# Finance – fundamentals of capital budgeting

The Fundamentals of Capital Budgeting

Section 10.1

1.      Why capital investments are considered the most important decisions made by a firm’s management?

2.     What are the differences between capital projects that are independent, mutually exclusive, and contingent?

Section 10.2

1.                  What is the NPV of a project?

2.                  If a firm accepts a project with a \$10,000 NPV, what is the effect on the value of the firm?

3.            What are the five steps used in NPV analysis?

The five-step process used in the NPV analysis can be listed as follows:

Section 10.3

1.                  What is the payback period?

2.                  Why does the payback period provide a measure of a project’s liquidity risk?

3.         What are the main shortcomings of the payback method?

Section 10.4

1.            What are the major shortcomings of using the ARR method as a capital budgeting method?

Section 10.5

1.      What is the IRR method?

2.      In capital budgeting, what is a conventional cash flow pattern?

3.      Why should the NPV method be the primary decision tool used in making capital investment decisions?

Section 10.6

1.   What changes have taken place in the capital budgeting techniques used by U.S. companies?

Self-Study Problems

10.1     Premium Manufacturing Company is evaluating two forklift systems to use in its plant that produces the towers for a windmill power farm. The costs and the cash flows from these systems are shown below. If the company uses a 12 percent discount rate for all projects, determine which forklift system should be purchased using the net present value (NPV) approach.

 Year 0 Year 1 Year 2 Year 3 Otis Forklifts −\$3,123,450 \$979,225 \$1,358,886 \$2,111,497 Craigmore Forklifts −\$4,137,410 \$875,236 \$1,765,225 \$2,865,110

10.2     Rutledge, Inc., has invested \$100,000 in a project that will produce cash flows of \$45,000, \$37,500, and \$42,950 over the next three years. Find the payback period for the project.

10.3     Perryman Crafts Corp. is evaluating two independent capital projects that together will cost the company \$250,000. The two projects will provide the following cash flows:

 Year Project A Project B 1 \$80,750 \$32,450 2 \$93,450 \$76,125 3 \$40,325 \$153,250 4 \$145,655 \$96,110

Which project will be chosen if the company’s payback criterion is three years?  What if the

company accepts all projects as long as the payback period is less than five years?

10.4     Terrell Corp. is looking into purchasing a machine for its business that will cost \$117,250 and will be depreciated on a straight-line basis over a five-year period. The sales and expenses (excluding depreciation) for the next five years are shown in the following table. The company’s tax rate is 34 percent.

 Year 1 Year 2 Year 3 Year 4 Year 5 Sales \$123,450 \$176,875 \$242,455 \$255,440 \$267,125 Expenses \$137,410 \$126,488 \$141,289 \$143,112 \$133,556

The company will accept all projects that provide an accounting rate of return (ARR) of at least 45 percent. Should the company accept this project?

The company will accept all projects that provide an accounting rate of return (ARR) of at least 45 percent. Should the company accept the project?

10.5          Refer to Problem 10.1. Compute the IRR for each of the two systems. Is the investment decision different from the one determined by NPV?

Critical Thinking Questions

10.1     Explain why the cost of capital is referred to as the “hurdle” rate in capital budgeting.

10.2     a.   A company is building a new plant on the outskirts of Smallesville. The town has offered to donate the land, and as part of the agreement, the company will have to build an access road from the main highway to the plant. How will the project of building the road be classified in capital budgeting analysis?

b.   Sykes, Inc., is considering two projects: a plant expansion and a new computer system for the firm’s production department. Classify these projects as independent, mutually exclusive, or contingent projects and explain your reasoning.

c.   Your firm is currently considering the upgrading of the operating systems of all the firm’s computers. The firm can choose the Linux operating system that a local computer services firm has offered to install and maintain. Microsoft has also put in a bid to install the new Windows operating system for businesses. What type of project is this?

10.3     In the context of capital budgeting, what is “capital rationing”?

10.4Provide two conditions under which a set of projects might be characterized as mutually exclusive.

