CHAPTER 13

PLANNING FOR CAPITAL INVESTMENTS

SUMMARY OF QUESTION TYPES BY LEARNING OBJECTIVE, BLOOM’S TAXONOMY, LEVEL OF DIFFICULTY, AACSB CODES, AND CPA CODES

Bloom’s: AN = Analysis AP = Application C = Comprehension

E = Evaluation K = Knowledge

LOD: E = Easy M = Medium H = Hard

AACSB: AN = Analytic

CPA: F = Financial Reporting MA = Management Accounting

SUMMARY OF QUESTION TYPES BY LEARNING OBJECTIVE, BLOOM’S TAXONOMY, LEVEL OF DIFFICULTY, AACSB CODES, AND CPA CODES (CONT’D)

Bloom’s: AN = Analysis AP = Application C = Comprehension

E = Evaluation K = Knowledge

LOD: E = Easy M = Medium H = Hard

AACSB: AN = Analytic

CPA: F = Financial Reporting MA = Management Accounting

SUMMARY OF LEARNING OBJECTIVES BY QUESTION TYPE

Note: TF = True-False C = Completion BE = Brief Exercise

MC = Multiple Choice Ex = Exercise SAE = Short-Answer Essay

Ma = Matching

CHAPTER LEARNING OBJECTIVES

1. Discuss capital budgeting inputs and apply the cash payback technique.

Project proposals are gathered from each department and submitted to a capital budget committee, which screens the proposals and recommends worthy projects. Company officers decide which projects to fund, and the board of directors approves the capital budget. In capital budgeting, estimated cash inflows and outflows, rather than accrual accounting numbers, are the preferred inputs.

The cash payback technique identifies the time period it will take to recover the cost of the investment. The formula when net annual cash flows are the same is as follows: Cost of capital expenditure ÷ estimated net annual cash inflow = cash payback period. The shorter the payback period, the more attractive the investment.

2. Explain the net present value method.

Under the net present value method, the present value of future cash inflows is compared with the capital investment to determine the net present value. The decision rule is as follows: Accept the project if the net present value is zero or positive. Reject the project if the net present value is negative.

3. Identify capital budgeting challenges and refinements.

Intangible benefits are difficult to measure, and thus are often ignored in capital budgeting decisions. This can result in incorrectly rejecting some projects. One method for considering intangible benefits is to calculate the NPV, ignoring intangible benefits. If the resulting NPV is below zero, evaluate whether the benefits are worth at least the amount of the negative net present value. Alternatively, intangible benefits can be included in the NPV calculation, using conservative estimates of their value.

The profitability index is a tool for comparing the relative merits of two alternative capital investment opportunities. It is calculated by dividing the present value of net cash flows by the initial investment. The higher the index, the more desirable is the project.

A post-audit is an evaluation of a capital investment’s actual performance. Post-audits create an incentive for managers to make accurate estimates. Post-audits are also useful for determining whether a project should be continued, expanded, or terminated. Finally, post-audits provide feedback that is useful for improving estimation techniques.

4. Explain the internal rate of return method.

The objective of the internal rate of return method is to find the interest yield of the potential investment, which is expressed as a percentage rate. The decision rule is this: Accept the project when the internal rate of return is equal to or greater than the required rate of return. Reject the project when the internal rate of return is less than the required rate of return.

5. Describe the annual rate of return method.

The annual rate of return uses accounting data to indicate the profitability of a capital investment. It is calculated by dividing the expected annual net income by the amount of the average investment. The higher the rate of return, the more attractive the investment.

TRUE-FALSE STATEMENTS

1. The capital budgeting committee ultimately approves the capital expenditure budget for the year.

2. The cost of capital is a weighted average of the rates of return paid on borrowed funds, as well as on funds provided by investors through the company's shares.

3. The profitability index allows for comparison of the relative desirability of projects that require differing initial investments.

4. The internal rate of return (or interest yield) is a rate that will cause the present value of the proposed capital expenditure to equal the present value of the expected annual cash inflows.

ANSWERS TO TRUE-FALSE STATEMENTS

MULTIPLE CHOICE QUESTIONS

5. The cash payback

a) technique is a quick way to calculate a project's net present value.

b) period is calculated by dividing the annual cash inflow by the cost of the capital investment.

c) method is frequently used as a screening tool, but it does not take into consideration the long-term profitability of a project.

d) rule says that the longer the payback period the more attractive the investment.

6. The capital budget for the year is approved by a company's

a) board of directors.

b) capital budgeting committee.

c) officers.

d) shareholders.

7. Which of the following describes the capital budgeting evaluation process?

a) The capital budget committee submits its proposals to the officers of the company who choose which projects will be forwarded to the shareholders for ultimate approval.

b) The officers of the company submit their proposals to the capital budget committee who choose which projects will be forwarded to the shareholders for ultimate approval.

c) The officers of the company submit their proposals to the capital budget committee who choose which projects will be forwarded to the board of directors for ultimate approval.

d) The capital budget committee submits its proposal to the officers of the company who choose which projects will be forwarded to the board of directors for ultimate approval.

8. Which of the following represents a cash inflow?

a) the initial investment

b) sale of old equipment

c) repairs and maintenance

d) increased operating costs

9. Which of the following represents a cash outflow?

a) overhaul of equipment

b) increased cash received from customers

c) reduced cash flows for operating costs

d) salvage value of equipment when project is completed

10. The capital budgeting decision depends in part on the

a) availability of funds.

b) relationships among proposed projects.

c) risk associated with a particular project.

d) all of these.

11. Capital budgeting is the process

a) used in sell or process further decisions.

b) of determining how many common shares to issue.

c) of making capital expenditure decisions.

d) of eliminating unprofitable product lines.

12. If an asset costs $60,000 and is expected to have a $5,000 salvage value at the end of its nine-year life, and generates annual net cash inflows of $10,000 each year, the cash payback period is

a) 6.5 years.

b) 6 years.

c) 5.5 years.

d) 9 years.

13. If a payback period for a project is greater than its expected useful life, the

a) project will always be profitable.

b) entire initial investment will not be recovered.

c) project would only be acceptable if the company's cost of capital was low.

d) project's return will always exceed the company's cost of capital.

14. The cash payback technique

a) should be used as a final screening tool.

b) can be the only basis for the capital budgeting decision.

c) is relatively easy to calculate and understand.

d) considers the expected profitability of a project.

15. The cash payback period is calculated by dividing the cost of the capital investment by the

a) annual net income.

b) net annual cash inflow.

c) present value of the cash inflow.

d) present value of the net income.

16. When using the cash payback technique, the payback period is expressed in terms of

a) a percent.

b) dollars.

c) years.

d) months.

17. A disadvantage of the cash payback technique is that it

a) ignores obsolescence factors.

b) ignores the cost of an investment.

c) is complicated to use.

d) ignores the time value of money.

18. Bark Company is considering buying a machine for $120,000 with an estimated life of ten years and no salvage value. The straight-line method of depreciation will be used. The machine is expected to generate net income of $8,000 each year. The cash payback period on this investment is

a) 15 years.

b) 10 years.

c) 6 years.

d) 3 years.

19. Carr Company is considering two capital investment proposals. Estimates regarding each project are provided below:

Project Soup Project Nuts

Initial investment $270,000 $600,000

Annual net income 27,000 45,000

Net annual cash inflow 90,000 142,000

Estimated useful life 5 years 6 years

Salvage value -0- -0-

The cash payback period for Project Soup is

a) 13.5 years.

b) 5 years.

c) 3.9 years.

d) 3 years.

20. A company is considering purchasing factory equipment that costs $400,000 and is estimated to have no salvage value at the end of its 5-year useful life. If the equipment is purchased, annual revenues are expected to be $150,000 and annual operating expenses exclusive of depreciation expense are expected to be $25,000. The straight-line method of depreciation would be used. The cash payback period on the equipment is

a) 8.89 years.

b) 5.0 years.

c) 3.2 years.

d) 2.67 years.

