security that cannot be
avoided through diversification. It is the covariance of a security or portfolio in relation to
the rest of the security market. The market has a beta of 1.0, any stock or portfolio with
betas larger than 1.0 have more systematic risk than average, and vice versa. The formula
for beta is:-
cov (Zp, Zm)
σ
2m
Where cov (Zp, Zm) is the covariance between the portfolio (or asset) return and the
market return, andσ
2m is the variance of the market’s return (volatility squared).
The Beta is also used to calculate cost of equity. The cost of capital represents the discount
rate used to arrive at the present value of company’s future cash flows. The higher a
company’s beta, the lower its present value, therefore Beta can impact a company’s share
valuation.
In determining Betas, it needs to plot for the return of the asset and the index for a period
of time and fit a straight line to the plot. The slop of the fitted line from the linear
least-squares calculation is Beta. Beta value of all UK shares could be obtained from the
Risk Management Service provided by The London Business School. Meanwhile, many
summary financial websites list beta as one of the company’s key statistics, for example
MSN Money’s website.
Return on
Stock j
x x
x Beta
x x x
x x
Return on the
x market portfolio (Rm)
x
The fitted regression line is:
Rj = σ+ βRm
Whereσis the intercept with the vertical axis,
βis the slope of the line of best fit,
Rj is the Rate of return on Stock j, and
Rm is the Rate of return on the market portfolio.
In determining Betas:-
(1) it needs a list for the asset and returns for the index, these returns can be daily, weekly or any period.
(2) make a graph with the index’s fluctuations on the X-axis and the stock’s fluctuations on the Y-axis.
Repeat this procedure for the entire range of dates.
(3) Finally, fit a straight line to the plot in order to check that there are no serious violations of the linear
regression model assumption. The slop of the fitted line from the linear least-squares calculation is Beta.
Figure 2: In determining Betas by regression analysis
Source: Master of Business Admin Text Book, 2608/9 Finance and Growth Strategies (6.13)
There are limitations of beta. First, Beta is using historical data, it does not incorporate
new information. For example, American Electric Power (AEP) has been considered as a
defensive stock with a low beta. However when it entered the merchant energy business and
assumed high debts levels, AEP’s historic beta no longer captured the substantial risks the
company took on. Second, Beta is not reliable for new stocks, as they have insufficient
price history to establish a reliable beta. Third, the past price movements are very poor
predicators of the future. Beta are merely rear-view mirrors, reflecting very little of what
lies ahead. Fourth, it is unreliable for investors with long-term horizons as the beta
measure on a single stock tends to flip around over time, which makes it unreliable. Fifth,
Beta indicates that it is the only reason that the return differ, it ignores the noises of the
market. Finally, Beta, as a proxy for risk, does not help the investors to distinguish
between upside and downside price movements of the stock.
INFORMATION THAT BETA GIVE TO A FINANCIAL MANAGER (SECTION C)
Financial Managers are required to utilize cash to achieve maximum benefits for the owners
of the company. They need to decide what assets to invest, how to pay for it and how
much dividend they should pay to shareholders. It is essential that they know the required
rate of return or cost of equity for valuing the company as it stands and for assessing the
value of new operations or investments which should enhance the value of the corporation.
According to CAPM, the relationship between Beta and required return is plotted on the
Security Market Line (SML) which shows expected return as a function of Beta.
Rate of
Return
(%) SML
20
15 M
ERm = 12.5
10
5———– Risk Free Rate
of Return =5%
0 1 2 3 Beta
Let’s assume the risk free rate is 5%, the overall
market will produce a rate of return of 12.5% next
year. Lucky Company has a beta of 1.7.
The rate of return for Lucky Company will be:
Ke = R
f +βj (ERm - Rf)
= 5% + 1.7 (12.5% – 5%)
= 17.75%
On the horizontal axis are the betas of all
companies in the market and the vertical axis are
the required rates of return, as a percentage.
Figure 3: The calculation of required rate of return by Security Market Line (SML).
Beta is a measure of a stock’s volatility in relation to the market. From the SML on Figure
3, the return on the market portfolio “M” has a Beta of 1.0. Lucky Company with a Beta
of 1.7, indicates that, on average, security return are 1.7 times as volatile as market return,
both up and down. This would considered an aggressive security because when the overall
market return rises or falls 10 percent, Lucky Company, on average, would rise or fall 17
percent. Stocks having a beta of less than 1.0 would be considered more conservative
investments than the overall markets. High-beta stocks are supposed to be riskier but
provide a potential for higher returns, low-betas stocks pose less risk but also lower returns.
Lucky Company has Beta of 1.7, is to be riskier but has a return of 17.75% which is higher
than the market return of 12.5%.
