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Because the last three cash inflows for project B are the same (CF3 CF4 CF5
10000), after inputting the first of these cash inflows, CF3, we merely input its
frequency, N 3.
The calculated NPVs for projects A and B of $11,071 and $10,924, respectively, agree with the NPVs cited above.
Spreadsheet Use The NPVs can be calculated as shown on the following Excel
spreadsheet. CHAPTER 9 Capital Budgeting Techniques 403 Project B
Input
45000 Function
CF0 28000 CF1 12000 CF2 10000 CF3 3 N 10 I
NPV Solution
10924.40 Review Questions
9–4
9–5 LG4 How is the net present value (NPV) calculated for a project with a conventional cash flow pattern?
What are the acceptance criteria for NPV? How are they related to the
firm’s market value? 9.4 Internal Rate of Return (IRR) internal rate of return (IRR)
A sophisticated capital
budgeting technique; the
discount rate that equates the
NPV of an investment opportunity
with $0 (because the present
value of cash inflows equals the
initial investment); it is the
compound annual rate of return
that the firm will earn if it invests
in the project and receives the
given cash inflows. The internal rate of return (IRR) is probably the most widely used sophisticated
capital budgeting technique. However, it is considerably more difficult than NPV
to calculate by hand. The internal rate of return (IRR) is the discount rate that
equates the NPV of an investment opportunity with $0 (because the present value
of cash inflows equals the initial investment). It is the compound annual rate of
return that the firm will earn if it invests in the project and receives the given cash
inflows. Mathematically, the IRR is the value of k in Equation 9.1 that causes
NPV to equal $0.
n $0
t1 (1 CFt
IRR)t CF0 (9.2) (1 CFt
IRR)t CF0 (9.2a) n
t1 The Decision Criteria
When IRR is used to make accept–reject decisions, the decision criteria are as
follows:
• If the IRR is greater than the cost of capital, accept the project.
• If the IRR is less than the cost of capital, reject the project. 404 PART 3 Long-Term Investment Decisions These criteria guarantee that the firm earns at least its required return. Such an
outcome should enhance the market value of the firm and therefore the wealth of
its owners. Calculating the IRR
WW
W FIGURE 9.3 The actual calculation by hand of the IRR from Equation 9.2a is no easy chore.
It involves a complex trial-and-error technique that is described and demonstrated on this text’s Web site: www.aw.com/gitman. Fortunately, many financial calculators have a preprogrammed IRR function that can be used to simplify the IRR calculation. With these calculators, you merely punch in all cash
flows just as if to calculate NPV and then depress IRR to find the internal rate
of return. Computer software, including spreadsheets, is also available for simplifying these calculations. All NPV and IRR values presented in this and subsequent chapters are obtained by using these functions on a popular financial
calculator. Calculation of IRRs for Bennett Company’s Capital Expenditure Alternatives
T...

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