Question

( Time-disparity problem ) The State Spartan Corporation is considering two mutually exclusive projects. The free cash flows associated with these projects are shown in the popup window:

	PROJECT A		PROJECT B
Initial outlay	− $70,000		− $70,000
Inflow year 1	19,625		0
Inflow year 2	19,625		0
Inflow year 3	19,625		0
Inflow year 4	19,625		0
Inflow year 5	19,625		120,000

The required rate of return on these projects is 9 percent.

A. What is each project's payback period?

B. What is each project's NPV ?

C. What is each project's IRR ?

D. What has caused the ranking conflict?

E. Which project should be accepted? Why?

Answer 1

a.Project A

Payback period= full years until recovery + unrecovered cost at the start of the year/cash flow during the year

                              = 3 years + ($70,000 - $58,875)/ $70,000

                              = 3 years + 0.1589

                              = 3.16 years.

Project B

Payback period= 4 years + ($120,000 - $70,000)/ $120,000

                              = 4 years + 50,000/70,000

                              = 4 years + 0.7143

                              = 4.71 years.

b.Project A

Net present value is solved here using a financial calculator. The steps to solve on the financial calculator:

• Press the CF button.
• CF0= -$70,000. It is entered with a negative sign since it is a cash outflow.
• Cash flow for all the years should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow, press the NPV button and enter the required rate of return of 9%.
• Press the down arrow and CPT buttons to get the net present value.

The net present value at 9% required rate of return is $6,334.41.

Project B

Net present value is solved here using a financial calculator. The steps to solve on the financial calculator:

• Press the CF button.
• CF0= -$70,000. It is entered with a negative sign since it is a cash outflow.
• Cash flow for all the years should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow, press the NPV button and enter the required rate of return of 9%.
• Press the down arrow and CPT buttons to get the net present value.

The net present value at 9% required rate of return is $7,991.77.

b. Project A

Internal rate of return is calculated using a financial calculator by inputting the below:

• Press the CF button.
• CF0= -$70,000. It is entered with a negative sign since it is a cash outflow.
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the IRR and CPT button to get the IRR of the project.

The IRR of project is 12.43%.  

Project B

Internal rate of return is calculated using a financial calculator by inputting the below:

• Press the CF button.
• CF0= -$70,000. It is entered with a negative sign since it is a cash outflow.
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the IRR and CPT button to get the IRR of the project.

The IRR of project is 11.38%.

c.There could be a conflict with project acceptance when projects are mutually exclusive. The reason is the NPV and IRR approaches use different reinvestment rate assumptions so there can be a conflict

in project acceptance when mutually exclusive projects are considered.

d.Project B should be accepted since it has the highest net present value.

In case of any query, kindly comment on the solution.