Beta is useful for comparing the relative systematic risk of different stocks and, in practice,
is used by Financial Manager to judge a stock’s riskiness. Because the variance of the
market is a constant across all securities for a particular period, ranking stocks by beta is the
same as ranking them by their absolute systematic risk. Stocks with high betas are said to
be high-risk securities. From the comparison of beta for some US stocks, American Online
with higher beta is riskier than Exxon because the systematic risk of online industry is
higher than oil production industry. Financial Manager could construct a portfolio with
zero market (or systematic) risk by choosing an appropriate combination of securities.
Company Beta
β
Exxon 0.65
AT&T 0.90
IBM 0.95
Wal-Mart 1.l0
General Motors 1.15
Hardley Davidson 1.65
American Online 2.40
Figure 4: Beta Coefficients for some US companies (
Source: Value Line Investment Survey)
Beta is also used to calculate cost of equity and identified mispriced assets/shares. Once
the expected return is calculated using CAPM, the future cash flows of the assets can be
discounted to their present value using this rate to establish the correct pricing for the assets.
A higher beta will be discounted at a higher rate and lower betas will be discounted at a
lower rate. In theory, an asset is correctly priced when its observed price is same as its
value calculated using the CAPM derived discounted rate. If the observed price is higher
than the valuation, then the asset is overvalued (undervalued if vice verse).
SUMMARY
The risk of a portfolio comprises systematic and unsystematic risk. Systematic risk refers
to the risk common to all securities – i.e. market risk. Unsystematic risk is the risk
associated with the individual assets. Unsystematic risk can be diversified away whereas
systematic risk cannot. Thus, systematic risk is often regarded as the only relevant risk.
Beta is a key component for the capital asset pricing model (CAPM), which is used to
measure of a stock’s volatility in relation to the market and to calculate cost of equity. The
stock market is assigned a beta of 1.0. Any stock or portfolio with a beta higher/lower than
1 is more/less volatile than the market. Beta has plenty of shortcomings as it is based on
historically data. Beta give information to a Financial Manager such as measuring a
security’s volatility, or fluctuations in price, relative to a benchmark, the market portfolio of
all stocks, the cost of capital and identifying mispriced shares.
PART TWO – CAPITAL INVESTMENT DECISIONS
INTRODUCTION
Globalization has brought about changes in the way that competing for resources like capital,
land and intellectual capital (labour). With these resources becoming more mobile,
stakeholders are exerting pressure on management to create value. A successful financial
decision is one that it is worth more than they cost to implement and thus create value. In
order to compare the value various projects might create, part two of the paper will discuss
the time value of money and the importance of “discount” future cash flows; examines
factors for choosing an appropriate discount rate; understand the terms “net present value”
(NPV) and “internal rate of return” (IRR) and their comparison and contrast.
TIME VALUE OF MONEY (SECTION A)
The basic idea of time value of money is that a dollar today is worth more than a dollar
tomorrow. Money has different values depending on when it is received. For example,
,000 received today is worth more than ,000 receivable in one year’s time, because it
could be re-invested and generated some sort of interest during the year, i.e. converted into a
higher sum. It is also related to the concept of opportunities cost – the cost of any decision
includes the cost of the best forgone opportunity. If taking the money over time, it would
lose the interest on investment or any other use for the money such as spending it on
something that would be enjoy more. Furthermore, people know how much the money
worth if it is received today, whereas people have only a guess of how much it will be worth,
due to inflation. Finally, there is uncertainty or risk associated with the cash flow in the
future reduces the value of the cash flow today. For example, the ,000 may not even be
there a year later so people might as well take it when it can be got.
There are 2 key terms for time value of money:- (1) Present Value is exactly that the amount
of money that it is at the present time and (2) Future Value is the amount of money that it
will have at a given point in the future. The process by which future cash flows are
adjusted to reflect the above factors is called discounting, and the magnitude of these factors
is reflected in the discount rate. The Present Value formula is listed below:
FV
PV = —————–
(1+r)
n
PV = the value of a dollar at time = 0
FV = the value of a dollar at time = n in the future
r = the interest rate that would be compounded for each period of time
n = the period of time that want to equate
It is important to “discount” future cash flows because cash flows at different points in
time cannot be compared and aggregated. All cash flows have to be brought to the same
point in time before comparisons and aggregations can be made. Furthermore, if present
values are estimated correctly, there is indifferent between the future cash flow and the
present value of that cash flow. In fact, the discount rate can be viewed as a composite of
the expected real return, the expected inflation and the uncertainty associated with the cash
flow.