21. What is the net annual cash flow?

a) $40,000

b) $90,000

c) $130,000

d) $140,000

22. What is the cash payback period?

a) 5 years

b) 3.56 years

c) 3.85 years

d) 3.57 years

23. Doris Co. is considering purchasing a new machine that will cost $200,000, but which will decrease costs each year by $50,000. The useful life of the machine is 10 years. The machine would be depreciated straight-line with no residual value over its useful life at the rate of $20,000/year. The payback period is

a) 5.0 years.

b) 4.5 years.

c) 4.0 years.

d) 10.0 years.

24. Mystery Co. is considering purchasing a new piece of equipment that will cost $600,000.The equipment has an estimated useful life of 8 years and no salvage value. The new equipment will produce annual cash inflows and net income of $215,000 and $140,000, respectively. Mystery requires a 10% rate of return. What is the payback period for this equipment?

a) 8.0 years

b) 3.75 years

c) 2.79 years

d) 6.67 years

25. Capital budgeting relies on cash inflows and outflows as preferred inputs for calculations because

a) managers prefer to use cash figures rather than accounting figures.

b) GAAP does not apply to capital budgeting decisions.

c) projects require cash paid out and firms want to know when cash will be returned.

d) cash figures are easier to calculate than accounting figures.

26. Which of the following would not be considered as an input into a capital budgeting decision?

a) scrap value of equipment sold at the end of a project

b) labour savings as a result of mechanization of a process

c) cost outlays many years after the project has started

d) amortization on a straight-line basis

27. The cash payback method is useful because

a) it gives a broad indication when outlays will be recovered by the firm.

b) it gives a specific date as to when outlays will be recovered by the firm.

c) it avoids using complicated accounting data in capital budgeting decisions.

d) it is easy to communicate the relation between cash received and ultimate profitability of a project to everyone in the organization.

28. The major difficulty of the cash payback method is

a) it includes salvage values at the end of a project.

b) it ignores net income in its calculation.

c) it ignores the overall cash flow of the project.

d) it ignores the overall profitability of the project.

29. When using the net present value method

a) a net present value of zero indicates that the project would be acceptable.

b) the expected cash flows from a project must be an equal amount each year.

c) net cashflows are discounted to their future value.

d) a proposal is only acceptable when the rate of return on the investment exceeds the required rate of return.

30. The discount rate is referred to by all of the following alternative names except the

a) maximum return rate.

b) cut-off rate.

c) hurdle rate.

d) required rate of return.

31. The rate that a company must pay to obtain funds from creditors and shareholders is known as the

a) hurdle rate.

b) cost of capital.

c) cut-off rate.

d) all of these.

32. The higher the risk component in a project, the

a) more attractive the investment.

b) higher the net present value.

c) higher the cost of capital.

d) higher the discount rate.

33. If a company's required rate of return is 10% and, in using the net present value method, a project's net present value is zero, this indicates that the

a) project's rate of return exceeds 10%.

b) project's rate of return is less than the minimum rate required.

c) project earns a rate of return of 10%.

d) project earns a rate of return of 0%.

34. Which of the following assumptions is made in order to simplify the net present value method?

a) All cash flows come at the end of the year.

b) All cash flows are immediately reinvested at the best rate available at the time.

c) All cash flows come at the beginning of the year.

d) All cash flows are not reinvested.

35. When the annual cash flows from an investment are unequal, the appropriate table to use is in the calculation of net present value is the

a) future value of 1 table.

b) future value of annuity table.

c) present value of 1 table.

d) present value of annuity table.

36. If a company uses a 12% discount rate with the net present value method, and then does the same analysis, but with a 15% discount rate, which of the following is likely to occur?

a) The 12% rate will show the project is more profitable than the 15% rate.

b) The 15% rate will show the project is more profitable than the 12% rate.

c) Both rates will produce the same net present value.

d) The relative profitability of the two studies depends only on the timing of the cash flows, not on the discount rate.

37. Present Value of an Annuity of 1

Periods 8% 9% 10%

1 .926 .917 .909

2 1.783 1.759 1.736

3 2.577 2.531 2.487

A company has a minimum required rate of return of 9% and is considering investing in a project that costs $50,000 and is expected to generate cash inflows of $30,000 at the end of each year for two years. The net present value of this project is

a) $20,000.

b) $10,000.

c) $6,920.

d) $2,770.

38. Present Value of an Annuity of 1

Periods 8% 9% 10%

1 .926 .917 .909

2 1.783 1.759 1.736

3 2.577 2.531 2.487

A company has a minimum required rate of return of 10% and is considering investing in a project that requires an investment of $68,000 and is expected to generate cash inflows of $30,000 at the end of each year for 3 years. The present value of future cash inflows for this project is

a) $68,000.

b) $74,610.

c) $7,930.

d) $6,610.

39. Carr Company is considering two capital investment proposals. Estimates regarding each project are provided below:

Project Soup Project Nuts

Initial investment $270,000 $600,000

Annual net income 27,000 45,000

Net annual cash inflow 90,000 142,000

Estimated useful life 5 years 6 years

Salvage value -0- -0-

The company requires a 10% rate of return on all new investments.

Present Value of an Annuity of 1

Periods 9% 10% 11% 12%

5 3.890 3.791 3.696 3.605

6 4.486 4.355 4.231 4.111

The net present value for Project Nuts is

a) $618,410.

b) $182,912.

c) $100,000.

d) $18,410.

40. Vault Company wants to purchase an asset with a 3-year useful life, which is expected to produce cash inflows of $10,000 each year for two years, and $15,000 in year 3. Vault has a 14% cost of capital, and uses the following factors. What is the present value of these future cash flows?

Present Value of 1

Period 14%

1 .88

2 .77

3 .67

a) $30,800

b) $30,400

c) $26,550

d) $17,750

41. Tammy Co. is considering purchasing a machine that will produce annual savings of $22,000 at the end of the year. Tammy requires a 12% rate of return and the asset has a 5-year useful life. What is the maximum Tammy would be willing to pay for this machine?

Present Value of Annuity of 1 Present Value of 1

Period 12% Period 12%

5 3.605 5 .567

a) $43,386

b) $79,310

c) $110,000

d) $62,370

42. Cleaners, Inc. is considering purchasing equipment costing $30,000 with a 6-year useful life. The equipment will provide cost savings of $7,300 and will be depreciated straight-line over its useful life with no salvage value. Cleaners, Inc. requires a 10% rate of return. What is the approximate net present value of this investment?

Present Value of an Annuity of 1_

Period 8% 9% 10% 11% 12% 15%

6 4.623 4.486 4.355 4.231 4.111 3.784

a) $13,800

b) $1,792

c) $886

d) $2,748

43. When evaluating a project, companies should always use

a) the Bank of Canada rate of interest.

b) the rate that is currently charged at its bank.

c) the current corporate borrowing rate.

d) the corporate borrowing rate adjusted for any perceived risk of the project.

44. Using a number of outcome estimates to get a sense of the variability among potential returns is

a) financial analysis.

b) post-audit analysis.

c) sensitivity analysis.

d) outcome analysis.

45. An approach that uses a number of outcome estimates to get a sense of the variability among potential returns is

a) the discounted cash flow technique.

b) the net present value method.

c) risk analysis.

d) sensitivity analysis.

46. Sensitivity analysis on a potential project

a) is only useful to perform when there are firm calculations on the project available.

b) is useful to perform when uncertainty exists, and calculations are based on estimates.

c) is designed to ensure that management is aware of all possible outcomes of the project.

d) is designed to provide an escape-hatch for management should the project not succeed.

47. A thorough evaluation of how well a project's actual performance matches the projections made when the project was proposed is called a

a) pre-audit.

b) post-audit.

c) risk analysis.

d) sensitivity analysis.

48. Using the profitability index method, the present value of cash inflows for Project Flower is $88,000 and the present value of cash inflows of Project Plant is $48,000. If Project Flower and Project Plant require initial investments of $90,000 and $40,000, respectively, and have the same useful life, the project that should be accepted is

a) Project Flower.

b) Project Plant.

c) Either project may be accepted.

d) Neither project should be accepted.

49. Intangible benefits in capital budgeting would include all of the following except increased

a) product quality.

b) employee loyalty.

c) salvage value.

d) product safety.

50. Intangible benefits in capital budgeting

a) should be ignored because they are difficult to determine.

b) include increased quality or employee loyalty.

c) are not considered because they are usually not relevant to the decision.

d) have a rate of return in excess of the company’s cost of capital.

