Solutions to Chapter 9 Problems

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  1. Payback period. Given the cash flow of 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 four-year cutoff period for recapturing the initial cash outflow? For payback period calculations, assume that the cash flow is equally distributed over the year.
Cash flow A B C D
Cost $40,000 $25,000 $45,000 $120,000
Cash flow Year 1 $ 4,000 $ 5,000 $20,000 $ 75,000
Cash flow Year 2 $ 6,000 $ 5,000 $12,000 $ 25,000
Cash flow Year 3 $ 9,000 $ 5,000 $26,000 $ 20,000
Cash flow Year 4 $ 14,000 $ 5,000 $9,000 $ 15,000
Cash flow Year 5 $ 16,000 $ 5,000 $13,000 $ 0
Cash flow Year 6 $ 20,000 $ 5,000 $18,000 $ 0
  1. Payback period. What are the payback periods of Projects E, F, G and H? Assume all the cash flows are evenly spread throughout the year. If the cutoff period is three years, which projects do you accept?
  2. 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.
  3. Discounted payback period. Becker Inc. 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 Becker Incorporated uses an 8% discount rate on these projects, are they accepted or rejected? If it uses 12% discount rate? A 16% discount rate? Why is it necessary to only look at the first four years of the projects’ cash flows?
  4. Comparing payback period and discounted payback period. Hydes Inc. is debating using payback period versus discounted payback period for small-dollar projects. The company’s information officer has submitted a new computer project with a $16,000 cost. The cash flow will be $4,000 each year for the next five years. The cutoff period used by the company is four years. The information officer states that it doesn’t matter which model the company uses for the decision; the project is clearly acceptable. Demonstrate for the information officer that the selection of the model does matter.
  5. Comparing payback period and discounted payback period. Nielsen Inc. is switching from the payback period to the discounted payback period for small-dollar projects. The cutoff period will remain at three years. Given the following four projects’ cash flows and using a 10% discount rate, determine which projects it would have accepted under the payback period and which it will now reject under the discounted payback period.
  6. Net present value. Garth Industries has a project with the following projected cash flows:

Initial Cost, Year 0: $320,000

Cash flow year one: $ 55,000

Cash flow year two: $ 75,000

Cash flow year three: $120,000

Cash flow year four: $180,000

  1. Using a 10% discount rate for this project and the NPV model, determine whether this

project should be accepted or rejected.

  1. Should it be accepted or rejected using a 12% discount rate?
  2. Net present value. Lepton Industries has a project with the following projected cash flows:

Initial Cost: $510,000

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, determine whether this

project should be accepted or rejected.

  1. Should it be accepted or rejected using a 14% discount rate?
  2. Should it be accepted or rejected using a 20% discount rate?
  3. Net present value. Quark Industries has four potential projects, all with an initial cost of $2,000,000. The capital budget for the year will allow Quark Industries to accept only one of the four projects. Given the discount rates and the future cash flows of each project, determine which project Quark should accept.
  4. Net present value. Lepton Industries has four potential projects, all with an initial cost of $1,500,000. The capital budget for the year will allow Lepton to accept only one of the four projects. Given the discount rates and the future cash flows of each project, determine which project Lepton should accept.
  5. NPV unequal lives. Grady Enterprises is looking at two project opportunities for a parcel of land that the company currently owns. The first project is a restaurant, and the second project is a sports facility. The projected cash flow of the restaurant is an initial cost of $1,500,000 with cash flows over the next six years of $200,000 (Year one), $250,000 (Year two), $300,000 (Years three through five), and $1,750,000 in Year six, when Grady plans on selling the restaurant. The sports facility has the following cash outflow: initial cost of $2,400,000 with cash flows over the next three years of $400,000 (Years one to three) and $3,000,000 in Year four, when Grady plans on selling the facility. If the appropriate discount rate for the restaurant is 11% and the appropriate discount rate for the sports facility is 13%, using NPV, determine which project Grady should choose for the parcel of land. Adjust the NPV for unequal lives with the equivalent annual annuity. Does the decision change?
  6. NPV unequal lives. Singing Fish Fine Foods has $2,000,000 for capital investments this year and is considering two potential projects for the funds. Project one is updating the deli section of the store for additional food service. The estimated annual after-tax cash flow of this project is $600,000 per year for the next five years. Project two is updating the wine section of the store. Estimated annual after-tax cash flow for this project is $530,000 for the next six years. If the appropriate discount rate for the deli expansion is 9.5% and the appropriate discount rate for the wine section is 9.0%, using NPV, determine which project Singing Fish should choose for the parcel of land. Adjust the NPV for unequal lives with the equivalent annual annuity. Does the decision change?
  7. Internal rate of return and modified internal rate of return. What are the IRRs and MIRRs of the four projects for Quark Industries in Problem 9?
  8. Internal rate of return and modified internal rate of return. What are the IRRs and MIRRs of the four projects for Lepton Industries in Problem 10?
  9. MIRR unequal lives. What is the MIRR for Grady Enterprises in Problem 11? What is the MIRR when you adjust for the unequal lives? Does the adjusted MIRR for unequal lives change the decision based on MIRR? Hint: Take all cash flows to the same ending period as the longest project.
Year Restaurant Sports Facility
0 -1500000 -2400000
1 200000 400000
2 250000 400000
3 300000 400000
4 300000 3000000
5 300000
6 1750000
Disc. Rate 11% 13%
  1. MIRR unequal lives. What is the MIRR for Singing Fish Fine Foods in Problem 12? What is the MIRR when you adjust for the unequal lives? Does the adjusted MIRR for unequal lives change the decision based on MIRR? Hint: Take all cash flows to the same ending period as the longest project.
Year Deli Section Wine Section
0 -2000000 -2000000
1 600000 530000
2 600000 530000
3 600000 530000
4 600000 530000
5 600000 530000
6 530000
Disc. Rate 9.5% 9%
  1. 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 correct? Under what conditions will IRR and NPV be consistent when accepting or rejecting projects?
  2. 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 IRR can cause errors, unlike NPV. Is Rachel correct? Show one type of error can be made with IRR and not with NPV.
  3. Profitability index. Given the discount rates and the future cash flows of each project, which projects should they accept using profitability index?
  4. Profitability index. Given the discount rates and the future cash flow of each project listed, use the PI to determine which projects the company should accept.
  5. Comparing all methods. Given the following after-tax cash flows on a new toy for Tyler’s Toys, find the project’s payback period, NPV, and IRR. The appropriate discount rate for the project is 12%. If the cutoff period is six years for major projects, determine whether management will accept or reject the project under the three 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 to 8 cash inflow: $750,000 each year

  1. Comparing all methods. 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 payback period, NPV, IRR, MIRR, and PI of this project. The appropriate discount rate for the project is 14%. If the cutoff period is six years for major projects, determine whether management at Risky Business will accept or reject the project under the five different decision models.

  1. NPV profile of a project. Given the following cash flows of Project L-2, draw the NPV profile. Hint: use a discount rate of zero for one intercept (y-axis) and solve for the IRR for the other intercept (x-axis).

Cash flows: Year 0 = -$250,000

                          Year 1 = $45,000

                          Year 2 = $75,000

                          Year 3 = $115,000

                          Year 4 = $135,000

  1. NPVprofile of two mutually exclusive projects. Moulton Industries has two potential projects for the coming year, Project B-12 and Project F-4. The two projects are mutually exclusive. The cash flows are listed below. Draw the NPV profile of each project and determine the cross-over rate of the two projects. If the appropriate hurdle rate is 10% for both projects which project, does Moulton Industries choose?

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