Question

A firm is considering the following mutually exclusive projects: Year 0 1 2 3 Project A -2500 1500 ??? 1500 Project B -1500 1000 500 1500 Assuming a rate of return of 10%, what must be the cash flow for Project A in year 2, for the firm to be indifferent for choosing these projects?

Answer 1

NPV of Project B is calculated as follows

NPV of PROJECT B
Year	Cash Flow	Discounting Factor @ 10	Present Value
0	-1,500	1.00	-1,500.00
1	1,000	0.91	909.09
2	500	0.83	413.22
3	1,500	0.75	1,126.97
NPV	949.29

NPV of project A excluding cash flow of year 2

NPV of PROJECT A
Year	Cash Flow	Discounting Factor @ 10	Present Value
0	-2,500	1.00	-2,500.00
1	1,500	0.91	1,363.64
2	-	0.83	-
3	1,500	0.75	1,126.97
NPV	-9.39

inorder for the firm to be indifferent for choosing the projects the NPV of Project A must be $949.29. The cashflow of year 2 discounted should increase the NPV from -9.39 to 949.29 , so the presnet value of cash flow on year 2 = $949.29-(-9.39) = $958.68.

So,

Present value of cash flow of year 2 = Cash flow of year 2 x Discount factor of year 2

958.68 = Cash flow of year 2 x 0.82644

Cash flow of year 2 = 958.68 /0.82644

Cash flow of year 2 =$1160