Question

PAYBACK, ACCOUNTING RATE OF RETURN, PRESENT VALUE, NET PRESENT VALUE, INTERNAL RATE OF RETURN

All four parts are independent of all other parts. Assume that all cash flows are after-tax cash flows:

a.    Randy Willis is considering investing in one of the following two projects. Either project will require an investment of $10,000. The expected cash flows for the two projects follow. Assume that each project is depreciable.

Year       Project A        Project B

1             $ 3,000           $3,000

2                4,000           4,000

3                5,000           6,000

4            10,000           3,000

5            10,000           3,000

b.    Wilma Golding is retiring and has the option to take her retirement as a lump sum of $225,000 or to receive $24,000 per year for 20 years. Wilma's required rate of return is 8 percent.

c.    David Booth is interested in investing in some tools and equipment so that he can do independent dry walling. The cost of the tools and equipment is $20,000. He estimates that the return from owning his own equipment will be $6,000 per year. The tools and equipment will last six years.

d.    Patsy Folson is evaluating what appears to be an attractive opportunity. She is currently the owner of a small manufacturing company and has the opportunity to acquire another small company's equipment that would provide production of a part currently purchased externally. She estimates that the savings from internal production will be $25,000 per year. She estimates that the equipment will last 10 years. The owner is asking $130,400 for the equipment. Her company's cost of capital is 10 percent.

Required:

1.    What is the payback period for each of Randy Willis's projects? If rapid payback is important, which project should be chosen? Which would you choose?

2.    Which of Randy's projects should be chosen based on the ARR?

3.    Assuming that Wilma Golding will live for another 20 years, should she take the lump sum or the annuity?

4.    Assuming a required rate of return of 8 percent for David Booth, calculate the NPV of the investment. Should David invest?

5.    Calculate the IRR for Patsy Folson's project. Should Patsy acquire the equipment?

Answer 1

1. Project A has a payback period of 2 years + 3,000 / 5,000 = 2.6 years

Project B has a payback period of 2 years + 3,000 / 6,000 = 2.5 years.

If rapid payback is important, Randy Willis should opt for Project B.

2. Accounting rate of return = Average Accounting Return / Investment.

Project A: [( Total Cash Flows - Total Depreciation) / 5 ] / Initial Investment =[ $ ( 32,000 - 10,000) / 5 ] / $ 10,000 = 44%

Project B : [ $ ( 19,000 - 10,000) / 5] / $ 10,000 = 18%

Based on ARR, Randy Willis should go for Project A.

3. Present vaue of $ 24,000 for 20 years at 8% = $ 24,000 x 9.8181 = $ 235,634.

As the present value of the annuity is greater than the present value of $ 225,000 of the lump-sum at retirement, Wilma Golding should take the annuity.

4. NPV of the investment = Present value of cash inflows - Initial Investment = $ 6,000 x 4.6229 - 20,000 = 27,737.40 - 20,000 = 7,737.40

As the NPV is greater than zero, David Booth should make the investment.

5. IRR ( from Excel) : 14%

As the cost of capital of 10% is lower than the IRR, Patsy should acquire the equipment.