Question

The following are the cash flows of two projects:

Year	Project A			Project B
0	$	(330	)	$	(330	)
1		160			230
2		160			230
3		160			230
4		160

a. If the opportunity cost of capital is 12%, calculate the NPV for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. Which of these projects is worth pursuing?

****NOTE**** You are finding the NPV, NOT the Profitability index!

Answer 1

a. Calculating NPV of Project A

NPV of Project A = Cash flow in year 0 + Present value of cash flow for year 1 to year 4

NPV of Project A = -330 + 160 / (1+12%)¹ + 160 / (1+12%)² + 160 / (1+12%)³ + 160 / (1+12%)⁴

We can find the present value of cash flow for year 1 to year 4 using PV function in excel

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

Using PV function in excel, we get present value of cash flow for year 1 to year 4 = 485.9758

NPV of Project A = -330 + 485.9758 = 155.9758 = $155.98 (rounded to two decimal places)

Calculating NPV of Project B

NPV of Project B = Cash flow in year 0 + Present value of cash flow for year 1 to year 3

NPV of Project A = -330 + 230 / (1+12%)¹ + 230 / (1+12%)² + 230 / (1+12%)³

We can find the present value of cash flow for year 1 to year 3 using PV function in excel

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

Using PV function in excel, we get Present value of cash flows for year 1 to year 3 = 552.4211

NPV of Project B = -330 + 552.4211 = 222.4211 = $222.42 (rounded to two decimal places)

Hence NPV of the Project =$222.42

b. As projects have unequal lives therefore to find which of these projects is worth pursuing, we need to calculate the equivalent annual annuity of both the Projects. The project with higher equivalent annual annuity should be pursued

Finding Equivalent annual annuity of Project A

We can find the equivalent annual annuity of project A by 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 = $51.35

Finding Equivalent annual annuity of Project B

We can find the equivalent annual annuity of project B by 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 = 92.60

Since Project B has higher Equivalent annual annuity as compared to Project A, therefore Project B is Worth Pursuing.

Answer: Project B