10.5a.A firm invests in a project that would earn a return of 12 percent. If the appropriate cost of capital is also 12 percent, did the firm make the right decision. Explain.

b.What is the impact on the firm if it accepts a project with a negative NPV?

10.6     Identify the weaknesses of the payback period method..

10.7     What are the strengths and weaknesses of the accounting rate of return (ARR) approach?

10.8     Under what circumstances might the IRR and NPV approaches have conflicting results?

10.9     The modified IRR (MIRR) alleviates two concerns with using the IRR method for evaluating capital investments. What are they?

10.10   Elkridge Construction Company has an overall (composite) cost of capital of 12 percent. This cost of capital reflects the cost of capital for an Elkridge Construction project with average risk. However, the firm takes on projects of various risk levels. The company experience suggests that low-risk projects have a cost of capital of 10 percent and high-risk projects have a cost of capital of 15 percent. Which of the following projects should the company select to maximize shareholder wealth?

Questions and Problems

BASIC

10.1     Net present value: Riggs Corp. management is planning to spend \$650,000 on a new marketing campaign. They believe that this action will result in additional cash flows of \$325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV on this project?

LO 2

10.2     Net present value: Kingston, Inc. management is considering purchasing a new machine at a cost of \$4,133,250. They expect this equipment to produce cash flows of \$814,322, \$863,275, \$937,250, \$1,017,112, \$1,212,960, and \$1,225,000 over the next six years. If the appropriate discount rate is 15 percent, what is the NPV of this investment?

LO 2

10.3     Net present value: Crescent Industries management is planning to replace some existing machinery in its plant. The cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses an 18 percent discount rate, should management go ahead with the project?

 Year Cash Flow 0 −\$3,300,000 1 \$875,123 2 \$966,222 3 \$1,145,000 4 \$1,250,399 5 \$1,504,445

LO 2

10.4     Net present value:Franklin Mints, a confectioner, is considering purchasing a new jellybean-making machine at a cost of \$312,500. The company’s management projects that the cash flows from this investment will be \$121,450 for the next seven years. If the appropriate discount rate is 14 percent, what is the NPV for the project?

LO

10.5     Net present value: Blanda Incorporated management is considering investing in two alternative production systems. The systems are mutually exclusive, and the cost of the new equipment and the resulting cash flows are shown in the accompanying table.  If the firm uses a 9 percent discount rate for their production systems, in which system should the firm invest?

LO 2

 Year System 1 System 2 0 -15,000 -45,000 1 15,000 32,000 2 15,000 32,000 3 15,000 32,000

10.6     Payback:  Refer to problem 10.5.  What are the payback periods for production systems 1 and 2?  If the systems are mutually exclusive and the firm always chooses projects with the lowest payback period, in which system should the firm invest?

LO 3

10.7     Payback: Quebec, Inc., is purchasing machinery at a cost of \$3,768,966. The company’s management expects the machinery to produce cash flows of \$979,225, \$1,158,886, and \$1,881,497 over the next three years, respectively. What is the payback period?

LO 3

10.8     Payback: Northern Specialties just purchased inventory-management computer software at a cost of \$1,645,276. Cost savings from the investment over the next six years will be reflected in the following cash flow stream: \$212,455, \$292,333, \$387,479, \$516,345, \$645,766, and \$618,325. What is the payback period on this investment?

LO 3

10.9     Payback: Nakamichi Bancorp has made an investment in banking software at a cost of \$1,875,000. Management expects productivity gains and cost savings over the next several years. If the firm is expected to generate cash flows of \$586,212, \$713,277, \$431,199, and \$318,697 over the next four years, what is the investment’s payback period?

LO 3

10.10   Average accounting rate of return (ARR): Capitol Corp. is expecting a project to generate after-tax income of \$63,435 over each of the next three years. The average book value of its equipment over that period will be \$212,500. If the firm’s acceptance decision on any project is based on an ARR of 37.5 percent, should this project be accepted?