51. To avoid rejecting projects that actually should be accepted,

1. intangible benefits should be ignored.

2. conservative estimates of the intangible benefits' value should be incorporated into the NPV calculation.

3. calculate net present value ignoring intangible benefits and then, if the NPV is negative, estimate whether the intangible benefits are worth at least the amount of the negative NPV.

a) 1

b) 2

c) 3

d) both 2 and 3 are correct.

52. All of the following statements about intangible benefits in capital budgeting are correct except that they

a) include increased quality and employee loyalty.

b) are difficult to quantify.

c) include improved safety.

d) should be completely ignored if the NPV is negative.

53. In evaluating high-tech projects

a) only tangible benefits should be considered.

b) only intangible benefits should be considered.

c) both tangible and intangible benefits should be considered.

d) neither tangible nor intangible benefits should be considered.

54. If a company's required rate of return is 9%, and in using the profitability index method, a project's index is greater than 1, this indicates that the project's rate of return is

a) equal to 9%.

b) greater than 9%.

c) less than 9%.

d) unacceptable for investment purposes.

55. The profitability index is calculated by dividing the

a) total cash flows by the initial investment.

b) present value of cash flows by the initial investment.

c) initial investment by the total cash flows.

d) initial investment by the present value of cash flows.

56. The capital budgeting method that takes into account both the size of the original investment and the discounted cash flows is the

a) cash payback method.

b) internal rate of return method.

c) net present value method.

d) profitability index.

57. The profitability index

a) does not take into account the discounted cash flows.

b) is calculated by dividing total cash flows by the initial investment.

c) allows comparison of the relative desirability of projects that require differing initial investments.

d) will never be greater than 1.

58. The capital budgeting method that allows comparison of the relative desirability of projects that require differing initial investments is the

a) cash payback method.

b) internal rate of return method.

c) net present value method.

d) profitability index.

59. The following information is available for a potential investment for Panda Company:

Initial investment $40,000

Net annual cash inflow 10,000

Net present value 18,112

Salvage value 5,000

Useful life 10 yrs.

The potential investment’s profitability index is

a) 4.00.

b) 2.85.

c) 2.50.

d) 1.45.

60. Post-audits of capital projects

a) are usually foolproof.

b) are done using different evaluation techniques than were used in making the original capital budgeting decision.

c) provide a formal mechanism by which the company can determine whether existing projects should be supported or terminated.

d) all of these.

61. A post-audit should be performed using

a) a different evaluation technique than that used in making the original decision.

b) the same evaluation technique used in making the original decision.

c) estimated amounts instead of actual figures.

d) an independent advisor.

62. Performing a post-audit is important because

a) managers will be more likely to submit reasonable data when they make investment proposals if they know their estimates will be compared to actual results.

b) it provides a formal mechanism by which the company can determine whether existing projects should be terminated.

c) it improves the development of future investment proposals because managers improve their estimation techniques by evaluating their past successes and failures.

d) all of these.

63. Present Value of an Annuity of 1

Periods 8% 9% 10%

1 .926 .917 .909

2 1.783 1.759 1.736

3 2.577 2.531 2.487

A company has a minimum required rate of return of 9% and is considering investing in a project that costs $50,000 and is expected to generate cash inflows of $20,000 at the end of each year for three years. The profitability index for this project is

a).99.

b) 1.00.

c) 1.01.

d) 1.20.

64. Cleaners, Inc. is considering purchasing equipment costing $30,000 with a 6-year useful life. The equipment will provide cost savings of $7,300 and will be amortized using the straight-line method over its useful life with no salvage value. Cleaners, Inc. requires a 10% rate of return. What is the approximate profitability index associated with this equipment?

Present Value of an Annuity of 1_

Period 8% 9% 10% 11% 12% 15%

6 4.623 4.486 4.355 4.231 4.111 3.784

a) 1.23

b) 1.03

c) 1.06

d) 73

65. An intangible benefit of a project would best be described as:

a) Goodwill that is increased on the balance sheet because of the project.

b) Lower bank rates offered by the company’s bankers for certain projects.

c) The company’s presence in its market is enhanced by the project, which may result in additional sales of the company’s other product lines.

d) The company may be allowed to defer income tax payment terms as a result of the project.

66. When accepting large capital projects, a company should

a) pay strict attention to what the numbers indicate and accept or reject a project accordingly.

b) pay close attention to trends in the marketplace before accepting or rejecting a project.

c) assess the numbers on the project and then go with management’s best judgment.

d) assess the numbers on the project then review the intangible benefits before accepting or rejecting a project.

67. Which of the following statements is false?

a) By ignoring intangible benefits, capital budgeting techniques might incorrectly eliminate projects that could be beneficial to the company.

b) To avoid accepting projects that actually should be rejected, a company should ignore intangible benefits in calculating net present value.

c) One way of incorporating intangible benefits into the capital budgeting decision is to project conservative estimates of the value of the intangible benefits and include them in the NPV calculation.

d) Intangible benefits include increased quality, improved safety or greater employment loyalty.

68. Peanut Co. is planning on investing in a new 2-year project, Project Jelly. Project Jelly is expected to produce cash flows of $100,000 and $120,000 in year 1 and year 2, respectively. Peanut requires an internal rate of return of 15%. What is the maximum amount that Peanut should invest immediately in Project Jelly?

Present Value of 1 Future Value of 1

Period 15% Period 15%

1 .870 1 1.150

2 .756 2 1.323

a) $191.400

b) $177,720

c) $220,000

d) $273,760

69. A post-audit

a) should be performed as an evaluation of an organization’s investment projects before their completion.

b) creates an incentive for managers to make lower estimates, since managers know that their results will be evaluated.

c) is an evaluation of how well a project's actual performance matches the projections made when the project was proposed.

d) provides an informal mechanism for deciding whether existing projects should be supported or terminated.

70. The internal rate of return method

a) is, like the NPV method, a discounted cash flow technique.

b) will reject a project when the internal rate of return is greater than or equal to the required rate of return.

c) finds the rate that results in a positive net present value.

d) does not recognize the time value of money.

71. A capital budgeting method that takes into consideration the time value of money is the

a) annual rate of return method.

b) return on shareholders' equity method.

c) cash payback technique.

d) internal rate of return method.

72. The internal rate of return is the interest rate that results in a

a) positive NPV.

b) negative NPV.

c) zero NPV.

d) positive or negative NPV.

73. In using the internal rate of return method, the internal rate of return factor was 4.0 and the equal annual cash inflows were $16,000. The initial investment in the project must have been

a) $8,000.

b) $16,000.

c) $64,000.

d) $32,000.

74. The capital budgeting technique that finds the interest yield of the potential investment is the

a) annual rate of return method.

b) internal rate of return method.

c) net present value method.

d) profitability index method.

75. All of the following statements about the internal rate of return method are correct except that it

a) recognizes the time value of money.

b) is widely used in practice.

c) is easy to interpret.

d) can be used only when the cash inflows are equal.

76. Present Value of an Annuity of 1

Periods 8% 9% 10%

1 .926 .917 .909

2 1.783 1.759 1.736

3 2.577 2.531 2.487

A company has a minimum required rate of return of 8% and is considering investing in a project that costs $67,145 and is expected to generate cash inflows of $27,000 each year for three years. The approximate internal rate of return on this project is

a) 8%.

b) 10%.

c) 9%.

d) less than the required 8%.

77. Carr Company is considering two capital investment proposals. Estimates regarding each project are provided below:

Project Soup Project Nuts

Initial investment $270,000 $600,000

Annual net income 27,000 45,000

Net annual cash inflow 90,000 142,000

Estimated useful life 5 years 6 years

Salvage value -0- -0-

The company requires a 10% rate of return on all new investments.

Present Value of an Annuity of 1

Periods 9% 10% 11% 12%

5 3.890 3.791 3.696 3.605

6 4.486 4.355 4.231 4.111

The internal rate of return for Project Nuts is approximately

a) 10%.

b) 11%.

c) 12%.

d) 9%.

78. Cleaners, Inc. is considering purchasing equipment costing $30,000 with a 6-year useful life. The equipment will provide cost savings of $7,300 and will be depreciated straight-line over its useful life with no salvage value. Cleaners, Inc. requires a 10% rate of return. What is the approximate internal rate of return for this investment?

