Npv For Varying Costs Of Capital Dane Cosmetics Is Evaluating A New Fragrance-mixing Machine. The Machine Requires An Initial Investment Of 24 000 And Will Generate After-tax Cash Inflows Of 5 000 Per Year For 8 Years. For Each Of The Costs Of Capital

Focus on Value

After estimating the relevant cash flows, the financial manager must apply appropriate decision techniques to assess whether the project creates value. Net present value (NPV) and internal rate of return (IRR) are the generally preferred capital budgeting techniques. Both use the cost of capital as the required return. The appeal of NPV and IRR stems from the fact that both indicate whether a proposed investment creates or destroys shareholder value.

NPV clearly indicates the expected dollar amount of wealth creation from a proposed project, whereas IRR provides the same accept-or-reject decision as NPV. As a consequence of some fundamental differences, NPV and IRR do not necessarily rank projects in the same way. NPV is the theoretically preferred approach. In practice, however, .ERR is preferred because of its intuitive appeal. Regardless, the application of NPV and IRR to good estimates of relevant cash flows should enable the financial manager to recommend projects that are consistent with the firm's goal of maximizing stock price.

Review of Learning Goals

Key formulas and decision criteria for this chapter are summarized in Table 9.8 on page 442.

ffgl Understand the role of capital budgeting techniques in the capital bud-geting process. Capital budgeting techniques are the tools used to assess project acceptability and ranking. Applied to each project's relevant cash flows, they indicate which capital expenditures are consistent with the firm's goal of maximizing owners' wealth.

Calculate, interpret, and evaluate the payback period. The payback period fzj is the amount of time required for the firm to recover its initial investment, as calculated from cash inflows. Shorter payback periods are preferred. The payback period is relatively easy to calculate, has simple intuitive appeal, considers cash flows, and measures risk exposure. Its weaknesses include lack of linkage to the wealth maximization goal, failure to consider time value explicitly, and the fact that it ignores cash flows that occur after the payback period.

§ Calculate, interpret, and evaluate the net present value {NPV}. Because it gives explicit consideration to the time value of money, NPV is considered a sophisticated capital budgeting technique. NPV measures the amount of value created by a given project; only positive NPV projects are acceptable. The rate at which cash flows are discounted in calculating NPV is called the discount rate, required return, cost of capital, or opportunity cost. By whatever name, this rate represents the minimum return that must be earned on a project to leave the firm's market value unchanged.

KT&uXBI Summary of Key Formulas/Definitions and Decision Criteria for Capital Budgeting Techniques


Formula/ definition

Decision criteria

Payback period"

For annuity:

Annual cash inflow

Initial investment

Accept if < maximum acceptable payback period.

Refect if > maximum acceptable payback period.

For mixed stream: Calculate cumulative cash inflows on year-to-year basis until the initial investment is recovered.

Net present value (NPV)fc Present value of cash inflows - Initial investment.

Internal rate of return (IRR)6 The discount rate that causes NPV- $0

Accept if>the cost of capital. Rejcct if < the cost of capital.

{present value of cash inflows equals the initial investment).

"Unsophisticated technique, because it does not give explicit consideration to the time value of money. ^Sophisticated technique, because it gives explicit consideration to the time value of money.

Calculate, interpret, and evaluate the internal rate of return (IRR). Like : NPV, IRR is a sophisticated capital budgeting technique. IRR is the com pound annual rate of return that the firm will earn by investing in a project and receiving the given cash inflows. By accepting only those projects with IRRs in excess of the firm's cost of capital, the firm should enhance its market value and the wealth of its owners. Both NPV and IRR yield the same accept-reject decisions, but they often provide conflicting rankings.

Use net present value profiles to compare NPV and ERR techniques.

A net present value profile is a graph that depicts projects' NPVs for var ious discount rates. The NPV profile is prepared by developing a number of "discount rate-net present value" coordinates (including discount rates of 0 percent, the cost of capital, and the IRR for each project) and then plotting them on the same set of discount rate-NPV axes.

Discuss NPV and IRR in terms of conflicting rankings and the theoretical and practical strengths of each approach. Conflicting rankings of projects frequently emerge from NPV and IRR as a result of differences in the magnitude and timing of cash flows. The underlying cause is the differing implicit assumptions with regard to the reinvestment of intermediate cash inflows. NPV assumes reinvestment of intermediate cash inflows at the more conservative cost of capital; IRR assumes reinvestment at the project's IRR. On a purely theoretical basis, NPV is preferred over IRR because NPV assumes the more conservative reinvestment rate and does not exhibit the mathematical problem of multiple IRRs that often occurs when IRRs are calculated for nonconventional cash flows. In practice, the IRR is more commonly used because it is consistent with the-general preference of businesspeople for rates of return, and corporate financial analysts can identify and resolve problems with the IRR before decision makers use it.