LO 4

10.11   Internal rate of return:Refer to Problem 10.4. What is the IRR that Franklin Mints management can expect on this project?

LO 5

10.12   Internal rate of return:Hathaway, Inc., a resort company, is refurbishing one of its hotels at a cost of \$7.8 million. The firm expects that this will lead to additional cash flows of \$1.8 million for the next six years. What is the IRR of this project? If the appropriate cost of capital is 12 percent, should Hathaway go ahead with this project?

LO 5

INTERMEDIATE

10.13   Net present value: Champlain Corp. is investigating two computer systems. The Alpha 8300 costs \$3,122,300 and will generate annual cost savings of \$1,345,500 over the next five years. The Beta 2100 system costs \$3,750,000 and will produce cost savings of \$1,125,000 in the first three years and then \$2 million for the next two years. If the company’s discount rate for similar projects is 14 percent, what is the NPV for the two systems? Which one should be chosen based on the NPV?

LO 2

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10.14   Net present value:Briarcrest Condiments is a spice-making firm. Recently, it developed a new process for producing spices. This process requires new machinery that would cost \$1,968,450, have a life of five years and would produce cash flows as shown in the table. What is the NPV if the firm uses a discount rate of 15.9 percent?

 Year Cash Flow 1 \$512,496 2 \$(242,637) 3 \$814,558 4 \$887,225 5 \$712,642

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10.15   Net present value:Cranjet Industries is expanding its product line and its production capacity. The costs and expected cash flows of the two independent projects are given in the following table. The firm typically uses a discount rate of 16.4 percent.

a.         What are the NPVs of the two projects?

b          Should both projects be accepted? Or either? Or neither? Explain your reasoning.

 Year Product Line Expansion Production Capacity Expansion 0 \$(2,575,000) \$(8,137,250) 1 \$600,000 \$2,500,000 2 \$875,000 \$2,500,000 3 \$875,000 \$2,500,000 4 \$875,000 \$3,250,000 5 \$875,000 \$3,250,000

LO 2

10.16   Net present value:Emporia Mills is evaluating two alternative heating systems. Costs and projected energy savings are given in the following table. The firm uses 11.5 percent to discount such project cash flows. Which system should be chosen?

 Year System 100 System 200 0 \$(1,750,000) \$(1,735,000) 1 \$275,223 \$750,000 2 \$512,445 \$612,500 3 \$648,997 \$550,112 4 \$875,000 \$384,226

LO 2

10.17   Payback: Creative Solutions, Inc., has just invested \$4,615,300 in equipment. The firm uses payback period criteria of not accepting any project that takes more than four years to recover its costs. The company anticipates cash flows of \$644,386, \$812,178, \$943,279, \$1,364,997, \$2,616,300, and \$2,225,375 over the next six years. Does this investment meet the firm’s payback criteria?

LO 3

10.18   Discounted payback: Timeline Manufacturing Co. is evaluating two projects. It uses payback criteria of three years or less. Project A has a cost of \$912,855, and project B’s cost is \$1,175,000. Cash flows from both projects are given in the following table. What are their discounted payback periods, and which will be accepted with a discount rate of 8 percent?

 Year Project A Project B 1 \$ 86,212 \$586,212 2 \$313,562 \$413,277 3 \$427,594 \$231,199 4 \$285,552

LO 3

10.19   Payback: Regent Corp. is evaluating three competing pieces of equipment. Costs and cash flow projections for all three are given in the following table. Which would be the best choice based on payback period?

 Year Type 1 Type 2 Type 3 0 \$(1,311,450) \$(1,415,888) \$(1,612,856) 1 \$212,566 \$586,212 \$786,212 2 \$269,825 \$413,277 \$175,000 3 \$455,112 \$331,199 \$175,000 4 \$285,552 \$141,442 \$175,000 5 \$121,396 \$175,000 6 \$175,000

LO 3

10.20   Discounted payback: Nugent Communication Corp. is investing \$9,365,000 in new technologies. The company expects significant benefits in the first three years after installation (as can be seen by the cash flows), and smaller constant benefits in each of the next four years. What is the discounted payback period for the project assuming a discount rate of 10 percent?

