LISTING OF EQUATIONS 8.1 NPV = PV - required investment 8.2 Profitability index = net present value initial investment 8.3 Equivalent annual annuity = present value of costs annuity factor QUESTIONS AND PROBLEMS connect Problems 1-9 refer to two projects with the following cash flows: Year Project A Project B -$200 -$200 80 100 80 100 80 100 80 1. IRR/NPV. If the opportunity cost of capital is 11%, which of these projects is worth pursuing? (LO8-1) 2. Mutually Exclusive Investments. Suppose that you can choose only one of these projects. Which would you choose? The discount rate is still 11%. (LO8-/) 3. IRR/NPV. Which project would you choose if the opportunity cost of capital is 16%? (LO8-/) 4. IRR. What are the internal rates of return on projects A and B? (LO8-2) 5. Investment Criteria. In light of your answers to Problems 2, 3, and 4, is the project with the higher IRR the better project? (LO8-2)Part Two Value o. Profitability Index. If the opportunity cost of capital is 11%. what is the profitability index each project? (108-3) . Profitability Index. Is the project with the highest profitability index also the one with highest NPV? (LO8-3) 8. Payback. What is the payback period of each project? (108-4) 9. Investment Criteria. Is the project with the shortest payback period also the one with the high est NPV? (LO8-4) 10. NPV and IRR. A project that costs $3,000 to install will provide annual cash flows of $80of each of the next 6 years. (LOS-] and LO8-2) a. What is NPV if the discount rate is 10%? b. How high can the discount rate be before you would reject the project? I1. 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 decommis sioned at a cost of $900 million. (LOS-1 and LO8-2) a. What is project NPV if the discount rate is 5%? b. What if the discount rate is 18%? 12. 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. (LO8-1) a. Is the system worth installing if the required rate of return is 9%? b. What if the required return is 14%? C. How high can the discount rate be before you would reject the project? 13. NPV/IRR. Here are the cash flows for a project under consideration: (LOS-1 and LO8-2) Co C, C2 -$6,750 +$4,500 +$18,000 a. Calculate the project's net present value for discount rates of 0, 50%, and 100%. b. What is the IRR of the project? 14. NPV versus IRR. Here are the cash flows for two mutually exclusive projects: (LOS-] and LO8-2) Project Co C1 C2 Ca A -$20,000 +$8,000 +$8,000 CO +$ 8,000 -20,000 0 0 +25,000 a. At what interest rates would you prefer project A to B? (Hint: Try drawing the NPV profile of each project.) b. What is the IRR of each project? 15. NPV/IRR. Growth Enterprises believes its latest project, which will cost $80,000 to install, will generate a perpetual growing stream of cash flows. Cash flow at the end of the first year will be $5,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5%. (LO8-1 and LO8-2) a. If the discount rate for this project is 10%, what is the project NPV? b. What is the project IRR? 16. IRR/NPV. Consider the following project with an internal rate of return of 13.1%. (LO8-2) Year Cash Flow O N - +$100 -60 -60 a. Should you accept or reject the project if the discount rate is 12%? b. What is project NPV? 17. Multiple IRRs. Strip Mining Inc. can develop a new mine at an initial cost of $5 million. Th mine will provide a cash flow of $30 million in 1 year. The land then must be reclaimed at a co of $28 million in the second year. (LO8-2)Chapter 8 Net Present Value and Other Investment Criteria 265 a. What are the IRRs of this project? b. Should the firm develop the mine if the discount rate is 10%? c. What if it is 20%? d. What if it is 350%? e. What if it is 400%? 18. IRR. Marielle Machinery Works forecasts the following cash flows on a project under consid eration. It uses the internal rate of return rule to accept or reject projects. (LO8-2) Co C1 C2 C3 -$10,000 0 +$7,500 +$8,500 a. What is the project's IRR? b. Should this project be accepted if the required return is 12%? 19. NPV/IRR. Consider projects A and B: (LO8-2) Cash Flows (dollars) Project Co C1 Cz NPV at 10% A -30,000 21,000 21,000 +$6,446 B -50,000 33,000 33,000 +7,273 a. Calculate IRRs for A and B. b. Which project does the IRR rule suggest is better? c. Which project is really better? 20. IRR. You are offered the chance to participate in a project that produces the following cash flows: Co C2 +$5,000 +$4,000 -$11,000 The internal rate of return is 13.6%. If the opportunity cost of capital is 12%, would you accept the offer? (What is the net present value of the project?) (LO8-2) 21. Multiple IRRs. Consider the following cash flows: (LO8-2) Co C 1 C2 C3 CA -$22 +$20 +$20 +$20 -$40 a. Which two of the following rates are the IRRs of this project: 2.5%, 7.2%. 14.3%, 33.7%, 40.0%? b. What is project NPV if the discount rate is 5%? c. What if it is 20%? d. What if it is 40%? 22. Profitability Index. What is the profitability index of a project that costs $10,000 and provides cash flows of $3,000 in years I and 2 and $5,000 in years 3 and 4? The discount rate is 9%. (LO8-3) 23 Profitability Index. Consider the following projects: (LO8-3) Project Co C 1 C2 A -$2,100 +$2,000 +$1,200 -2,100 +1,440 +1,728 a. Calculate the profitability index for A and B assuming a 22% opportunity cost of capital. b. According to the profitability index rule, which project(s) should you accept