Question

Two projects being considered by a firm are mutually exclusive and have the following projected cash flows: Project A Project B Year Cash Flow Cash Flow

Proj A Project B

0 -$300,000 -$300,000

1 145,500 $150,000

2 145,500 -$ 40,000

3 145,500 $370,000

The firm’s cost of capital is 10 percent. Based only on the information given,

1. What are the NPV for Project A and B? Which project do you choose based on the NPV?

2. What are the payback periods for Project A and B? Which project do you choose based on the payback periods?
3. What are the IRR for Projects A and B? Which project do you choose based on the IRR?

Answer 1

a.Project A

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

• Press the CF button.
• CF0= -$300,000. Indicate the initial cash flow by 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 NPV button and enter the cost of capital of 10%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 10% cost of capital is $61,836.96.

Project B

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

• Press the CF button.
• CF0= -$300,000. Indicate the initial cash flow by 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 NPV button and enter the cost of capital of 10%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 10% cost of capital is $81,292.26.

I will choose project B according to the NPV decision rule since it generates the highest net present value.

b.Project A

Cumulative cash flow in year 1= $145,500

Cumulative cash flow in year 2= $291,000

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

= 2 years + ($300,000 - $291,000)/ $145,500

= 2 years + $9,000/ $145,500

= 2 years + 0.0619

= 2.06 years.

Project B

Cumulative cash flow in year 1= $150,500

Cumulative cash flow in year 2= $110,000

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

= 2 years + ($300,000 - $110,000)/ $370,000

= 2 years + $190,000/ $370,000

= 2 years + 0.51

= 2.51 years.

I will choose project A according to the NPV decision rule since it has the shortest payback period.

c.Project A

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

• Press the CF button.
• CF0= -$300,000. The initial cash flow is indicated by a negative sign since it is a cash outflow.  
• Cash flow for each of the fifteen years 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 the project is 21.38%.

Project B

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

• Press the CF button.
• CF0= -$300,000. The initial cash flow is indicated by a negative sign since it is a cash outflow.  
• Cash flow for each of the fifteen years 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 the project is 21.97%.

I will choose project B according to the IRR decision rule since it generates the highest IRR.