 Years 1 2 3 4 – 7 Cash flows \$2,265,433 \$4,558,721 \$3,378,911 \$1,250,000

LO 3

10.21   Modified internal rate of return (MIRR): Morningside Bakeries has recently purchased equipment at a cost of \$650,000. The firm expects to generate cash flows of \$275,000 in each of the next four years. The cost of capital is 14 percent. What is the MIRR for this project?

LO 5

10.22   Modified internal rate of return (MIRR): Sycamore Home Furnishings is considering acquiring a new machine that can create customized window treatments. The equipment will cost \$263,400 and will generate cash flows of \$85,000 over each of the next six years. If the cost of capital is 12 percent, what is the MIRR on this project?

LO 5

10.23   Internal rate of return:Great Flights, Inc., an aviation firm, is considering purchasing three aircraft for a total cost of \$161 million. The company would lease the aircraft to an airline. Cash flows from the proposed leases are shown in the following table. What is the IRR of this project?

 Years Cash Flow 1–4 \$23,500,000 5–7 \$72,000,000 8–10 \$80,000,000

LO 5

10.24   Internal rate of return:  Refer to problem 10.5.  Compute the IRR for both production system 1 and production system 2.  Which has the higher IRR?  Which production system has the highest NVP?  Explain why the IRR and NPV rankings of systems 1 and 2 are different?

LO 5

10.25  Internal rate of return:  Ancala Corporation is considering investments in two new golf apparel lines for next season: golf hats and belts.  Due to a funding constraint, these lines are mutually exclusive.  A summary of each project’s estimated cash flows over its three -year life, as well as the IRRs and NPVs of each are outlined below.  The CFO of the firm has decided to manufacture the belts; however, the CEO of Ancala is questioning this decision given that the IRR is higher for manufacturing hats.   Explain to the CEO why the IRRs and NPVs of the belt and hat projects disagree?  Is the CFO’s decision the correct .

 Year Golf Belts Golf Hats 0 -\$1,000 -\$500 1 1,000 500 2 500 300 3 500 300 NPV \$697.97 \$427.87 IRR 54% 61%

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10.26   Internal rate of return:Compute the IRR on the following cash flow streams:

a.         An initial investment of \$25,000 followed by a single cash flow of \$37,450 in year 6.

b.         An initial investment of \$1 million followed by a single cash flow of \$1,650,000 in year 4.

c.         An initial investment of \$2 million followed by cash flows of \$1,650,000 and \$1,250,000 in years 2 and 4, respectively.

LO 5

10.27   Internal rate of return:Compute the IRR for the following project cash flows.

a.         An initial outlay of \$3,125,000 followed by annual cash flows of \$565,325 for the next eight years

b.         An initial investment of \$33,750 followed by annual cash flows of \$9,430 for the next five years

c.         An initial outlay of \$10,000 followed by annual cash flows of \$2,500 for the next seven years

LO 5

10.28   Draconian Measures, Inc., is evaluating two independent projects. The company uses a 13.8 percent discount rate for such projects. The cost and cash flows are shown in the following table. What are the NPVs of the two projects?

 Year Project 1 Project 2 0 \$(8,425,375) \$(11,368,000) 1 \$3,225,997 \$2,112,589 2 \$1,775,882 \$3,787,552 3 \$1,375,112 \$3,125,650 4 \$1,176,558 \$4,115,899 5 \$1,212,645 \$4,556,424 6 \$1,582,156 7 \$1,365,882

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10.29   Refer to Problem 10.28.

a.         What are the IRRs for the projects?

b.         Does the IRR criterion indicate a different decision than the NPV criterion?

c.         Explain how you would expect the management of Draconian Measures to decide.