Present Value of an Annuity of 1_

Period 8% 9% 10% 11% 12% 15%

6 4.623 4.486 4.355 4.231 4.111 3.784

a) 9%

b) 10%

c) 11%

d) 12%

79. In using the internal rate of return method

a) management can ignore the cost of capital for the project.

b) management must understand its own required rate of return for projects.

c) the net present value method can be ignored in assessing the project.

d) both the net present value and Cash Payback methods can be ignored in assessing the project.

80. The major difference between the net present value method and the annual rate of return method in evaluating a capital project is

a) the ARR method is easier for accountants to justify than the NPV method.

b) the NPV method is easier for managers to justify than the ARR method.

c) the ARR method focuses on overall profitability of a project.

d) the NPV method focuses on the overall profitability of a project.

81. Using the annual rate of return method,

a) a project is acceptable if its rate of return is greater than management's minimum rate of return.

b) requires dividing a project's annual cash inflows by the economic life of the project.

c) is advantageous as it considers the time value of money.

d) is advantageous as it relies on accrual accounting numbers rather than actual cash flows.

82. Carr Company is considering two capital investment proposals. Estimates regarding each project are provided below:

Project Soup Project Nuts

Initial investment $270,000 $600,000

Annual net income 27,000 45,000

Net annual cash inflow 90,000 142,000

Estimated useful life 5 years 6 years

Salvage value -0- -0-

The company requires a 10% rate of return on all new investments.

Present Value of an Annuity of 1

Periods 9% 10% 11% 12%

5 3.890 3.791 3.696 3.605

6 4.486 4.355 4.231 4.111

The annual rate of return for Project Soup is

a) 13.3%.

b) 20%.

c) 33.3%.

d) 30%.

83. A company is considering purchasing factory equipment that costs $400,000 and is estimated to have no salvage value at the end of its 5-year useful life. If the equipment is purchased, annual revenues are expected to be $150,000 and annual operating expenses exclusive of depreciation expense are expected to be $25,000. The straight-line method of depreciation would be used. If the equipment is purchased, the annual rate of return expected on this equipment is

a) 37.5%.

b) 31.25%.

c) 22.5%.

d) 6.25%.

84. The annual rate of return method is also referred to as

a) simple rate of return method.

b) accounting rate of return method.

c) unadjusted rate of return method.

d) all of the above

85. The annual rate of return method is based on

a) accounting data.

b) the time value of money data.

c) market values.

d) cash flow data.

86. What is the main disadvantage of the annual rate of return method?

a) It is only valid for investments with a one year time perspective.

b) It incorporates depreciation into the calculations, which increases the uncertainty of the calculations associated with estimating the life and salvage value of the investment.

c) No consideration is given as to when the cash inflows occur.

d) It does not consider the time value of money.

87. A company projects an increase in net income of $40,000 each year for the next five years if it invests $500,000 in new equipment. The equipment has a five-year life and an estimated salvage value of $50,000. The company uses the straight-line method of depreciation. What is the annual rate of return?

a) 8%

b) 14.5%

c) 18%

d) 26.7%

88. All of the following statements about the annual rate of return method are correct except that it

a) indicates the profitability of a capital expenditure.

b) ignores the salvage value of an investment.

c) does not consider the time value of money.

d) compares the annual rate of return to management’s minimum rate of return.

ANSWERS TO MULTIPLE CHOICE QUESTIONS

BRIEF Exercises

Brief Exercise 89

Diamond Co. is considering investing in new equipment that will cost $800,000 with an 8-year useful life. The new equipment is expected to produce annual net income of $25,000 over its useful life. Depreciation expense, using the straight-line rate, is $100,000 per year.

Instructions

Calculate the payback period.

Solution 89 (5 min.)

$800,000 ÷ ($25,000 + $100,000) = 6.4 years

Brief Exercise 90

Johnstown Ltd. wants to buy a new machine for its main product line. It costs $60,000 and will save the company $9,000 per year for the next ten years.

Calculate the payback for the company on this machine.

Solution 90 (5 min.)

$60,000 ÷ $9,000 = 6.67 years

Brief Exercise 91

Madeline Company is proposing to spend $170,000 to purchase a machine that will provide annual cash flows of $37,000. The appropriate present value factor for 8 periods is 6.73.

Instructions

Calculate the proposed investment’s net present value, and indicate whether the investment should be made by Madeline Company.

Solution 91 (5 min.)

The investment should be made because the net present value is positive.

Brief Exercise 92

LeMo Co. is considering investing in a cottage that will cost $310,000. The company expects to rent the cottage for 7 years, after which it will be sold for $400,000 at that time. LeMo anticipates cash flows of $60,000 resulting from the cottage and the company’s borrowing rate is 9%, while its cost of capital is 12%.

Instructions

Calculate the net present value of the cottage and indicate whether LeMo should make the investment.

Present Value of an Annuity of 1

Period 9% 12%

7 5.03295 4.56376

Present Value of 1

Period 9% 12%

7 0.54703 0.45235

Solution 92 (5 min.)

Since the net present value is positive, LeMo should accept the project.

Brief Exercise 93

LakeFront Company is considering investing in a new dock that will cost $560,000. The company expects to use the dock for 5 years, after which it will be sold for $300,000. LakeFront anticipates annual cash flows of $110,000 resulting from the new dock. The company’s borrowing rate is 8%, while its cost of capital is 10%.

Instructions

Calculate the net present value of the dock and indicate whether LakeFront should make the investment.

Present Value of an Annuity of 1

Period 8% 10%

5 3.99271 3.79079

Present Value of 1

Period 8% 10%

5 0.68058 0.62092

Solution 93 (5 min.)

Cash Flows × 10% Discount Factor = Present Value

Present value of annual cash flows $110,000 × 3.79079 = $416,987

Present value of salvage value 300,000 × .62092 = 186,276

603,263

Capital investment 560,000

Net present value $ 43,263

Since the net present value is positive, LakeFront should accept the project.

Brief Exercise 94

EKPN Co. has hired a consultant to propose a way to increase the company’s revenues. The consultant has evaluated two mutually exclusive projects with the following information provided for each project:

Project Chicken Project Rooster

Capital investment $810,000 $200,000

Annual cash flows 210,000 60,000

Estimated useful life 5 years 5 years

Estimated salvage value $130,000 $50,000

EKPN Co. uses a discount rate of 8% to evaluate both projects.

Present Value of an Annuity of 1

Period 8%

5 3.99271

Present Value of 1

Period 8%

5 0.68058

Instructions

a) Calculate the net present value of both projects.

b) Calculate the profitability index for each project.

c) Which project should EKPN accept?

Solution 94 (10–15 min.)

Project Chicken

Profitability index = $926,944 / $810,000 = 1.144

Project Rooster

Profitability index = $273,592 / $200,000 = 1.368

Project Rooster has a lower net present value than Project Chicken, but because of its lower capital investment, it has a higher profitability index. Based on its profitability index, Project Rooster should be accepted.

Brief Exercise 95

Stanton Company is performing a post-audit of a project completed one year ago. The initial estimates were that the project would cost $490,000, would have a useful life of 9 years, zero salvage value, and would result in net annual cash flows of $90,000 per year. Now that the investment has been in operation for 1 year, revised figures indicate that it actually cost $510,000, will have a useful life of 11 years, and will produce net annual cash flows of $77,000 per year with zero salvage value. Evaluate the success of the project. Assume a discount rate of 10%. The PV of an annuity for 11 years at 10% is 6.49506 and the PV of $1 for 11 years at 10% is 0.42410. Calculate the post-audit NPV

Solution 95 (5 min.)

Cash Flows × 10% Discount Factor = Present Value

Present value of net annual
cash flows $77,000 × 6.49506 = 500,120

Capital investment 510,000

Net present value $ 9,880

Brief Exercise 96

The manager of Induction Ltd. wants to evaluate the profitability of four potential new projects and has provided you with the following information:

Project Investment Net Present Value

1 $150,000 $25,000

2 140,000 25,000

3 130,000 35,000

4 60,000 15,000

Instructions

Using the profitability index approach, rank the four projects

Solution 96 (5 min.)

