Citibank: basic of corporate finance

5-30 INTRODUCTION TO CAPITAL BUDGETING

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ANSWER KEY

1. If an analyst compares the net present value of several projects, s/he will know which

project:

b) has cash flows that will exceed the initial investment by the

greatest amount.

2. An investor with a one-year bond is interested in the number of compounding periods

in the year because:

d) the more frequently the nominal interest rate is compounded, the

greater will be the effective interest rate.

3. If the internal rate of return (IRR) of a project is 35% and the hurdle rate is 42%, then:

c) the project should be rejected because it will reduce the

shareholder's value.

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PROGRESS CHECK

(Continued)

4. An investor with a payback hurdle time of three years is evaluating two potential

projects. The cash flows from Project A will equal the initial investment after two

years and nine months; the cash flows from Project B will equal the initial investment

after three years and two months.

The internal rate of return for Project A is less than the required rate of return.

Project B has a positive NPV. Ignoring other factors that may influence the decision,

what is the best choice for the investor?

_______a) Project A, because the required rate of return exceeds the IRR and the

payback will occur before the hurdle time.

_______b) Project B, because even though the payback period exceeds the hurdle

time by a few months, the project has a positive NPV.

_______c) The wise investor would reject both Project A, because of the IRR, and

Project B, because of the payback period.

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ANSWER KEY

4. An investor with a payback hurdle time of three years is evaluating two potential

projects. The cash flows from Project A will equal the initial investment after two

years and nine months; the cash flows from Project B will equal the initial

investment after three years and two months.

The internal rate of return for Project A is less than the required rate of return.

Project B has a positive NPV. Ignoring other factors that may influence the

decision, what is the best choice for the investor?

b) Project B, because even though the payback period exceeds the

hurdle time by a few months, the project has a positive NPV.

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Unit 6

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UNIT 6: CORPORATE VALUATION – RISK

INTRODUCTION

In your study of interest rates and their role in corporate finance, you focused on

securities with well-defined, predictable cash flows. In the real world of finance, there are

many securities or projects with uncertain returns. This uncertainty translates into an

exposure to risk. In this unit we will see how risk is required for individual securities and

for portfolios of securities. We will also see how to calculate the rate of return that is

required by an investor for investing in a security.

UNIT OBJECTIVES

After you successfully complete this unit, you will be able to:

• Calculate the expected rate of return for an individual security and a

portfolio of investments

• Determine the variance and standard deviation of possible returns on

investment

• Analyze and compare payoff matrices to determine best expected rate of

return or least amount of risk

• Differentiate between systematic and unsystematic risk

• Recognize the beta coefficient as a measure of volatility

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6-4 CORPORATE VALUATION – RISK

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CALCULATING EXPECTED CASH FLOWS

The dictionary defines risk as "a hazard; a peril; exposure to loss or

injury." The concept of risk is very important in the study of

corporate finance.

Investor

expectations

A company that invests in a project and an investor that buys stock in

a company expect to earn a return on their investments. However,

there are no guarantees; it is possible that the project or investment

may lose money for the company or investor. Exposure to a possible

loss occurs at the time an investment is made. To compensate for this

exposure to risk, an investor expects a higher possible return on

investment.

In Unit Two, you learned about risk and identified it as a component

of interest rates — investors require that a premium be added to the

risk-free interest rate to compensate for risk. In this section, you

will be introduced to the methods that are used to measure and

quantify risk. Many of these concepts have been derived from

statistical theory. Don't let that worry you; the concepts and

applications are usually straightforward.

Expected Return

Probability

distribution

The term "probability" refers to the chance that an event will occur.

Suppose that you flip a coin. The probability of the coin landing tails up

on one toss is 0.50, or 1/2, or 50%. (To be consistent, we will use

decimal numbers (0.50) to represent probabilities throughout this

discussion.) A probability distribution is a list of all possible

outcomes and the chance of each outcome occurring.

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CORPORATE VALUATION – RISK 6-5

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Example

A simple example will illustrate a probability distribution. Suppose that

economists predict a 30% chance for a boom economy in the coming

year, a 40% chance for a normal economy, and a 30% chance for a

recession. Figure 6.1 illustrates what the probability distribution for

the state of the economy in the next year would look like.

(1) (2)

State of

Economy Probability

Boom 0.30

Normal 0.40

Recession 0.30

Figure 6.1: Probability Distribution for the Economy

Each possible outcome for the economy is listed, along with the

chance or probability of its occurrence.

Possible rates

of return

Let's expand this example to include the financial data of a corporation.

Suppose that in a boom economy, XYZ Corporation is expected to

earn a 100% annual rate of return on investment. They think that XYZ

will earn a 15% return in a normal economy and will have a negative

70% return in a recession. The probability distribution can now be

revised to include the possible expected

rates of return for XYZ Corporation (Figure 6.2).

(1) (2) (3)

State of Possible

Economy Probability

Return

Boom 0.30 100%

Normal 0.40 15%

Recession 0.30 -70%

Figure 6.2: Possible Expected Rates of Return

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Payoff matrix

The question now becomes, what is the expected rate of return for XYZ

Corporation in the coming year? To calculate the expected rate of

return E(k), we calculate a weighted average of the possible returns that

XYZ could earn. The concept of a weighted average is that each value

has a different contribution to the total based on the probability of its

occurrence. A value with a higher probability of occurrence weighs

more in the calculation. When the data is arranged in a table, it is often

referred to as a payoff matrix (Figure 6.3).

(1) (2) (3) (4)

State of Possible Weighted Possible

Economy Probability Return Return = (2) x (3)c

Boom 0.30 100% 30%

Normal 0.40 15% 6%

Recession 0.30 -70% -21%

Expected Return E(k) = 15%

Figure 6.3: Payoff Matrix for XYZ Corporation

To calculate the weighted average of the possible returns, multiply

each possible return by its probability (Column 2 x Column 3). The

sum of all of these products equals XYZ's expected return for the

coming year. The mathematical formula to calculate the expected

return E(k) is:

n

Expected Return = E(k) = S = P

i

k

i

i = 1

Where:

E(k) = Expected rate of return

S = Sum of the series of all possible occurrences

i = 1 = Series begins at the first possible occurrence

n = Number of possible occurrences

P

i =

Probability of each return

k

i

= Each possible return

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The expected return is the sum of these products. Using the formula,

XYZ's expected annual return is:

E (k) = 0.30 x (100%) + 0.40 x (15%) + 0.30 x (-70%)

E (k) = 30% + 6% + -21%

E (k) = 15%

Expected Cash Flows

Although we used stock returns to illustrate the concept of expected

return, we just as easily could have calculated an expected cash flow.

Projects A

and B payoff

matrix

Suppose, for example, that analysts want to forecast the expected

cash flow for a given project. (Let's call it Project A.) They try to

anticipate future conditions and their effect on the cash flow. The

analysts decide that there are five possible cash flow payoffs for the

project and estimate the probability of each cash flow occurring.

Their analysis of the project's expected cash flow is summarized in a

payoff matrix (Figure 6.4).

(1) (2) (3) (4)

Estimate

Number Probability

Possible

Cash

Flow

Weighted

Cash Flow

(2) x (3)

1

2

3

4

5

0.15

0.40

0.15

$31,000

32,000

33,000

34,000

35,000

E(CF) =

$4,650

4,800

13,200

5,100

5,250

$33,000

Figure 6.4: Project A — Payoff Matrix

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Citibank: basic of corporate finance

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