LO 5

10.30   Dravid, Inc., is currently evaluating three projects that are independent. The cost of funds can be either 13.6 percent or 14.8 percent depending on their financing plan. All three projects cost the same at \$500,000. Expected cash flow streams are shown in the following table. Which projects would be accepted at a discount rate of 14.8 percent? What if the discount rate was 13.6 percent?

 Year Project 1 Project 2 Project 3 1 0 0 \$245,125 2 \$125,000 0 \$212,336 3 \$150,000 \$500,000 \$112,500 4 \$375,000 \$500,000 \$74,000

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10.31   Intrepid, Inc., is looking to invest in two or three independent projects. The costs and the cash flows are given in the following table. The appropriate cost of capital is 14.5 percent. Compute the IRRs and identify the projects that will be accepted.

 Year Project 1 Project 2 Project 3 0 \$(275,000) \$(312,500) \$(500,000) 1 \$63,000 \$153,250 \$212,000 2 \$85,000 \$167,500 \$212,000 3 \$85,000 \$112,000 \$212,000 4 \$100,000 \$212,000

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10.32   Jekyll & Hyde Corp. is evaluating two mutually exclusive projects. The cost of capital is 15 percent. Costs and cash flows are given in the following table. Which project should be accepted?

 Year Project 1 Project 2 0 \$(1,250,000) \$(1,250,000) 1 \$250,000 \$350,000 2 \$350,000 \$350,000 3 \$450,000 \$350,000 4 \$500,000 \$350,000 5 \$750,000 \$350,000

LO 5

10.33   Larsen Automotive, a manufacturer of auto parts, is considering investing in two projects. The company typically compares project returns to a cost of funds of 17 percent. Compute the IRRs based on the given cash flows, and state which projects will be accepted.

 Year Project 1 Project 2 0 \$(475,000) \$(500,000) 1 \$300,000 \$117,500 2 \$110,000 \$181,300 3 \$125,000 \$244,112 4 \$140,000 \$278,955

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10.34   Compute the IRR for each of the following projects:

 Year Project 1 Project 2 Project 3 0 \$(10,000) \$(10,000) \$(10,000) 1 \$4,750 \$1,650 \$800 2 \$3,300 \$3,890 \$1,200 3 \$3,600 \$5,100 \$2,875 4 \$2,100 \$2,750 \$3,400 5 \$800 \$6,600

LO 5

10.35   Primus Corp. is planning to convert an existing warehouse into a new plant that will increase its production capacity by 45 percent. The cost of this project will be \$7,125,000. It will result in additional cash flows of \$1,875,000 for the next eight years. The company uses a discount rate of 12 percent.

a.         What is the payback period?

b.         What is the NPV for this project?

c.         What is the IRR?

LO 2, LO 3, LO 5

10.36   Quasar Tech Co. is investing \$6 million in new machinery that will produce the next-generation routers. Sales to its customers will amount to \$1,750,000 for the next three years and then increase to \$2.4 million for three more years. The project is expected to last six years and cost, excluding depreciation will be \$898,620 annually. The machinery will be depreciated to a salvage value of 0 over 6 years using the straight-line method. The company’s tax rate is 30 percent, and the cost of capital is 16 percent.

a.         What is the payback period?

b.         What is the average accounting return (ARR)?

c.         Calculate the project NPV.

d.         What is the IRR for the project?

LO 2, LO 3, LO 5

10.37   Skywards, Inc., an airline caterer, is purchasing refrigerated trucks at a total cost of \$3.25 million. After-tax net income from this investment is expected to be \$750,000 for the next five years. Annual depreciation expense will be \$650,000. The cost of capital is 17 percent.

a.         What is the discounted payback period?

b.         Compute the ARR.

c.         What is the NPV on this investment?

d.         Calculate the IRR.

LO 2, LO 3, LO 4, LO 5

10.38   Trident Corp. is evaluating two independent projects. The costs and expected cash flows are given in the following table. The company’s cost of capital is 10 percent.