Self-Test Problem (Solution in Appendix B)

§|Te| jjf|| ST9-1 All techniques with NPV profile—Mutually exclusive projects Fitch Industries is in

IJj '4J the process of choosing the better of two equal-risk, mutually exclusive capital

. expenditure projects—M and N. The relevant cash flows for each project are shown

|p| J|pj in the following table. The firm's cost of capital is 14%.

Initial investment (CF0) $23,500 $27,000

$10,000 10,000 10,000 10,000

a. Calculate each project's payback period.

b. Calculate the net present value (NPV) for each project.

c. Calculate the internal rate of return (IRR) for each project.

d. Summarize the preferences dictated by each measure you calculated, and indicate which project you would recommend. Explain why.

e. Draw the net present value profiles for these projects on the same set of axes, and explain the circumstances under which a conflict in rankings might exist.

Warm-Up Exercises A blue box (ffl) indicates exercises available in

E9-I Elysian Fields, Inc., uses a maximum payback period of 6 years, and currently must choose between two mutually exclusive projects. Project Hydrogen requires an initial outlay of $25,000; project Helium requires an initial ouday of $35,000. Using the expected cash inflows given for each project in the following table, calculate each project's payback period. Which project meets Elysian's standards?

Herky Foods is considering acquisition of a new wrap- ¡'v'Ye^'^ ping machine. The initial investment is estimated at uiij.i'^ji^i^ii^^^^iUi $1.25 million, and the machine will have a 5-year life 1 $400,000

with no salvage value. Using a 6% discount rate, deter- 2 375,000

mine the net present value (NPV) of the machine given 3 300,000

its expected operating cash inflows shown in the table at 4 350,000

the right. Based on the project's NPV, should Herky 5 200,000

make this investment?

E9-3 Axis Corp. is considering investment in the best of two mutually exclusive projects. Project Kelvin involves an overhaul of the existing system; it will cost $45,000 and generate cash inflows of $20,000 per year for the next 3 years. Project Thompson involves replacement of the existing system; it will cost $275,000 and generate cash inflows of $60,000 per year for 6 years. Using an 8% cost of capital, calculate each project's NPV and make a recommendation based on your findings.

Billabong Tech uses the internal rate of return (IKK) to select projects. Calculate the IRR for each of the following projects and recommend the best project based on this measure. Project T-Shirt requires an initial investment of $15,000 and generates cash inflows of $8,000 per year for 4 years. Project Board Shorts requires an initial investment of $25,000 and produces cash inflows of $12,000 per year for 5 years.

E9-5 Cooper Electronics uses NPV profiles to visually evaluate competing projects. Key data for the two projects under consideration is given in the following table. Using these data, graph, on the same set of axes, the NPV profiles for each project using discount rates of 0%, 8%, and the IRR.

Initial investment 530,000 $25,000

2 10,000 9,000

3 12,000 9,000

4 10,000 8,000

Problems A blue box (ffi) indicates problems available in EaWflnancelabl

Payback period Jordan Enterprises is considering a capital expenditure that requires an initial investment of $42,000 and returns after-tax cash inflows of $7,000 per year for 10 years. The firm has a maximum acceptable payback period of 8 years.

a. Determine the payback period for this project.

b. Should the company accept the project? Why or why not?

littfMI NPV for varying costs of capital Dane Cosmetics is evaluating a new fragrance-mixing machine. The machine requires an initial investment of $24,000 and will generate after-tax cash inflows of $5,000 per year for 8 years. For each of the costs of capital listed, (1) calculate the net present value (NPV), (2) indicate whether to accept or reject the machine, and (3) explain your decision.

a. The cost of capital is 10%.

b. The cost of capital is 12%.

c. The cost of capital is 14%.

Klfflrll Net present value—Independent projects Using a 14% cost of capital, calculate the net present value for each of the independent projects shown in the following table, and indicate whether each is acceptable.

Initial investment (CF0) $26,000 $500,000 $170,000 $950,000 $80,000 I '.v.1 Year .(i) '■', V{^S-^ ^/f;:r-1 ■/■ I V-r.'iLL'■"¿Djiiows;:■ !7:\';'v'v^i' •

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