CHOOSING AN APPROPRIATE DISCOUNT RATE (SECTION B)
The discounted value of cash flow is determined by reducing its value by the appropriate
discount rate for each unit of time between the time when the cashflow is to be valued to the
time of the cash flow. Most often the discount rate is expressed as an annual rate. When
choosing an appropriate discount rate, the length of time until the cash is due, the amount of
risk that the cash will not be tendered when due and the rate of return available from
comparably risk investments need to be taken into account. The discount rate is the
opportunity cost plus risk factor (or the time value of money). It is made up of an interest
rate and an equity yield rate. Discount rates are the safe rate earned from a completely
riskless investment (this rate may reflect anticipated loss of purchasing power due to
inflation) and compensation for risk, lack of liquidity, and investment management expenses.
The discount rate has several components: – the inflation rate; the risk-free component;
general risk premium and specific risk premium.
Discount Rate Components Description Measured by
INFLATION RATE The annual rate of price change for a basket
of consumer goods.
Consumer Price Index
THE RISK-FREE
COMPONENT
A return to compensate the investor for a
loss of liquidity
Risk-free rate minus
inflation rate
GENERAL RISK
PREMIUM
A return to compensate the investor for
assuming diversified company-wide risk
The weighted average cost
of capital (WACC) minus
the risk-free rate
SPECIFIC RISK PREMIUM A return to compensate the investor for
assuming the unique risk
The discount rate minus the
WACC.
Figure 5: Discount Rate Components
When estimating the discount rate, it is good to apply the concepts of the weighted average
cost of capital (WACC). The WACC is a function of the mix between debt and equity and
the cost of that debt and equity. It is essentially a blend of the cost of equity and the
after-tax cost of debt. For calculating cost of equity, Capital Asset Pricing Model (CAPM)
is an accepted method: where cost of equity (Re) = Rf + Beta (Rm-Rf). The rate applied to
determine the cost of debt should be the current market rate the company is paying on its
debt. As Companies benefit from the tax deductions available on interest paid, the net cost
of the debt is actually the interest paid less the tax savings resulting from the tax-deductible
interest payment. From the following example, the discount rate for ABC company would
be 8.26% (see Figure 6).
Cost of Debt Example of ABC Company: Cost of Equity
Capital structure: 60% debt and
40% of equity
Tax rate (T) = 30%
Risk Free Rate (Rf) = 5%
Beta (β) = 1.3
Risk Premium (RP) = 8%
Debt Ratio (RF x (1 – T)
= 0.6 (0.05 x (1-0.3)
= 0.6 (0.035)
= 0.021
= 2.1%
Equity Ratio (Rf +β(RP)
= 0.4 (0.05 + 1.3 (0.08))
= 0.4 (0.154)
= 0.0616
=6.16%
WACC = 2.1% + 6.16% = 8.26%
Figure 6: Calculation of WACC for ABC Company
NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR)
(SECTION C)
The Net Present Value (NPV) is the discounted or present value of a project or investment
after meeting the finance charge, including return of initial capital. The cash flows are
discounted or adjusted by incorporating the uncertainty and time value of money. The
discount rate for NPV should reflect inflation and opportunity costs. However, it is no
need to deduct interest payments and depreciation from the cash flows. The NPV formula
is:-
n
NVP =
Σ
t=1
CF
t
(1+r)
t
- I
0
Where CF
t denotes each cash flow in each year t;
r is the required rate of return; and
Io is the initial investment expenditure.
If the NPV results in a positive amount, the project should be undertaken. If it is negative,
it should be rejected. When calculating NPV, the discount table (Present Value Interest
Factor –“PVIF”) could be used as a short cut. It shows the discount factors for any
combination of discount rate and number of year. There are three special cases in using the
NPV:- (1) Annuities; (2) Perpetuities and (3) Growing Perpetuity.
Subject Description Its Present Value is
Annuities It is an investment with a constant
annual cash flow.
Using the annuity tales (Present Value Interest
Factors for Annuities)
Perpetuity It is an investment with a constant
cash flow and which goes on
forever.
CF x 1/r where
CF = annual cash flow
r = discount rate
Growing Perpetuity This is where the perpetuity grows
at a constant rate.
NCF x (1/(r-g)) where
NCF = Next cash flow
r = discount rate
g = grow rate
Figure 7: Different between Annuities, Perpetuity and Growing Perpetuity
The internal rate of return (IRR) is the most often used alternative of NPV for evaluating
investments without estimating the discount rate. IRR defined as the discount rate which
NPV is equal zero, and it is usually interpreted as the expected return generated by the
investment. IRR calculates the break-even discount rate, the rate at which the value of
cash outflows equals to the value of cash inflows. In general, if the IRR is greater than the
project’s cost of capital or hurdle rate, the project will add value for the company.
