# Answers to Chapter 6: Making Investment Decisions with the Net Present Value Rule

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Multiple Choice Questions

1. Preferably, cash flows for a project are estimated as:

A) Cash flows before taxes

B) Cash flows after taxes

C) Earnings before taxes

D) Earnings after taxes

2. Important points to remember while estimating cash flows of projects are:

A) only cash flow is relevant

B) always estimate cash flows on an incremental basis

C) be consistent in the treatment of inflation

D) all of the above

E) none of the above

3. Net Working Capital is the:

A) Difference between short-term assets and short term liabilities

B) Difference between long-term assets and long term liabilities

C) Difference between long-term assets and short term liabilities

D) None of the above

4. Net Working Capital should be considered in project cash flows because:

A) They are sunk costs

B) Firms must invest cash in short-term assets to produce finished goods

C) Firms need positive NPV projects for investment

D) None of the above

5. Investment in net working capital is not depreciated because:

A) it is not a cash flow

B) it is a sunk cost

C) it is recovered during or at the end of the project and is not a depreciating asset

D) all of the above

6. The principal short-term assets are:

A) Cash

B) Accounts receivable

C) Inventories

D) All of the above

7. Investment in inventories includes investment in:

A) Raw material

B) Work-in-progress

C) Finished goods

D) All of the above

8. The cost of a resource that may be relevant to an investment decision even when no cash changes hand is called a (an):

A) sunk cost

B) working capital

C) opportunity cost

D) none of the above

9. The following cash flows should be treated as incremental flows when deciding whether to go ahead with an electric car except:

A) The consequent deduction in sales of the company’s existing gasoline models

B) The expenditure on new plants and equipment

C) The value of tools that can be transferred from the company’s existing plants

D) Interest payment on debt

10. Which of the following cash flows should be treated as incremental flows when deciding whether to go ahead with an electric car?

A) The cost of research and development undertaken for developing the electric car in the past three years

B) The annual depreciation charge

C) The reduction in taxes resulting from the depreciation charges

D) Dividend payments

11. Money that a firm has already spent or committed to spend regardless of whether a project is taken is called:

A) Sunk cost

B) Opportunity cost

C) Fixed cost

D) None of the above

12. The value of a previously purchased machine expected to be used by a proposed project is an example of:

A) Sunk cost

B) Opportunity cost

C) Fixed cost

D) None of the above

13. A firm owns a building with a book value of $150,000 and a market value of $250,000. If the building is utilized for a project, then the opportunity cost ignoring taxes is:

A) $100,000

B) $150,000

C) $250,000

D) None of the above

14. A firm has a general purpose machine which has a book value of $400,000 and is sold for $600,000 in the market. If the tax rate is 30%, what is the opportunity cost of using the machine in a project?

A) $500,000

B) $600,000

C) $540,000

D) None of the above

15. A reduction in the sales of existing products caused by the introduction of a new product is an example of:

A) sunk cost

B) opportunity cost

C) incidental effects

D) none of the above

16. The real rate of interest is 2% and the inflation is 5%. What is the nominal rate of interest?

A) 3%

B) 4%

C) 7.1%

D) 1%

17. A cash flow received in two years is expected to be $11,236. If the real rate of interest is 4% and the inflation rate is 6%, what is the real cash flow for year-2?

A) $11,236

B) $10,388

C) $10,000

D) $9,246

18. The real interest rate is 2% and the inflation rate is 4%. What is the nominal interest rate?

A) 3%

B) 4%

C) 6.08%

D) 2%

19. If the nominal interest rate is 6.5% and the inflation rate is 3%, what is the real interest rate?

A) 3.4%

B) 9.5%

C) 4%

D) None of the above

20. Proper treatment of inflation in the NPV calculation involves:

A) Discounting nominal cash flows using the nominal discount rate

B) Discounting real cash flows using the real discount rate

C) Discounting nominal cash flows using the real discount rates

D) A and B

21. Real cash flow occurring in year-2 is 50,000. If the inflation rate is 10% per year, calculate nominal cash flow for year-2.

A) 60,500

B) 50,000

C) 55,000

D) None of the above

22. The NPV value obtained by discounting nominal cash flows using the nominal discount rate is:

A) The same as the NPV value obtained by discounting real cash flows using the real discount rate

B) The same as the NPV value obtained by discounting real cash flows using the nominal discount rate

C) The same as the NPV value obtained by discounting nominal cash flows using the real discount rate

D) None of the above

23. A capital equipment costing $100,000 today has no (zero) salvage value at the end of 5 years. If straight-line depreciation is used, what is the book value of the equipment at the end of three years?

A) $110,000

B) $80,000

C) $60,000

D) $40,000

24. Capital equipment costing $200,000 today has 50,000 salvage value at the end of 5 years. If the straight line depreciation method is used, what is the book value of the equipment at the end of two years?

A) $200,000

B) $170,000

C) $140,000

D) $50,000

25. For project A in year – 2, inventories increase by $10,000 and accounts payable by $4,000. Calculate the increase or decrease in net working capital for year-2.

A) Increases by $14,000

B) Decreases by $14,000

C) Increases by $6,000

D) Decreases by $6,000

E) None of the above

26. For project X, year – 5 inventories increase by $5,000, accounts receivables by $3,000 and accounts payables by $2,000. Calculate the increase or decrease in working capital for year-5.

