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IRR/NPV

If the opportunity cost of capital is 11 percent, which of these projects is worth pursuing?

2. Mutually Exclusive Investments. Suppose that you can choose only one of these projects. Which would you choose? The discount rate is still 11 percent.

3. IRR/NPV. Which project would you choose if the opportunity cost of capital were 16 percent?

4. IRR. What are the internal rates of return on projects A and B?

5. Investment Criteria. In light of your answers to problems 2 4, is there any reason to believe that the project with the higher IRR is the better project?

6. Profitability Index. If the opportunity cost of capital is 11 percent, what is the profitability index for each project? Does the profitability index rank the projects correctly?

7. Payback. What is the payback period of each project?

8. Investment Criteria. Considering your answers to problems 2, 3, and 7, is there any reason to believe that the project with the lower payback period is the better project?

9. Book Rate of Return. Accountants have set up the following depreciation schedules for the two projects:

Year: 1 2 3 4

Project A $25 $25 $25 $25

Project B 33.33 33.33 33.34

Calculate book rates of return for each year. Are these book returns the same as the IRR?

10. NPV and IRR. A project that costs $3,000 to install will provide annual cash flows of $800 for each of the next 6 years. Is this project worth pursuing if the discount rate is 10 percent? How high can the discount rate be before you would reject the project?

11. Payback. A project that costs $2,500 to install will provide annual cash flows of $600 for the next 6 years. The firm accepts projects with payback periods of less than 5 years. Will the project be accepted? Should this project be pursued if the discount rate is 2 percent? What if the discount rate is 12 percent? Will the firm s decision change as the discount ratechanges?

12. Profitability Index. What is the profitability index of a project that costs $10,000 and provides cash flows of $3,000 in Years 1 and 2 and $5,000 in Years 3 and 4? The discount rate is 10 percent.

13. NPV. A proposed nuclear power plant will cost $2.2 billion to build and then will produce cash flows of $300 million a year for 15 years. After that period (in Year 15), it must be decommissioned at a cost of $900 million. What is project NPV if the discount rate is 6 percent?

What if it is 16 percent?

18. NPV/IRR. A new computer system will require an initial outlay of $20,000 but it will increase the firm s cash flows by $4,000 a year for each of the next 8 years. Is the system worth installing if the required rate of return is 9 percent? What if it is 14 percent? How high can the discount rate be before you would reject the project?

19. Investment Criteria. If you insulate your office for $1,000, you will save $100 a year in heating expenses. These savings will last forever.

a. What is the NPV of the investment when the cost of capital is 8 percent? 10 percent?

b. What is the IRR of the investment?

c. What is the payback period on this investment?

20. NPV versus IRR. Here are the cash flows for two mutually exclusive projects:

25. Book Rate of Return. A machine costs $8,000 and is expected to produce profit before depreciation of $2,500 in each of Years 1 and 2 and $3,500 in each of Years 3 and 4. Assuming that the machine is depreciated at a constant rate of $2,000 a year and that there are no taxes, what is the average return on book?

26. Book Rate of Return. A project requires an initial investment of $10,000, and over its 5- year life it will generate annual cash revenues of $5,000 and cash expenses of $2,000. The firm will use straight-line depreciation, but it does not pay taxes.

a. Find the book rates of return on the project for each year.

b. Is the project worth pursuing if the opportunity cost of capital is 8 percent?

c. What would happen to the book rates of return if half the initial $10,000 outlay were treated as an expense instead of a capital investment? Hint: Instead of depreciating all of the $10,000, treat $5,000 as an expense in the first year.

d. Does NPV change as a result of the different accounting treatment proposed in (c)?