The IRR equation:
n
NVP = 0 =
Σ
t=1
CF
t
(1+r)
t
+ I
0
Where CF
t denotes each cash flow in each year t;
r is the required rate of return; and
Io is the initial investment
IRR can be easily for comparing the rate of the cost of capital against the IRR of projects or
investment. If the IRR is higher, then the project can be approved. However, it can be
easily misinterpreted and confused with the actual project rate of return. When dealing
with negative net benefits, the IRR concept can generate multiple IRR values for the same
project, making it difficult to compare which IRR is the true value.
COMPARE AND CONTARST NPV AND IRR (SECTION D)
Net Present Value (NPV) and Internal Rate of Return (IRR) are capital budgeting methods
for financial evaluation of long-term projects and are complementary measures of
Discounted Cash Flow (DCF). The major difference is that NPV is expressed in monetary
units and the IRR is the true interest yield expected from an investment expressed as a
percentage. NPV measure project value more directly than IRR because NPV actually
calculates the project value. If there is more than one project lined up, the manager can
simply add the values together to get a total. IRR is very good for screening project, NPV
is highly sensitive to the discount rate, while IRR bypasses the problem of deciding it. As
IRR is a rate or ratio, it is more useful for comparing unlike investments (e.g. bonds and
stocks) and for making comparisons between different sized firms and different period.
It seems that most investors would argue that NPV is the most accurate measure of (1)
telling whether the project is a good investment and (2) telling which investments are better
than others. IRR may lead to incorrect decisions in comparisons of mutual exclusive
investments or if there are unconventional cash flows. For example, during the life of a
project, cash flows must be reinvested to cover depreciation. This will give a negative
cash flow for that period, thus leading to more than one IRR and an unreliable result.
Moreover, IRR cannot be calculated when the payback period is too short to complete a
single process or when process profit is negative or zero. There is no mathematical
approach to finding IRR. The only way to find an IRR is by trial and error.
It is argue that using both measures gives better results than using either alone. The IRR
graph can be plotted to understand the dynamics of the discount rates considering the cash
flows. From the example below, it shows the discount rate below the IRR which
investment results in a positive NPV and above which an investment results in a negative
NPV. The higher the discount rate the more the cash flows will be reduced, results to the
lower NPV of the project. The company should approve any project or investment where
the IRR is higher than the cost of capital as the NPV is greater than zero. Otherwise, the
company can restructure the negative NPV project to lower the project risk to a level that
will yield a positive NPV.
NPV
($’000)
1,500
1,300
1,100
900
700
500
300
100
IRR = 17.25%
-100
-300
-500
0% 5% 10% 15% 20% 25% 30% 35% 40%
Discount Rate (r)
Calculating the IRR is
done through a
trial-and-error that looks
for the discount rate that
yield an NPV equal to
zero.
The Discount Rate below
the IRR results positive
NPV and above the IRR
results negative NPV.
Figure 8: The relationship between NPV and IRR
SUMMARY
Discounting reflects one of the most fundamental concepts in finance, the time value of
money. Money now has a greater value than money in future because the price level which
would undermine future purchasing power by inflation; foregone the opportunity cost and
increase the uncertainty or risk associate with the cash flow. It is important to discount
future cash flows for comparison. The discount rate is usually chosen to be equal to the
cost of capital. Some adjustment may be made to the discount rate to take account of risks
associated with uncertain cashflows, with other developments. The NPV and IRR are
investment decision tools that include time value of money which discount the cash flow.
They are complementary ways of looking at a problem or opportunity. The IRR model is a
good first approximation as to the value of a project but it is better to combine it with more
comprehensive financial evaluation tools, such as NPV.
C O N C L U S I O N
Company needs a metric that appropriately reflects the three elements of risk, capital and
value in a single performance measure. Without an integrated approach, conflicting
objective are likely to hinder effective decision making. The capital asset pricing model,
weight average cost of capital, return on equity, payback method, profitability index, net
present value and internal rate of return are some techniques for Manager to evaluate the
required return on investment and capital investment decision. As each method has its
advantages and limitations, it is essential for manager to use different methods as
complement.
R E F R E N C E S
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PART TWO
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Guide to Implementation
Susan Combs, Manual for Discounting Oil and Gas Income, Window on State Government
Tom Copeland, Tim Koller, Jack Murrin (1998): Valuation. J Wiley & Sons, 2
nd ed
Time Value of Money (
http://www.studyfinance.com) from University of Arizona
http://en.wikipedia.org/wiki/Internal_rate_of_return
http://www.valuebasedmanagement.net/methods_irr.html
Credit:ivythesis.typepad.com
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