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Chapter5: Net Present Value and Other Investment Rules

Questions and Problems

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BASIC
(Questions 1–8)

  1. Calculating Payback Period and NPV Fuji Software, Inc., has the following mutually exclusive projects.

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    1. Suppose Fuji's payback period cutoff is two years. Which of these two projects should be chosen?

    2. Suppose Fuji uses the NPV rule to rank these two projects. Which project should be chosen if the appropriate discount rate is 15 percent?

  2. Calculating Payback An investment project provides cash inflows of $970 per year for eight years. What is the project payback period if the initial cost is $4,100? What if the initial cost is $6,200? What if it is $8,000?

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  1. Calculating Discounted Payback An investment project has annual cash inflows of $6,000, $6,500, $7,000, and $8,000, and a discount rate of 14 percent. What is the discounted payback period for these cash flows if the initial cost is $8,000? What if the initial cost is $13,000? What if it is $18,000?

  2. Calculating Discounted Payback An investment project costs $10,000 and has annual cash flows of $2,600 for six years. What is the discounted payback period if the discount rate is 0 percent? What if the discount rate is 10 percent? If it is 15 percent?

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  1. Calculating IRR Teddy Bear Planet, Inc., has a project with the following cash flows:

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    The company evaluates all projects by applying the IRR rule. If the appropriate interest rate is 8 percent, should the company accept the project?

  2. Calculating IRR Compute the internal rate of return for the cash flows of the following two projects:

    p. 163

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  3. Calculating Profitability Index Bill plans to open a self-serve grooming center in a storefront. The grooming equipment will cost $190,000, to be paid immediately. Bill expects aftertax cash inflows of $65,000 annually for seven years, after which he plans to scrap the equipment and retire to the beaches of Nevis. The first cash inflow occurs at the end of the first year. Assume the required return is 15 percent. What is the project's PI? Should it be accepted?

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  1. Calculating Profitability Index Suppose the following two independent investment opportunities are available to Greenplain, Inc. The appropriate discount rate is 10 percent.

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    1. Compute the profitability index for each of the two projects.

    2. Which project(s) should Greenplain accept based on the profitability index rule?

INTERMEDIATE
(Questions 9–20)

  1. Cash Flow Intuition A project has an initial cost of I, has a required return of R, and pays C annually for N years.

    1. Find C in terms of I and N such that the project has a payback period just equal to its life.

    2. Find C in terms of I, N, and R such that this is a profitable project according to the NPV decision rule.

    3. Find C in terms of I, N, and R such that the project has a benefit–cost ratio of 2.

  2. Problems with IRR Suppose you are offered $8,000 today but must make the following payments:

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    1. What is the IRR of this offer?

    2. If the appropriate discount rate is 10 percent, should you accept this offer?

    3. If the appropriate discount rate is 20 percent, should you accept this offer?

      p. 164

    4. What is the NPV of the offer if the appropriate discount rate is 10 percent? 20 percent?

    5. Are the decisions under the NPV rule in part (d) consistent with those of the IRR rule?

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  1. NPV versus IRR Consider the following cash flows on two mutually exclusive projects for the Bahamas Recreation Corporation (BRC). Both projects require an annual return of 14 percent.

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    As a financial analyst for BRC, you are asked the following questions:

    1. If your decision rule is to accept the project with the greater IRR, which project should you choose?

    2. Because you are fully aware of the IRR rule's scale problem, you calculate the incremental IRR for the cash flows. Based on your computation, which project should you choose?

    3. To be prudent, you compute the NPV for both projects. Which project should you choose? Is it consistent with the incremental IRR rule?

  2. Problems with Profitability Index The Robb Computer Corporation is trying to choose between the following two mutually exclusive design projects:

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    1. If the required return is 10 percent and Robb Computer applies the profitability index decision rule, which project should the firm accept?

    2. If the company applies the NPV decision rule, which project should it take?

    3. Explain why your answers in (a) and (b) are different.

  3. Problems with IRR Cutler Petroleum, Inc., is trying to evaluate a generation project with the following cash flows:

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    1. If the company requires a 10 percent return on its investments, should it accept this project? Why?

    2. Compute the IRR for this project. How many IRRs are there? If you apply the IRR decision rule, should you accept the project or not? What's going on here?

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p. 165

  1. Comparing Investment Criteria Mario Brothers, a game manufacturer, has a new idea for an adventure game. It can market the game either as a traditional board game or as an interactive CD-ROM, but not both. Consider the following cash flows of the two mutually exclusive projects for Mario Brothers. Assume the discount rate for Mario Brothers is 10 percent.

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    1. Based on the payback period rule, which project should be chosen?

    2. Based on the NPV, which project should be chosen?

    3. Based on the IRR, which project should be chosen?

    4. Based on the incremental IRR, which project should be chosen?

  2. Profitability Index versus NPV Hanmi Group, a consumer electronics conglomerate, is reviewing its annual budget in wireless technology. It is considering investments in three different technologies to develop wireless communication devices. Consider the following cash flows of the three independent projects for Hanmi. Assume the discount rate for Hanmi is 10 percent. Further, Hanmi Group has only $15 million to invest in new projects this year.

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    1. Based on the profitability index decision rule, rank these investments.