3 4 2 1

165÷130 = 1.27 75÷60 = 1.25 165÷140 = 1.18 175÷150 = 1.17

Brief Exercise 97

An investment costing $72,000 is being contemplated by Mint Co. The investment will have a life of 5 years with no salvage value and will produce annual cash flows of $19,481.

Instructions

What is the approximate internal rate of return associated with this investment?

Solution 97 (5 min.)

When net annual cash inflows are expected to be equal, the internal rate of return can be approximated by dividing the capital investment by the net annual cash inflows to determine the discount factor, and then locating this discount factor on the present value of an annuity table.

$72,000 / $19,481 = 3.69591

By tracing across on the 5-year row we see that the discount factor for 11% is 3.69590. Thus, the internal rate of return on this project is approximately 11%.

Brief Exercise 98

Mint Company is contemplating an investment costing $135,000. The investment will have a life of 8 years with no salvage value and will produce annual cash flows of $25,305.

Instructions

What is the approximate internal rate of return associated with this investment?

Solution 98 (5 min.)

When net annual cash inflows are expected to be equal, the internal rate of return can be approximated by dividing the capital investment by the net annual cash inflows to determine the discount factor and then locating this discount factor on the present value of an annuity table.

$135,000 ÷ $25,305 = 5.33

By tracing across on the 8-year row, we see that the discount factor of 10% is 5.33493. Thus the internal rate of return on this project is approximately 10%.

Brief Exercise 99

White Wave Company is contemplating an investment costing $250,000. The investment will have a life of 6 years with no salvage value and will produce annual cash flows of $46,200. White Wave has a required rate of return of 5%.

Instructions

1. What is the approximate internal rate of return associated with this investment?
2. Should White Wave Company make the investment given the company’s required rate of return?

Solution 99 (5-7 min.)

1. When net annual cash inflows are expected to be equal, the internal rate of return can be approximated by dividing the capital investment by the net annual cash inflows to determine the discount factor and then locating this discount factor on the present value of an annuity table.

$250,000 ÷ $46,200 = 5.41

By tracing across on the 6-year row, we see that the discount factor of 3% is 5.417. Thus the internal rate of return on this project is approximately 3%.

The IRR decision rule is to accept the project when the internal rate of return is equal to or greater than the required rate of return and reject the project when the internal rate of return is less than the required rate of return. Given that the IRR of 3% is less than the required rate of return of 5%, While Wave company should reject the project.

Brief Exercise 100

Salt Co. is considering investing in a new facility to extract and produce salt. The facility will increase revenues by $170,000, but will also increase annual expenses by $50,000 including depreciation. The facility will cost $720,000 to build, but will have a $30,000 salvage value at the end of its 15-year useful life.

Instructions

Calculate the annual rate of return on this facility.

Solution 100 (5 min.)

The annual rate of return is calculated by dividing expected annual income by the average investment. The company’s expected annual income is:

$170,000 – $50,000 = $120,000

Its average investment is:

Therefore, its annual rate of return is:

$120,000 / $375,000 = 32%

Exercises

Exercise 101

Jillian Grapes is thinking of purchasing a new grape-crushing machine for its factory. The cost of the new equipment is $50,000. The current machine must be scrapped and will have no value. The costs associated with operating the two machines are:

Current Machine New Machine

Labour $7,000 $2,000

Maintenance 3,000 1,000

Utilities 2,000 1,500

Amortization 9,000 11,000

Calculate the payback period if the new machine is purchased.

Solution 101

The new machine will have an outlay of $25,000 but will save the company the following money:

Labour $7,000 – $2,000 = $5,000

Maint. 3,000 – 1,000 = 2,000

Utilities 2,000 – 1,500 = 500

Amort. 0

Total $7,500

Payback period $50,000 / $7,500 = 6.67 years

Exercise 102

A certain investment proposal requires an initial outlay of $450,000, and has an expected useful life of 6 years, with an annual cash inflow of $90,000 received at the end of each year. The company uses the straight-line method of depreciation. Ignore income taxes. The company has a 12% incremental cost of borrowing.

Instructions

a) Compute the payback for the proposal.

b) Compute the net present value of the proposal.

c) Would you recommend this proposal be accepted? Explain.

Present Value of an Annuity of 1

Period 12%

6 4.111

Present Value of 1

Period 12%

6 0.507

Solution 102

a) 5 years = $450,000 / $90,000

b) NPV using 12%:

Initial outlay ($450,000)

PV of cash flows ($90,000 x 4.111) $ 369,990

NPV $ (80,010)

c) The company should not accept the proposal. The payback period of 5 years is less than the expected life of the project, which is positive. However, the NPV is negative which suggests that the proposal does not meet the company’s desired rate of return.

Exercise 103

Hutton’s Feed Supply wishes to purchase a new computerized weigh scales system, which will weigh and price the crops brought in by local farmers. Data on this new system are as follows:

Cost $12,000

Salvage value at end of 5 years $1,000

Useful life 5 years

Annual operating cost $4,000

If the existing computerized weigh scale is kept and used, it would require the purchase and installation of additional hardware, one year from now, costing $2,000. Management believes the system will last another 5 years from today, at which time the salvage value is expected to be $300. Additional information on the existing system is as follows:

Annual operating costs $9,000

Remaining book value $12,000

Current salvage value $3,000

Cost of capital 12%

The company uses the straight-line method of depreciation.

Instructions

Should Hutton’s purchase the new system? Explain.

Present Value of an Annuity of 1

Period 10% 11% 12% 15%

1 0.909 0.901 0.893 0.870

5 3.791 3.696 3.605 3.352

Present Value of 1

Period 10% 11% 12% 15%

1 0.909 0.901 0.893 0.870

5 0.621 0.593 0.567 0.497

Solution 103

Buying New System Now:

Period Cash Flow PV Factor Total Notes

0 ($12,000) 1.0 ($12,000) Initial purchase cost of weigh scales

0 $ 3,000 1.0 3,000 Salvage value of old scales, now

1 $ 2,000 0.893 1,786 Savings from not purchasing new hardware next year

1-5 $ 5,000 3.605 18,025 Net savings in annual operating costs

5 700 0.567 397 Difference in salvage value in 5 years

$11,208 NPV of new weigh scales.

The positive NPV indicates that the new weigh scales’ savings are greater than the company’s cost of capital, so the new equipment should be purchased.

Note: the incremental analysis approach has been used here, rather than showing 2 separate NPV calculations for the new and old systems. Had 2 separate NPV calculations been done, the NPV for the new weigh scales would have been higher by $11,208.

Exercise 104

Explain what a capital investment decision is. In your answer, distinguish between independent and mutually exclusive capital investment decisions.

Solution 104

Such decisions are the outcome of planning, setting goals and priorities, arranging financing and using various selection criteria to choose among a variety of competing projects. Such projects would be taken on with the view of furthering the company, with the purchase of some type of asset which would generate an acceptable rate of return.

Independent projects are those that, once accepted or rejected, do not affect the cash flows of other projects within the company.

Mutually exclusive projects are those that, once accepted or rejected, preclude the acceptance of all other competing projects.

Exercise 105

Vista Company is considering two new projects, each requiring an equipment investment of $87,000. Each project will last for three years and produce the following cash inflows:

Year Cool Hot

1 $ 37,000 $ 40,000

2 40,000 40,000

3 45,000 40,000

$122,000 $120,000

The equipment will have no salvage value at the end of its three-year life. Vista Company depreciates equipment using the straight-line method, and requires a minimum rate of return of 9%.

Present value data are as follows:

Present Value of 1 Present Value of an Annuity of 1

Period 9% Period 9%

1 .917 1 .917

2 .842 2 1.759

3 .772 3 2.531

Instructions

a) Calculate the net present value of each project.

b) Calculate the profitability index of each project.

c) Which project should be selected? Why?

Solution 105 (12–16 min.)

a) Project Cool

Year Annual Cash Inflows Present Value of 1 Present Value

1 $ 37,000 .917 $ 33,929

2 40,000 .842 33,680

3 45,000 .772 34,740

$122,000 $102,349

Present value of cash inflows $102,349

Capital investment 87,000

Net present value $ 15,349

Project Hot

Present value of cash inflows ($40,000 × 2.531) $101,240

Capital investment 87,000

Net present value $ 14,240

b) Cool Hot __

Profitability index: $102,349 ÷ $87,000 = 1.176 ($101,240 ÷ $87,000) = 1.164

c) Both projects are acceptable because both show a positive net present value. Project Cool is the preferred project because its net present value is greater than project Hot's net present value and it has a slightly higher profitability index.

