Question

The following are the cash flows of two projects:

Year	Project A			Project B
0	$	(260	)	$	(260	)
1		140			160
2		140			160
3		140			160
4		140

a. Calculate the NPV for both projects if the opportunity cost of capital is 16%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Project A

Project B

b. Suppose that you can choose only one of these projects. Which would you choose?

Project A

Project B

Neither

Answer 1

a. Calculating NPV of project A

Cash flows for Project A are

Cash Flow for the Project A
Year	0	1	2	3	4
Cash flow	-260	140	140	140	140

NPV of Project A = Cash flow in year 0 + Sum of present values of cash flows for year 1 to 4 discounted at Opportunity cost of capital of 16% = -260 + 140 / (1 + 16%) + 140 / (1 + 16%)² + + 140 / (1 + 16%)³ + 140 / (1 + 16%)⁴

NPV of project A = -260 + 120.6896 + +104.0428 + 89.6920 + 77.3207 = 131.7451 = $131.75 (rounded to two places of decimal)

Calculating NPV of project B

Cash flows for Project B are

Cash Flow for the Project B
Year	0	1	2	3
Cash flow	-260	160	160	160

NPV of Project B = Cash flow in year 0 + Sum of present values of cash flows for year 1 to 3 discounted at Opportunity cost of capital of 16% = -260 + 160 / (1 + 16%) + 160 / (1 + 16%)² + 160 / (1 + 16%)³

NPV of Project B = -260 + 137.9310 + 118.9060 + 102.5052 = 99.3422 = 99.34 (rounded to two places of decimal)

b. Since both the projects are of unequal lives, therefore we cannot directly compare their NPVs.

We need to find the equivalent annual annuity for both the projects. Now the project with higher equivalent annual annuity should be chosen.

Finding equivalent annual annuity of project A

We can find the equivalent annual annuity of Project A using pmt function in excel

Formula to be used in excel: =pmt(rate,nper,-pv)

Using pmt function in excel, we get Equivalent Annual annuity of Project A = $47.08

Finding equivalent annual annuity of project B

We can find the equivalent annual annuity of Project B using pmt function in excel

Formula to be used in excel: =pmt(rate,nper,-pv)

Using pmt function in excel, we get equivalent annual annuity of Project B = 44.23

Since project A has higher equivalent annual annuity, therefore Project A should be Chosen.

Answer : Project A