 Year A B 0 \$(312,500) \$(395,000) 1 \$121,450 \$153,552 2 \$121,450 \$158,711 3 \$121,450 \$166,220 4 \$121,450 \$132,000 5 \$121,450 \$122,000

a.         Calculate the projects’ NPV.

b.         Calculate the projects’ IRR.

c.         Which project should be chosen based on NPV? Based on IRR? Is there a conflict?

d.         If you are the decision maker for the firm, which project or projects will be accepted? Explain your reasoning.

LO 2,  LO 5

10.39   Tyler, Inc., is considering switching to a new production technology. The cost of equipment will be \$4 million. The   discount rate is 12 percent. The cash flows that the firm expects to generate are as follows.

 Years CF 0 \$(4,000,000) 1-2 0 3–5 \$845,000 6–9 \$1,450,000

a.         Compute the payback and discounted payback period for the project.

b.         What is the NPV for the project? Should the firm go ahead with the project?

c.         What is the IRR, and what would be the decision under the IRR?

LO 2, LO 3, LO 5

10.40.  Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent.

 Year 0 1 2 3 4 5 Cash flow –50,000 15,000 15,000 20,000 10,000 5,000

NPV                IRR

a.         \$1,905             10.9%

b.         \$1,905             26.0%

c.         \$3,379             10.9%

d.         \$3,379             26.0%

LO 2

10.41.  Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent.

 Year 0 1 2 3 4 5 Cash flow –50,000 15,000 15,000 20,000 10,000 5,000

The discounted payback period is

a.         0.16 years longer than the payback period.

b.         0.80 years longer than the payback period.

c.         1.01 years longer than the payback period.

d.         1.85 years longer than the payback period.

LO 3

10.42.  An investment of \$100 generates after-tax cash flows of \$40 in Year 1, \$80 in Year 2, and \$120 in Year 3. The required rate of return is 20 percent. The net present value is closest to

a.         \$42.22

b.         \$58.33

c.         \$68.52

d.         \$98.95

LO 2

10.43.  An investment of \$150,000 is expected to generate an after-tax cash flow of \$100,000 in one year and another \$120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return?

a.         28.19 percent

b.         28.39 percent

c.         28.59 percent

d.         28.79 percent

LO 5

10.44.  An investment requires an outlay of 100 and produces after-tax cash flows of \$40 annually for four years. A project enhancement increases the outlay by \$15 and the annual after-tax cash flows by \$5. How will the enhancement affect the NPV profile?  The vertical intercept of the NPV profile of the project shifts:

a.         up and the horizontal intercept shifts left.

b.         up and the horizontal intercept shifts right.

c.         down and the horizontal intercept shifts left.

d.         down and the horizontal intercept shifts right.

LO 2

Sample Test Problems

10.1     Net present value: Techno Corp. is considering developing new computer software. The cost of development will be \$675,000, and the company expects the revenue from the sale of the software to be \$195,000 for each of the next six years. If the company uses a discount rate of 14 percent, what is the net present value of this project?

10.2     Payback method:Parker Office Supplies is considering replacing the company’s outdated inventory-management software. The cost of the new software will be \$168,000. Cost savings is expected to be \$43,500 for each of the first three years and then to drop off to \$36,875 for the following two years. What is the payback period for this project?

10.3     Accounting rate of return: Fresno, Inc., is expecting to generate after-tax income of \$156,435 in each of the next three years. The average book value of its equipment over that period will be \$322,500. If the firm’s acceptance decision on any project is based on an ARR of 40 percent, should this project be accepted?

10.4     Internal rate of return: Refer to  Sample Test Problem 10.1. What is the IRR on this project?

10.5     Net present value: Raycom, Inc. needs a new overhead crane and two alternatives are available. Crane T costs \$1.35 million and will produce cost savings of \$765,000 for the next three years. Crane R will cost \$1.675 million and will yield cost savings of \$815,000 for the next three years. The required rate of return is 15 percent. Which of the two options should Raycom choose based on NPV criteria and why?