Exercise 106

Platoon Company is performing a post-audit of a project that was estimated to cost $300,000, have a useful life of 6 years with a zero salvage value, and result in net cash inflows of $70,000 per year. After the investment has been in operation for a year, revised figures indicate that it actually cost $340,000, will have a 9-year useful life, and will produce net cash inflows of $58,000. The present value of an annuity of 1 for 6 years at 10% is 4.355 and for 9 years is 5.759.

Instructions

Determine whether the project should have been accepted based on

a) the original estimates and then on

b) the actual amounts.

Solution 106 (8–12 min.)

a) Present value of the estimated net cash inflows ($70,000 × 4.355) $304,850

Estimated capital investment 300,000

Net present value $ 4,850

Yes, Platoon Company should have invested in the project based on the original estimates, since the net present value is positive.

b) Present value of the actual net cash inflows ($58,000 x 5.759) $334,022

Actual capital investment 340,000

Net present value ($ 5,978)

Platoon should not have invested in the project based on the actual amounts, since the net present value is negative. The decrease of $10,828 in net present value was caused due to a decrease of $12,000 per year in net cash inflows and a $40,000 increase in the cost of the capital investment. This more than offsets the 3-year increase in useful life.

Exercise 107

Sophie’s Pet Shop is considering the purchase of a new delivery van. Sophie Smith, owner of the shop, has compiled the following estimates in trying to determine whether the delivery van should be purchased:

Cost of the van $25,000

Annual net cash flows 4,300

Salvage value 3,000

Estimated useful life 8 years

Cost of capital 10%

Present value of an annuity of 1 5.335

Present value of 1 .467

Sophie's assistant manager is trying to convince Sophie that the van has other benefits that she hasn't considered in the initial estimates. These additional benefits, including the free advertising the store's name painted on the van's doors will provide, are expected to increase net cash flows by $500 each year.

Instructions

a) Calculate the net present value of the van, based on the initial estimates. Should the van be purchased?

b) Calculate the net present value, incorporating the additional benefits suggested by the assistant manager. Should the van be purchased?

c) Determine how much the additional benefits would have to be worth in order for the van to be purchased.

Solution 107 (15–19 min.)

a) Present value of annual net cash flows ($4,300 × 5.335) $22,941

Present value of salvage value ($3,000 ×.467) 1,401

$24,342

Capital investment 25,000

Net present value ($ 658)

Based on the negative net present value of $658, the van should not be purchased.

b) Present value of annual cash flows [($4,300 + $500) × 5.335] $25,608

Present value of salvage value ($3,000 ×.467) 1,401

$27,009

Capital investment 25,000

Net present value $ 2,009

Incorporating the additional benefits of $500/year into the calculation produces a positive net present value of $2,009. Therefore, the van should be purchased.

c) The additional benefits would need to have a total present value of at least $658 in order for the van to be purchased.

Exercise 108

Blue Jay Corp. is thinking about opening a baseball camp in Oakville. In order to start the camp, the company would need to purchase land, build five baseball fields, and a dormitory-type sleeping and dining facility to house 100 players. Each year the camp would be run for 10 sessions of 1 week each. The company would hire college baseball players as coaches. The camp attendees would be baseball players age 12-18. Property values in Oakville have enjoyed a steady increase in value. It is expected that after using the facility for 20 years, Blue Jay can sell the property for more than it was originally purchased for. The following amounts have been estimated:

Cost of land $ 600,000

Cost to build dorm and dining facility 2,100,000

Annual cash inflows assuming 100 players and 10 weeks 2,520,000

Annual cash outflows 2,250,000

Estimated useful life 20 years

Salvage value 3,900,000

Discount rate 10%

Present value of an annuity of 1 8.514

Present value of 1 .149

Instructions

a) Calculate the net present value of the project.

b) To gauge the sensitivity of the project to these estimates, assume that if only 80 campers attend each week, revenues will be $2,085,000 and expenses will be $1,875,000. What is the net present value using these alternative estimates? Discuss your findings.

c) Assuming the original facts, what is the net present value if the project is actually riskier than first assumed, and a 12% discount rate is more appropriate? The present value of 1 at 12% is.104 and the present value of an annuity of 1 is 7.469.

Solution 108 (15–20 min.)

a) Present value of net cash flows ($270,000 × 8.514) $2,298,780

Present value of salvage value ($3,900,000 ×.149) 581,100

$2,879,880

Capital investment ($600,000 + $2,100,000) 2,700,000

Net present value $ 179,880

b) Present value of net cash flows ($210,000 × 8.514) $1,787,940

Present value of salvage value 581,100

$2,369,040

Capital investment 2,700,000

Net present value ($ 330,960)

If the number of campers attending each week is only 80 instead of 100, the net present value decreases by $510,840 (from a positive $179,880 to a negative $330,960). This indicates that the camp should not be invested in unless the number attending is closer to 100.

c) Present value of net cash flows ($270,000 × 7.469) $2,016,630

Present value of salvage value ($3,900,000 ×.104) 405,600

$2,422,230

Capital investment 2,700,000

Net present value ($ 277,770)

Exercise 109

Myrna’s Gardening is considering the purchase of new lawn equipment. A supplier has offered a package that will replace Myrna’s current equipment. The package price is $30,000. Myrna believes the equipment will make her more efficient, and therefore it will increase her annual net cashflow by $5,000. The equipment will have a 9-year useful life and have no salvage value. Myrna’s cost of capital is 8%.

Instructions

a) Calculate the cash payback period.

b) Calculate the machine’s internal rate of return.

c) Calculate the machine’s net present value using a discount rate of 8%.

d) Is the investment acceptable? Why or why not?

Present Value of an Annuity of 1

Period 6% 8% 9% 10%

9 6.80169 6.24689 5.99525 5.75902

Present Value of 1

Period 6% 8% 9% 10%

9 0.59190 0.50025 0.46043 0.42410

Solution 109 (13–18 min.)

a) Cash payback period: $30,000 ÷ $5,000 = 6 years

b) Internal rate of return: Scanning the 9-year line, a factor of 6 represents an internal rate of return of approximately 9%. The factor at 9% is actually 5.99525.

c) Net present value using a discount rate of 8%:

Time Period Cash Flow PV Factor Present Value

-0- ($30,000) 1.0000 ($30,000.00)

1–9 5,000 6.24689 31,234.45

Net Present Value $ 1,234.45

d) Yes, the investment is acceptable. Indications are that the investment will earn a return greater than 8%. The internal rate of return is estimated to be 9%, and the net present value is positive.

Exercise 110

Tom Bat became a baseball enthusiast at a very early age. All of his baseball experience has provided him valuable knowledge of the sport, and he is thinking about going into the batting cage business. He estimates the construction of a state-of-the-art facility and the purchase of the necessary equipment will cost $539,000. Both the facility and the equipment will be depreciated over 14 years using the straight-line method and are expected to have zero salvage values. His required rate of return is 12% (present value factor of 6.6282). Estimated annual net income is as follows:

Revenue $270,000

Less:

Utility cost 28,000

Supplies 7,500

Labour 110,000

Depreciation 38,500

Other 23,000 207,000

Net income $63,000

Instructions

For this investment, calculate:

a) The net present value.

b) The internal rate of return.

c) The cash payback period.

Solution 110 (12–16 min.)

a) Net present value of the investment:

Item Present Value Cash Flow Factor Present Value

Initial Investment ($539,000) 1.0000 ($539,000)

Revenue $270,000

Expense (168,500)* 101,500 6.6282 672,762

Net Present Value $133,762

*$28,000 + $7,500 + $110,000 + $23,000

b) Internal rate of return of the investment:

$539,000 ÷ $101,500 = 5.310

Scanning the 14-year line, a factor of 5.310 represents an IRR of between 16 and 17%, well above the required rate of return of 12%

c) Cash payback period of the investment:

$539,000 ÷ $101,500 = 5.31 years.

