Unformatted text preview: firm’s cash flows at a specified rate.
This rate—often called the discount rate, required return, cost of capital, or
opportunity cost—is the minimum return that must be earned on a project to
leave the firm’s market value unchanged. In this chapter, we take this rate as a
“given.” In Chapter 11 we will explore how it is calculated.
The net present value (NPV) is found by subtracting a project’s initial investment (CF0) from the present value of its cash inflows (CFt) discounted at a rate
equal to the firm’s cost of capital (k).
NPV Present value of cash inflows
1 Initial investment
CF0 (9.1) n (CFt PVIFk,t) CF0 (9.1a) t1 When NPV is used, both inflows and outflows are measured in terms of present
dollars. Because we are dealing only with investments that have conventional
cash flow patterns, the initial investment is automatically stated in terms of
today’s dollars. If it were not, the present value of a project would be found by
subtracting the present value of outflows from the present value of inflows. The Decision Criteria
When NPV is used to make accept–reject decisions, the decision criteria are as
• If the NPV is greater than $0, accept the project.
• If the NPV is less than $0, reject the project.
If the NPV is greater than $0, the firm will earn a return greater than its cost of
capital. Such action should enhance the market value of the firm and therefore
the wealth of its owners.
EXAMPLE We can illustrate the net present value (NPV) approach by using Bennett
Company data presented in Table 9.1. If the firm has a 10% cost of capital, the net
present values for projects A (an annuity) and B (a mixed stream) can be calculated
as shown on the time lines in Figure 9.2. These calculations result in net present 402 PART 3 Long-Term Investment Decisions FIGURE 9.2 Calculation of NPVs for Bennett Company’s Capital Expenditure Alternatives
Time lines depicting the cash flows and NPV calculations for projects A and B Project A
$42,000 End of Year
1 2 3 4 5 $14,000 $14,000 $14,000 $14,000 $14,000 k = 10% 53,071
NPVA = $11,071 Project B
7,513 $55,924 6,830
6,209 End of Year
k = 10% 2 3 4 5 $12,000 $10,000 $10,000 $10,000 k = 10%
k = 10%
k = 10%
k = 10% NPVB = $10,924 values for projects A and B of $11,071 and $10,924, respectively. Both projects
are acceptable, because the net present value of each is greater than $0. If the projects were being ranked, however, project A would be considered superior to B,
because it has a higher net present value than that of B ($11,071 versus $10,924). Project A
CF0 14000 CF1 5 N
I 10 NPV
11071.01 Calculator Use The preprogrammed NPV function in a financial calculator can
be used to simplify the NPV calculation. The keystrokes for project A—the annuity—typically are as shown at left. Note that because project A is an annuity, only
its first cash inflow, CF1 14000, is input, followed by its frequency, N 5.
The keystrokes for project B—the mixed stream—are as shown on...
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