SEATTLEUNIVERSITY

PROF. KEN SHAHFINC 340Spring 2007

Homework 3

Due: May 15th

Notes: As usual, show timelines with cash flows, and your work. Staple pages.

Questions 3, and 4 should be done in Excel spreadsheet. Attach printouts showing cash flows, NPV etc. Make sure that the printouts are properly formatted and legible to get full credit.

Total Points: 40

Answers:

1.

Proj X / Proj Y
NPV
IRR
PI
Payback
Disc. Payback
Cross over rate

2.

Proj X / Proj Y
IRR
NPV @ 10%
NPV @ 15.6%
NPV @ 20%
NPV @ 33%

3. The Gap

NPV / IRR / PI
Project
Accept/Reject because

4. Replacement machine

NPV / IRR
Project
Accept/Reject because

5. Obsolete Technologies

Replace in Year ______

Because: (short reason)

Make sure you attach all your work!!!

  1. Each of the two mutually exclusive projects X and Y involves an investment of $130,000 at time 0. The estimated cash flows are as follows:

Year / X / Y
1 / $70,000 / $10,000
2 / 40,000 / 25,000
3 / 35,000 / 35,000
4 / 15,000 / 50,000
5 / 10,000 / 90,000

The required rate of return is 10 percent. i) Calculate the NPV, IRR, PI, payback and discounted payback for both projects. Which project should be taken and why? Discuss why each of the rule is superior or inferior.ii) Find the cross over rate of the two projects in problem

  1. The estimated cash flows for two mutually exclusive projects are as follows:

Year / X / Y
0 / -$20,000 / -$20,000
1 / 12,000 / 3,600
2 / 10,000 / 3,600
3 / 8,000 / 3,600
4 / 0 / 3,600
5 / 0 / 3,600
etc. to infinity / 0 / 3,600 continue indefinitely
  1. Calculate the IRR for both projects.
  2. Calculate the NPV for both projects when the discount rate is i) 10% ii) 15.6% iii) 20% iv) 33%. At each discount rate, which project should be taken and why?
  1. The Gap is considering buying cash register software from Microsoft so that it can more effectively deal with its retail sales. The software package costs $750,000 and will be depreciated down to zero using the straight-line method over its five-year economic life. The marketing department predicts that sales will be $600,000 per year for the next three years, after which the market will cease to exist. Cost of goods sold and operating expenses are predicted to be 25% of sales. After three years the software can be sold for $40,000. The Gap also needs to add net working capital of $25,000 immediately. The additional NWC will be recovered in full at the end of the project life. The corporate tax rate for the Gap is 35% and the require rate of return is 17%. What is the i) NPV, ii) IRR, iii) PI of the project. Should the project be accepted according to each of the rules?
  2. A firm is considering an investment of $28 million (purchase price) in new equipment to replace old equipment with a book value of $12 million and a market value of $20 million. If the firm replaces the old equipment with the new equipment, it expects to save $17.5 million in operating costs the first year. The amount of these savings will grow at the rate of 12% per year for each of the following three years. The old equipment has a remaining life of four years. It is being depreciated by the straight-line method. The new equipment depreciation schedule is 33.3% in the first year, 39.9% in the second year, 14.8% in the third year, and 12% in the fourth and final year. The salvage value of both the old equipment and the new equipment at the end of four years is 0. In addition, replacement of the old equipment with the new equipment requires an immediately increase in net working capital of $5million, which will not be recovered until the end of the four-year replacement. Assume that the purchase and sale of equipment occurs today and all other cash flows occur at the end of their respective years. If the firm’s cost of capital is 14%, and tax rate is 40%, find:
    i) The net investment
    ii) The after-tax incremental cash flows at the end of each year
    iii) The internal rate of return IRR on the investment

iv) The NPV of the investment

  1. This is somewhat novel question about investment timing. Obsolete Technologies knows that it could enhance efficiency by installing a new computer system. The efficiency gains would easily justify the expense of the system. But the firm sees that the price of computers is continually falling and therefore decides to postpone the purchase, arguing that the NPV of the system will be even higher if it waits until the following year. Unfortunately, it has been making this argument since 1976, and it steadily losing business to competitors with more efficient systems.

The cost of the computer is expected to decline from current (t = 0) cost of $50,000 to $45,000, $40,000, $36,000, $33,000, and $31,000 over the next 5 years. Regardless of when the computer is bought, the present value of expected savings from the computer is $70,000 in the year the computer is bought. The cost of capital is 10%. In which year should Obsolete Tech. buy the computer?

(Hint: Think of investing in new computer in each of the six years (0 to 5) individually as separate, mutually exclusive projects, each associated with a certain amount of NPV. The question then becomes, would you rather be richer by $X today or $Y tomorrow? Again, you must compare alternative cash flows at the same point in time. This is a question of timing of investment!)

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