Exercise 111

Santana Company is considering investing in a project that will cost $67,000 and have no salvage value at the end of its 7-year life. It is estimated that the project will generate annual cash inflows of $16,000 each year. The company requires a 10% rate of return and uses the following compound interest table:

Present Value of an Annuity of 1 _

Period 6% 8% 9% 10% 11% 12% 15%

7 5.582 5.206 5.033 4.868 4.712 4.564 4.160

Instructions

a) Calculate (1) the net present value and (2) the profitability index of the project.

b) Calculate the internal rate of return on this project.

c) Should Santana invest in this project?

Solution 111 (10–18 min.)

a) (1) Present value of cash inflows ($16,000 × 4.868) $77,888

Capital investment 67,000

Net present value $10,888

(2) Profitability index: $77,888 ÷ $67,000 = 1.163

b) Capital Investment

—————————–— = Internal Rate of Return Factor

Net Annual Cash Inflow

$67,000

———— = 4.188

$16,000

Since the calculated internal rate of return factor of 4.188 is very near the factor 4.160 for seven periods and 15% interest, this project has an approximate interest yield of 15%.

c) Santana should invest in this project because it has a positive net present value, a profitability index above 1, and its internal rate of return of 15% is greater than the company's 10% required rate of return.

Exercise 112

Johnson Company is considering purchasing one of two new machines. The following estimates are available for each machine:

Machine 1 Machine 2

Initial cost $152,000 $170,000

Annual cash inflows 50,000 60,000

Annual cash outflows 15,000 20,000

Estimated useful life 6 years 6 years

The company's minimum required rate of return is 9%.

Present Value of an Annuity of 1

Period 8% 9% 10% 11% 12% 15%

6 4.623 4.486 4.355 4.231 4.111 3.784

Instructions

a) Calculate the (1) net present value, (2) profitability index, and (3) internal rate of return for each machine.

b) Which machine should be purchased?

Solution 112 (12–16 min.)

a) Machine 1 Machine 2

(1) Present value of net cash flows $157,010* $179,440**

Capital investment 152,000 170,000

Net present value $ 5,010 $ 9,440

*($35,000 × 4.486)

**($40,000 × 4.486)

Machine 1 Machine 2

$157,010 $179,440

(2) Profitability index ———–— = 1.03 ———–— = 1.06

$152,000 $170,000

(3) Machine 1 Machine 2___

Internal rate of return factor $152,000 $170,000

———–— = 4.34 ———–— = 4.25

$35,000 $40,000

Internal rate of return 10% (4.355 factor) 11% (4.231 factor)

b) Both machines are acceptable because both show a positive net present value, have a profitability index above 1, and have an internal rate of return greater than the company's minimum required rate of return. Machine 2 is preferred because its net present value, profitability index, and internal rate of return are all greater than Machine 1's amounts.

Exercise 113

M&H Inc. delivers groceries for seniors. The company is considering purchasing a new van for $27,000. The van is expected to last 7 years and have a salvage value of $2,000. M&H will use the straight-line depreciation method. M&H estimates the van will generate revenue of $15,000 per year, and incur expenses of $7,000 plus depreciation. M&H’s cost of capital is 6%.

Instructions

For the new van, calculate the:

a) cash payback period.

b) net present value.

c) annual rate of return.

Present Value of an Annuity of 1

Period 6%

7 5.58238

Present Value of 1

Period 6%

7 0.66506

Solution 113 (16–22 min.)

a) Total annual cash flow: $15,000 – $7,000 = $8,000

$27,000

Cash payback: ———— = 3.375 years

$8,000

b) Present value of cash flow ($8,000 × 5.58238) = $44,659.04

Present value of salvage ($2,000 x 0.66506) = 1,330.12

45,989.16

Capital investment 27,000.00

Net present value $ 18,989.16

c) $27,000 + $2,000

Average Investment: ————————— = $14,500

2

$27,000 - $2,000

Annual Depreciation: ————————— = $3,571

7 years

Annual Net Income: $8,000 – $3,571 = $4,429

$4,429

Average Annual Rate of Return: ———— = 30.5%

$14,500

Exercise 114

Mimi Company is considering a capital investment of $570,000 in new equipment. The equipment is expected to have a 15-year useful life with no salvage value. Depreciation is calculated using the straight-line method. During the life of the investment, annual net income and cash inflows are expected to be $63,000 and $101,000, respectively. Mimi's minimum required rate of return is 11%. The present value of 1 for 15 periods at 11% is 0.209 and the present value of an annuity of 1 for 15 periods at 11% is 7.191.

Instructions

Calculate each of the following:

a) cash payback period.

b) net present value.

c) annual rate of return.

Solution 114 (10–15 min.)

a) Cash payback period = $570,000 ÷ $101,000 = 5.64 years

b) Present value of cash inflows ($101,000 × 7.191) = $726,291

Capital investment 570,000

Net present value $ 156,291

c) Annual rate of return = $63,000 ÷ [($570,000 + $0) ÷ 2] = 22.1%

Exercise 115

Dog River Company is considering two capital investment proposals. Relevant data on each project are as follows:

Project Red Project Blue

Capital investment $210,000 $980,000

Annual net income 15,000 90,000

Estimated useful life 7 years 7 years

Depreciation is calculated using the straight-line method with no salvage value. Dog River requires a 10% rate of return on all new investments. The present value of 1 for 7 periods at 10% is 0.513 and the present value of an annuity of 1 for 7 periods is 4.868.

Instructions

a) Calculate the cash payback period for each project.

b) Calculate the net present value for each project.

c) Calculate the annual rate of return for each project.

d) Which project should Dog River select?

Solution 115 (14–18 min.)

a) Project Red Project Blue

Annual net income $15,000 $90,000

Annual depreciation 30,000* 140,000**

Annual cash inflow $45,000 $230,000

*($210,000 ÷ 7)

**($980,000 ÷ 7)

$210,000 $980,000

Cash payback period: ———— = 4.67 years ———— = 4.26 years

$45,000 $230,000

b) Project Red Project Blue

Present value of cash inflows: $219,060* $1,119,640**

Capital investment 210,000 980,000

Net present value $ 9,060 $ 139,640

*($45,000x4.868)

**(230,000 x 4.868)

c) Annual rate of return: Project Red Project Blue

$15,000 $90,000

————————— = 14.3% ————————— = 18.4%

($210,000 + $0) ÷ 2 ($980,000 + $0) ÷ 2

d) Dog River should select Project Blue because it has a larger positive net present value and a higher annual rate of return. In addition, Project Blue has a slightly shorter cash payback period.

Exercise 116

Yappy Company is considering a capital investment of $320,000 in additional equipment. The new equipment is expected to have a useful life of 8 years with no salvage value. Depreciation is calculated by the straight-line method. During the life of the investment, annual net income and cash inflows are expected to be $22,000 and $62,000, respectively. Yappy requires a 9% return on all new investments.

Present Value of an Annuity of 1

Period 8% 9% 10% 11% 12% 15%

8 5.747 5.535 5.335 5.146 4.968 4.487

Instructions

a) Calculate each of the following:

1. Cash payback period.

2. Net present value.

3. Profitability index.

4 Internal rate of return.

5. Annual rate of return.

b) Indicate whether the investment should be accepted or rejected.

Solution 116 (15–20 min.)

a) 1. Cash payback period: $320,000 ÷ $62,000 = 5.16 years

2. Present value of cash inflows ($62,000 × 5.535) $343,170

Capital investment 320,000

Net present value $ 23,170

3. Profitability index: $343,170 ÷ $320,000 = 1.07

4. Internal rate of return factor: $320,000 ÷ $62,000 = 5.16

Internal rate of return = 11% (5.146 factor)

5. Annual rate of return: $22,000 ÷ [($320,000 + $0) ÷ 2] = 13.75%

b) Yappy should accept the investment, since its net present value is positive and its internal rate of return of 11% is greater than the company's required rate of return of 9%. In addition, its cash payback period of 5.16 years is significantly shorter than the equipment's useful life of 8 years.

