What is the NPV of a $45,000 project that is expected to have an after-tax cash flow of $14,000 for the first two years, $10,000 for the next two years, and $8,000 for the fifth year? Use a 10% discount rate. Would you accept the project?
Answer:
After-tax PVIF Present
Year Cash Flow at 10% Value
1 $14,000 .909 $12,726
2 14,000 .826 11,564
3 10,000 .751 7,510
4 10,000 .683 6,830
5 8,000 .621 4,968
Present value cash flow $43,598
Initial outlay 45,000
Net present value $-1,402
Project should be rejected.
Dieyard Battery Recyclers is considering a project with the following cash flows:
Initial outlay = $13,000
Cash flows: Year 1 = $5,000
Year 2 = $3,000
Year 3 = $9,000
If the appropriate discount rate is 15%, compute the NPV of this project.
Answer: NPV=13,000 + 5,000/(1.15) + 3,000/(1.15)2 + 9,000/(1.15)3
Two projects are under consideration by the same company at the same time. Project Alpha has a NPV of $20 million and an estimated useful life of 10 years. Project Beta has a NPV of $12 million and also an estimated useful life of 10 years. What should the company's decision be
a) if the project's involve unrelated expansion decisions or
b) if the project's are mutually exclusive because they would have to occupy the same space?
Answer: If the projects involve unrelated expansion decisions, they should both be accepted because they both add significant value to the firm. If they are mutually exclusive, they cannot both be accepted so the company should accept project Alpha because it has the higher NPV and reject project Beta.
Dudster Manufacturing has 2 options for installing legally required safety equipment. Option Ex has an initial cost of $25,000 and annual operating costs over 3 years of $5,000, $5,250, $5,600. Option WYE has an initial cost of $40,000 and annual operating costs of $4,000, $4,200, $4,450, $4,750, $5,100. Whether Dudster chooses Ex or Wye, the equipment is always needed and must be replaced at the end of its useful life. Which choice is least expensive over the long run? Use a discount rate of 9%.
Answer:
NPV Project X = -$25,000 - $5,000/(1.09)1 - $5,250/(1.09)2 - $5,600/(1.09)3 =-$38,330.20
NPV = -$40,000 - $4,000/(1.09)1 - $4,200/(1.09)2 - $4,450/(1.09)3 - $4,750/(1.09)4 - $5,100/(1.09)5 = -$57,320.67. Using a financial calculator, the EAC for project Ex is N = 3, i = 9,PV = -38,330.20, PMT = 15,138.57, FV = 0. For Project Wye N = 5, i = 9,PV = -57,320.67, PMT = 14,736.71, FV = 0. Project Wye has the lower EAC (PMT) and should be selected.
What is the NPV of a $45,000 project that is expected to have an after-tax cash flow of $14,000 for the first two years, $10,000 for the next two years, and $8,000 for the fifth year? Use a discount rate of 8%. Would you accept or reject the investment?
Answer:
After-tax PVIF Present
Year Cash Flow at 8% Value
1 $14,000 .926 $12,964
2 14,000 .857 11,998
3 10,000 .794 7,940
4 10,000 .735 7,350
5 8,000 .681 5,448
Present value of cash flows $45,700
Initial outlay $45,000
Net present value $ 700
The project is acceptable.
