# Solutions For Chapter 9

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Questions:

1. Payback Period – Given the cash flows of the four projects, A, B, C, and D, and using the Payback Period decision model, which projects do you accept and which projects do you reject with a three year cut-off period for recapturing the initial cash outflow? Assume that the cash flows are equally distributed over the year for Payback Period calculations.
 Projects A B C D Cost \$10,000 \$25,000 \$45,000 \$100,000 Cash Flow Year One \$4,000 \$2,000 \$10,000 \$40,000 Cash Flow Year Two \$4,000 \$8,000 \$15,000 \$30,000 Cash Flow Year Three \$4,000 \$14,000 \$20,000 \$20,000 Cash Flow Year Four \$4,000 \$20,000 \$20,000 \$10,000 Cash Flow year Five \$4,000 \$26,000 \$15,000 \$0 Cash Flow Year Six \$4,000 \$32,000 \$10,000 \$0
1. Payback Period – What are the Payback Periods of Projects E, F, G and H? Assume all cash flows are evenly spread throughout the year. If the cut-off period is three years, which projects do you accept?
 Projects E F G H Cost \$40,000 \$250,000 \$75,000 \$100,000 Cash Flow Year One \$10,000 \$40,000 \$20,000 \$30,000 Cash Flow Year Two \$10,000 \$120,000 \$35,000 \$30,000 Cash Flow Year Three \$10,000 \$200,000 \$40,000 \$30,000 Cash Flow Year Four \$10,000 \$200,000 \$40,000 \$20,000 Cash Flow year Five \$10,000 \$200,000 \$35,000 \$10,000 Cash Flow Year Six \$10,000 \$200,000 \$20,000 \$0
1. Discounted Payback Period – Given the following four projects and their cash flows, calculate the discounted payback period with a 5% discount rate, 10% discount rate, and 20% discount rate. What do you notice about the payback period as the discount rate rises? Explain this relationship.
 Projects A B C D Cost \$10,000 \$25,000 \$45,000 \$100,000 Cash Flow Year One \$4,000 \$2,000 \$10,000 \$40,000 Cash Flow Year Two \$4,000 \$8,000 \$15,000 \$30,000 Cash Flow Year Three \$4,000 \$14,000 \$20,000 \$20,000 Cash Flow Year Four \$4,000 \$20,000 \$20,000 \$10,000 Cash Flow year Five \$4,000 \$26,000 \$15,000 \$10,000 Cash Flow Year Six \$4,000 \$32,000 \$10,000 \$0
1. Discounted Payback Period – Graham Incorporated uses discounted payback period for projects under \$25,000 and has a cut off period of 4 years for these small value projects. Two projects, R and S are under consideration. The anticipated cash flows for these two projects are listed below. If Graham Incorporated uses an 8% discount rate on these projects are they accepted or rejected? If they use 12% discount rate? If they use a 16% discount rate? Why is it necessary to only look at the first four years of the projects’ cash flows?
 Cash Flows Project R Project S Initial Cost \$24,000 \$18,000 Cash flow year one \$6,000 \$9,000 Cash flow year two \$8,000 \$6,000 Cash flow year three \$10,000 \$6,000 Cash flow year four \$12,000 \$3,000
1. Comparing Payback Period and Discounted Payback Period – Mathew Incorporated is debating using Payback Period versus Discounted Payback Period for small dollar projects. The Information Officer has submitted a new computer project of \$15,000 cost. The cash flows will be \$5,000 each year for the next five years. The cut-off period used by Mathew Incorporated is three years. The Information Officer states it doesn’t matter what model the company uses for the decision, it is clearly an acceptable project. Demonstrate for the IO that the selection of the model does matter!
1. Comparing Payback Period and Discounted Payback Period – Neilsen Incorporated is switching from Payback Period to Discounted Payback Period for small dollar projects. The cut-off period will remain at 3 years. Given the following four projects cash flows and using a 10% discount rate, which projects that would have been accepted under Payback Period will now be rejected under Discounted Payback Period?
 Cash Flows Project One Project Two Project Three Project Four Initial cost \$10,000 \$15,000 \$8,000 \$18,000 Year One \$4,000 \$7,000 \$3,000 \$10,000 Year Two \$4,000 \$5,500 \$3,500 \$11,000 Year Three \$4,000 \$4,000 \$4,000 \$0
1. Net Present Value – Swanson Industries has a project with the following projected cash flows:

Initial Cost, Year 0: \$240,000

Cash flow year one: \$25,000

Cash flow year two: \$75,000

Cash flow year three: \$150,000

Cash flow year four: \$150,000

1. Using a 10% discount rate for this project and the NPV model should this project be accepted or rejected?
2. Using a 15% discount rate?
3. Using a 20% discount rate?
1. Net Present Value – Campbell Industries has a project with the following projected cash flows:

Initial Cost, Year 0: \$468,000

Cash flow year one: \$135,000

Cash flow year two: \$240,000

Cash flow year three: \$185,000

Cash flow year four: \$135,000

1. Using an 8% discount rate for this project and the NPV model should this project be accepted or rejected?
2. Using a 14% discount rate?
3. Using a 20% discount rate?
1. Net Present Value – Swanson Industries has four potential projects all with an initial cost of \$2,000,000. The capital budget for the year will only allow Swanson industries to accept one of the four projects. Given the discount rates and the future cash flows of each project, which project should they accept?
 Cash Flows Project M Project N Project O Project P Year one \$500,000 \$600,000 \$1,000,000 \$300,000 Year two \$500,000 \$600,000 \$800,000 \$500,000 Year three \$500,000 \$600,000 \$600,000 \$700,000 Year four \$500,000 \$600,000 \$400,000 \$900,000 Year five \$500,000 \$600,000 \$200,000 \$1,100,000 Discount Rate 6% 9% 15% 22%
1. Net Present Value – Campbell Industries has four potential projects all with an initial cost of \$1,500,000. The capital budget for the year will only allow Swanson industries to accept one of the four projects. Given the discount rates and the future cash flows of each project, which project should they accept?
 Cash Flows Project Q Project R Project S Project T Year one \$350,000 \$400,000 \$700,000 \$200,000 Year two \$350,000 \$400,000 \$600,000 \$400,000 Year three \$350,000 \$400,000 \$500,000 \$600,000 Year four \$350,000 \$400,000 \$400,000 \$800,000 Year five \$350,000 \$400,000 \$300,000 \$1,000,000 Discount Rate 4% 8% 13% 18%
1. Internal Rate of Return – What are the IRRs of the four projects for Swanson Industries in problem #9?
2. Internal Rate of Return — Internal Rate of Return – What are the IRRs of the four projects for Campbell Industries in problem #10?
3. Comparing NPV and IRR – Chandler and Joey were having a discussion about which financial model to use for their new business. Chandler supports NPV and Joey supports IRR. The discussion starts to get heated when Ross steps in and states, “gentlemen, it doesn’t matter which method we choose, they give the same answer on all projects.” Is Ross right? Under what conditions will IRR and NPV be consistent when accepting or rejecting projects?
4. Comparing NPR and IRR – Monica and Rachel are having a discussion about IRR and NPV as a decision model for Monica’s new restaurant. Monica wants to use IRR because it gives a very simple and intuitive answer. Rachel states that there can be errors made with IRR that are not made with NPV. Is Rachel right? Show one type of error can be made with IRR and not with NPV?
5. Profitability Index — Given the discount rates and the future cash flows of each project, which projects should they accept using profitability index?
 Cash Flows Project U Project V Project W Project X Year zero -\$2,000,000 -\$2,500,000 -\$2,400,000 -\$1,750,000 Year one \$500,000 \$600,000 \$1,000,000 \$300,000 Year two \$500,000 \$600,000 \$800,000 \$500,000 Year three \$500,000 \$600,000 \$600,000 \$700,000 Year four \$500,000 \$600,000 \$400,000 \$900,000 Year five \$500,000 \$600,000 \$200,000 \$1,100,000 Discount Rate 6% 9% 15% 22%
1. Profitability Index — Given the discount rates and the future cash flows of each project, which projects should they accept using profitability index?
 Cash Flows Project A Project B Project C Project D Year zero -\$1,500,000 -\$1,500,000 -\$2,000,000 -\$2,000,000 Year one \$350,000 \$400,000 \$700,000 \$200,000 Year two \$350,000 \$400,000 \$600,000 \$400,000 Year three \$350,000 \$400,000 \$500,000 \$600,000 Year four \$350,000 \$400,000 \$400,000 \$800,000 Year five \$350,000 \$400,000 \$300,000 \$1,000,000 Discount Rate 4% 8% 13% 18%
1. Comparing All Methods — Given the following After Tax Cash Flows for Tyler’s Tinkering Toys on a new toy find the Payback Period, NPV, and Profitability Index of this project. The appropriate discount rate for the project is 12%. If the cut-off period is six years for major projects, determine if the project is accepted or rejected under the four different decision models.

Year 0 cash outflow: \$10,400,000

Years 1 to 4 cash inflow: \$2,600,000 each year

Year 5 cash outflow: \$1,200,000

Years 6 – 8 cash inflow: \$750,000 each year

1. Comparing All Methods — Tom’s Risky Business is looking at a project with the estimated cash flows as follows:

Initial Investment at start of project: \$3,600,000

Cash Flow at end of Year 1: \$500,000

Cash Flow at end of Years 2 through 6: \$625,000 each year

Cash Flow at end of Year 7 through 9: \$530,000 each year

Cash Flow at end of Year 10: \$385,000

Risky Business wants to know the Payback Period, NPV, and Profitability Index of this project. The appropriate discount rate for the project is 14%. If the cut-off period is six years for major projects, determine if the project is accepted or rejected under the four different decision models.