Question

Consider the following mutually exclusive investments

	T=0	1	2
Investment A:	-200	40	210
Investment B:	-200	170	70

1. Find IRRs for both projects
2. “Draw” a graph of NPV schedules using Excel, in which you will show the NPV of each project as a function of its discount rate (i.e NPV on the vertical axis and r on the horizontal axis). Both NPV schedules should be on the same graph.
3. Solve for the crossover rate
4. Please describe as fully as possible which project is the best and under which circumstances.

Answer 1

IRR can be calculated using the same function on a calculator or excel.

IRR (A) = 12.96% and IRR (B) = 7.69%

Crossover rate is the rate at which NPV of both projects are equal. It can be calculated as the IRR of the difference in the cash flows of both projects. We get Crossover rate = IRR(0, 130, -140) = 7.69%

NPV schedule is as follows:

r	NPV (A)	NPV (B)
0%	$   50.00	$   40.00
2.00%	$   41.06	$   33.95
4.00%	$   32.62	$   28.18
6.00%	$   24.64	$   22.68
7.69%	$   18.22	$   18.22
8.00%	$   17.08	$   17.42
10.00%	$      9.92	$   12.40
12.00%	$      3.12	$      7.59
14.00%	$    (3.32)	$      2.99
16.00%	$    (9.45)	$    (1.43)
18.00%	$ (15.28)	$    (5.66)
20.00%	$ (20.83)	$    (9.72)