A) Increases by $6,000

B) Decreases by $6,000

C) Increases by $8,000

D) Decreases by $7,000

27. If the depreciation amount is $100,000 and the marginal tax rate is 30%, then the tax shield due to depreciation is:

A) $333,333

B) $100,000

C) $30,000

D) None of the above

28. If the depreciation amount is 600,000 and the marginal tax rate is 30%, then the tax shield due to depreciation is:

A) $180,000

B) $600,000

C) $210,000

D) None of the above

Use the following to answer questions 29-30:

You own 100 acres of timberland, with young timber worth $20,000 if logged today. This represents 500 cords of wood at $40 per cord. After logging, the land can be sold today for $10,000 ($100 per acre). The opportunity cost of capital is 10%. You have made the following estimates:

(i) The price of a cord of wood will increase by 5% per year.

(ii) The price of land will increase by 3% per year.

(iii) The yearly growth rate of the cords of wood on your land are: years 1-2: 15%; years 3-4: 10%; years 5-8: 5%; years thereafter: 2%.

29. The present value of the optimal decision is approximately:

A) $30,000

B) $32,800

C) $34,250

D) $33,830

30. The optimal decision is to sell after:

A) 8 years

B) 5 years

C) 4 years

D) 3 years

31. You have been asked to evaluate a project with infinite life. Sales and costs are projected to be $1000 and $500 respectively. There is no depreciation and the tax rate is 30%. The real required rate of return is 10%. The inflation rate is 4% and is expected to be 4% forever. Sales and costs will increase at the rate of inflation. If the project costs $3000, what is the NPV?

A) $365.38

B) $1629.62

C) $500.00

D) None of the above

32. A project costs $100 today. It has sales of $100 per year forever. Costs will be $50 the first year and increase by 19% per year. Ignoring taxes calculate the NPV of the project at the discount rate of 10%.

A) $11.62

B) $65.00

C) $100.00

D) Cannot be calculated as g > r

33. A project requires an initial investment of $200,000 and is expected to produce a cash flow before taxes of 120,000 per year for two years. [i.e. cash flows will occur at t = 1 and t = 2]. The corporate tax rate is 30%. The assets will be depreciated using MACRS – 3 year schedule: t=1, 33.33%; t = 2: 44.45%; t = 3: 14.81%; t = 4: 7.4%. The company’s tax situation is such that it can make use of all applicable tax shields. The opportunity cost of capital is 12%. Assume that the asset can be sold for book value. Calculate the NPV of the project at the end of two years. (approximately)

A) $16,510

B) $19,571

C) $47,035

D) None of the above

34. The IRR for the project in the previous question is: (approximately)

A) 12%

B) 10%

C) 17.8%

D) None of the above

35. OM Construction Company must choose between two types of cranes. Crane A costs $600,000, will last for 5 years, and will require $60,000 in maintenance each year. Crane B costs $750,000 and will last for seven years and will require $30,000 in maintenance each year. Maintenance costs for cranes A and B are incurred at the end of each year. The appropriate discount rate is 12% per year. Which machine should OM Construction purchase?

A) Crane A as EAC is $226,444

B) Crane B as EAC is $194,336

C) Crane A as the PV is $816,286

D) Cannot be calculated as the revenues for the project are not given

36. The projects have the following NPVs and project lives.

Project NPV Life

Project A $5,000 4 years

Project B $7,000 7 years

If the cost of capital is 12%, which project would you accept?

A) A

B) B

C) Both A and B

D) Reject both A and B

37. Two machines, A and B, which perform the same functions, have the following costs and lives.

Which machine would you choose? The two machines are mutually exclusive and the cost of capital is 15%.

A) Machine A as the EAC is $1789.89

B) Machine B as the EAC is $1922.88

C) Don’t buy either machine

True/False Questions

T F 38. When calculating cash flows, it is important to consider all incidental effects.

T F 39. Sunk costs are unaffected by the decision to accept or reject and should be ignored.

T F 40. Opportunity costs should not be included as they are missed opportunities.

T F 41. By undertaking the analysis in real terms, the financial manager avoids having to forecast inflation.

T F 42. Do not forget to include interest and dividend payments when calculating the project’s cash flow.

T F 43. Depreciation acts as a tax shield in reducing the taxes.

T F 44. An investment should be postponed as long as the opportunity cost of capital is less than the growth rate of the value of the project.

T F 45. The rule for comparing machines with different lines is to select the machine with the lowest equivalent annual cost (EAC).

T F 46. You should replace a machine when the EAC of continuing to operate it exceeds the EAC of the next machine.

T F 47. You should always replace all old machines with new ones.

Short Answer Questions

48. Define the term cash flow for a project.

49. What are some of the important points to remember while estimating the cash flows of a project?

50. Briefly discuss how taxes are taken into consideration in other countries like Japan.

51. What are some of the additional factors that have to be considered while estimating cash flows in other countries and currencies:

52. How do you compare projects with different lives?

53. Briefly explain how the decision to replace an existing machine is made?

54. Briefly explain the term ” project interactions”

55. Explain the idea behind the optimal timing of investment.

56. Briefly explain how peak demand can be met economically.