    2. Based on the NPV, rank these investments.

    3. Based on your findings in (a) and (b), what would you recommend to the CEO of Hanmi Group and why?

  3. Comparing Investment Criteria Consider the following cash flows of two mutually exclusive projects for AZ-Motorcars. Assume the discount rate for AZ-Motorcars is 10 percent.

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    1. Based on the payback period, which project should be accepted?

    2. Based on the NPV, which project should be accepted?

      p. 166

    3. Based on the IRR, which project should be accepted?

    4. Based on this analysis, is incremental IRR analysis necessary? If yes, please conduct the analysis.

  4. Comparing Investment Criteria The treasurer of Amaro Canned Fruits, Inc., has projected the cash flows of projects A, B, and C as follows.

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    Suppose the relevant discount rate is 12 percent a year.

    1. Compute the profitability index for each of the three projects.

    2. Compute the NPV for each of the three projects.

    3. Suppose these three projects are independent. Which project(s) should Amaro accept based on the profitability index rule?

    4. Suppose these three projects are mutually exclusive. Which project(s) should Amaro accept based on the profitability index rule?

    5. Suppose Amaro's budget for these projects is $600,000. The projects are not divisible. Which project(s) should Amaro accept?

  5. Comparing Investment Criteria Consider the following cash flows of two mutually exclusive projects for Tokyo Rubber Company. Assume the discount rate for Tokyo Rubber Company is 10 percent.

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    1. Based on the payback period, which project should be taken?

    2. Based on the NPV, which project should be taken?

    3. Based on the IRR, which project should be taken?

    4. Based on this analysis, is incremental IRR analysis necessary? If yes, please conduct the analysis.

  6. Comparing Investment Criteria Consider two mutually exclusive new product launch projects that Nagano Golf is considering. Assume the discount rate for Nagano Golf is 15 percent.

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    Please fill in the following table:

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  7. Comparing Investment Criteria You are a senior manager at Poeing Aircraft and have been authorized to spend up to $400,000 for projects. The three projects you are considering have the following characteristics:

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    Assume the corporate discount rate is 10 percent.

    Please offer your recommendations, backed by your analysis:

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CHALLENGE
(Questions 21–28)

  1. Payback and NPV An investment under consideration has a payback of six years and a cost of $574,000. If the required return is 12 percent, what is the worst-case NPV? The best-case NPV? Explain. Assume the cash flows are conventional.

    p. 168

  2. Multiple IRRs This problem is useful for testing the ability of financial calculators and computer software. Consider the following cash flows. How many different IRRs are there? (Hint: Search between 20 percent and 70 percent.) When should we take this project?

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  3. NPV Valuation The Yurdone Corporation wants to set up a private cemetery business. According to the CFO, Barry M. Deep, business is “looking up.” As a result, the cemetery project will provide a net cash inflow of $115,000 for the firm during the first year, and the cash flows are projected to grow at a rate of 6 percent per year forever. The project requires an initial investment of $1,400,000.

    1. If Yurdone requires a 13 percent return on such undertakings, should the cemetery business be started?

    2. The company is somewhat unsure about the assumption of a 6 percent growth rate in its cash flows. At what constant growth rate would the company just break even if it still required a 13 percent return on investment?

  4. Calculating IRR The Utah Mining Corporation is set to open a gold mine near Provo, Utah. According to the treasurer, Monty Goldstein, “This is a golden opportunity.” The mine will cost $900,000 to open and will have an economic life of 11 years. It will generate a cash inflow of $175,000 at the end of the first year, and the cash inflows are projected to grow at 8 percent per year for the next 10 years. After 11 years, the mine will be abandoned. Abandonment costs will be $125,000 at the end of year 11.

    1. What is the IRR for the gold mine?

    2. The Utah Mining Corporation requires a 10 percent return on such undertakings. Should the mine be opened?

  5. NPV and IRR Anderson International Limited is evaluating a project in Erewhon. The project will create the following cash flows:

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    All cash flows will occur in Erewhon and are expressed in dollars. In an attempt to improve its economy, the Erewhonian government has declared that all cash flows created by a foreign company are “blocked” and must be reinvested with the government for one year. The reinvestment rate for these funds is 4 percent. If Anderson uses an 11 percent required return on this project, what are the NPV and IRR of the project? Is the IRR you calculated the MIRR of the project? Why or why not?

    p. 169

  6. Calculating IRR Consider two streams of cash flows, A and B. Stream A's first cash flow is $8,900 and is received three years from today. Future cash flows in stream A grow by 4 percent in perpetuity. Stream B's first cash flow is −$10,000, is received two years from today, and will continue in perpetuity. Assume that the appropriate discount rate is 12 percent.

    1. What is the present value of each stream?

    2. Suppose that the two streams are combined into one project, called C. What is the IRR of project C?

    3. What is the correct IRR rule for project C?

  7. Calculating Incremental Cash Flows Darin Clay, the CFO of MakeMoney.com, has to decide between the following two projects:

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    The expected rate of return for either of the two projects is 12 percent. What is the range of initial investment (Io)for which Project Billion is more financially attractive than Project Million?

  8. Problems with IRR McKeekin Corp. has a project with the following cash flows:

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    What is the IRR of the project? What is happening here?

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