Exercise 117

Franklin Corporation is considering purchasing a machine that would cost $450,000. It has an estimated life of five years and no salvage value. The company estimates that annual revenues would increase by $200,000 and that annual expenses excluding depreciation would increase by $95,000. It uses the straight-line method to calculate depreciation expense. Management has a required rate of return of 7%.

Instructions

Calculate the annual rate of return and indicate if Franklin should make the purchase.

Solution 117 (15 min.)

Revenues $200,000

Less:

Expenses (excluding depreciation) $95,000

Depreciation ($450,000 ÷ 5 years) 90,000 185,000

Annual net income $ 15,000

Average investment = ($450,000 + 0) ÷ 2 = $225,000.

Annual rate of return = $15,000 ÷ $225,000 = 6.66%.

Since the annual rate of return (6.66%) is less than Franklin’s required rate of return (7%),

the proposed project is rejected.

COMPLETION STATEMENTS

118. For purposes of capital budgeting, estimated ___ and outflows are preferred for inputs into the capital budgeting decision tools.

119. The technique that identifies the time period required to recover the cost of the investment is called the ___ method.

120. Under the net present value method, the interest rate to be used in discounting the future cash inflows is the ___.

121. In using the net present value approach, a project is acceptable if the project's net present value is ___ or ___.

122. A project’s ___ benefits, such as increased quality or safety, are often incorrectly ignored in capital budgeting decisions.

123. The ___ is a method of comparing alternative projects that takes into account both the size of the investment and its discounted future cash flows.

124. A well-run organization should perform an evaluation, called a ___, of its investment projects after their completion.

125. The two discounted cash flow techniques used in capital budgeting are (1) the ___ method and (2) the ___ method.

126. The internal rate of return method differs from the net present value method in that it results in finding the ___ of the potential investment.

127. A major limitation of the annual rate of return approach is that it does not consider the ___ of money.

ANSWERS TO COMPLETION STATEMENTS

118. cash inflows

119. cash payback

120. required rate of return (or hurdle rate, discount rate, or cut off rate)

121. zero, positive

122. intangible

123. profitability index

124. post-audit

125. net present value, internal rate of return

126. interest yield

127. time value

MATCHING

128. Match the items below by entering the appropriate code letter in the space provided.

A. Profitability index E. Annual rate of return method

B. Internal rate of return method F. Cash payback technique

C. Discounted cash flow techniques G. Cost of capital

D. Capital budgeting H. Net present value method

___ 1. A capital budgeting technique that identifies the time period required to recover the cost of a capital investment from the annual cash inflow produced by the investment.

___ 2. Capital budgeting techniques that consider both the estimated total cash inflows from the investment and the time value of money.

___ 3. A method used in capital budgeting in which cash inflows are discounted to their present value and then compared to the capital outlay required by the capital investment.

___ 4. A method of comparing alternative projects that take into account both the size of the investment and its discounted cash flows.

___ 5. A method used in capital budgeting that results in finding the interest yield of the potential investment.

___ 6. The average rate of return that the firm must pay to obtain debt and equity funds.

___ 7. The determination of the profitability of a capital expenditure by dividing expected annual net income by the average investment.

___ 8. The process of making capital expenditure decisions in business.

ANSWERS TO MATCHING

1. F

2. C

3. H

4. A

5. B

6. G

7. E

8. D

SHORT-ANSWER ESSAY QUESTIONS

SAE 129

Sam Stanton is on the capital budgeting committee for his company, Stanton Tile. Ed Rhodes is an engineer for the firm. Ed expresses his disappointment to Sam that a project that was given to him to review before submission looks extremely good on paper. "I really hoped that the cost projections wouldn't pan out," he tells his friend. "The technology used in this is pie in the sky kind of stuff. There are a hundred things that could go wrong. But the figures are very convincing. I haven't sent it in yet, though I probably should."

"You can keep it if it's really that bad," assures Sam. "Anyway, you can probably get it shot out of the water pretty easily, and not have the guy who submitted it mad at you for not turning it in. Just fix the numbers. If you figure, for instance, that a cost is only 50% likely to be that low, then double it. We do it all the time, informally. Best of all, the rank and file don't get to come to those sessions. Your engineering genius need never know. He'll just think someone else's project was even better than his."

Instructions

a) Who are the stakeholders in this situation?

b) Is it ethical to adjust the figures to compensate for risk? Explain.

c) Is it ethical to change the proposal before submitting it? Explain.

Solution 129

a) The stakeholders include:

Ed Rhodes

Stanton Tile

the engineer who submitted the proposal.

b) It is ethical, in general, to adjust projections to compensate for risk. However, it should be clearly stated that the projections have been adjusted for risk, and the method used should be available for review. Otherwise, the entire selection process is undermined, and it becomes entirely subjective.

c) It is probably not ethical to modify a proposal at all; certainly not in the way described. The person submitting the proposal should have the right to know about any changes that were made, and should have the right to review those changes.

SAE 130

You are a general accountant for North Saskatchewan River Health Centre, a hospital based in a northern Saskatchewan city. The hospital has decided to upgrade its health records system. The hospital wishes to invest in electronic health records software and to improve its documentation and retrieval of records capabilities.

Two options have emerged. Option #1 is for the hospital to keep its existing computer system, and upgrade its scanning and retrieval software. The memory of each individual work station would be enhanced, and larger, more efficient scanners would be used. Better telecommunications equipment would allow for the electronic transmission of some documents as well.

Option #2 would be for the hospital to invest in an entirely different computer system. The software for this system is extremely impressive, and it automatically creates a permanent electronic health record, which could be accessed by various health care providers. However, the software provider is not well known, and the software does not connect well with other software used by the hospital. The net present value information for these options follows:

Option #1 Option #2

Initial Investment ($950,000) ($2,700,000)

Discounted Returns

Year 1 550,000 900,000

Year 2 300,000 900,000

Year 3 100,000 900,000

Net present value 0 0

Instructions

Prepare a brief report for management making a recommendation for one system or the other, using the information given.

Solution 130

I recommend that the hospital accept Option #1, to purchase upgrades to our present system and to buy more efficient scanners. In the first place, the changes will be easier to implement because the equipment is similar to what is already used. Secondly, the hospital will have less money invested in the project, which decreases our risk of loss should the project fail. Option #2 appears to be too risky.

SAE 131

What is the internal rate of return and explain how does it differ from the net present value method?

Solution 131

The internal rate of return is the interest rate that will cause the present value of the proposed capital expenditure to equal the present value of the expected net annual cash flows. It is the rate that results in an NPV equal to zero.

The internal rate of return method differs from the net present value method since it finds the interest yield of the potential investment. As it solves for only a single discount rate over the life of the project we cannot use more than one discount rate to make risk adjustments.

On the other hand, the net present value method can be used in situations where the discount rate varies over the life of the project because of risk considerations. In addition, in evaluating different combinations of individual projects, we can add the NPVs of the individual projects in each combination to estimate the effect of accepting or rejecting a combination of projects as the result of the NPV method is a dollar amount, not a percentage.

SAE 132

Management uses several capital budgeting methods in evaluating projects for possible investment. Identify those methods that are more desirable from a conceptual standpoint, and briefly explain what features these methods have that make them more desirable than other methods. Also identify the least desirable method and explain its major weaknesses.

Solution 132

From a conceptual standpoint, the discounted cash flow methods (net present value and internal rate of return) are considered more desirable because they consider both the estimated cash flows and the time value of money. The time value of money is critical because of the long-term impact of capital budgeting decisions. Capital budgeting methods which do not consider the time value of money include annual rate of return and cash payback. The cash payback method is the least desirable because it also ignores the expected profitability of the project.

SAE 133

Explain two advantages and disadvantage of the annual rate of return method.

*Solution 133

The main advantages of the annual rate of return method are the simplicity of its calculation

and management’s familiarity with the accounting terms used in the calculation.

A major limitation of the annual rate of return method is that it does not consider the time value of money, as no consideration is given to whether cash inflows will occur early or late in the life of the investment. The time value of money can make a significant difference between the future value and the discounted present value of an investment. A second disadvantage is that this method relies on accrual accounting numbers rather than expected cash flows.

LEGAL NOTICE

Copyright © 2021 by John Wiley & Sons Canada, Ltd. or related companies. All rights reserved.

© John Wiley & Sons, Canada Ltd. or the author, All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course. Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.