Question

You are considering the following two mutually exclusive projects. The crossover rate between these two projects is ___ percent and Project ___ should be accepted if the required return is greater than the crossover rate.

Year	Project A			Project B
0		−$39,000			−$39,000
1		21,500			13,720
2		13,500			11,500
3		13,500			25,600

• 12.85%; B

• 12.52%; A

• 12.52%; B

• 12.93%; A

• 12.93%; B

Answer 1

The crossover rate is the rate at which the NPV of the two projects is the same

Substituting the option values, the equation holds at 12.52% so the crossover rate is 12.52%

Below is the NPV schedules for both the projects at the crossover rates:

Project A:

Year	CF	Discount Factor	Discounted CF
0	$-39,000.00	1/(1+0.125176224326535)^0=	1	1*-39000=	$      -39,000.00
1	$ 21,500.00	1/(1+0.125176224326535)^1=	0.888749672	0.888749671722349*21500=	$        19,108.12
2	$ 13,500.00	1/(1+0.125176224326535)^2=	0.789875979	0.789875978986583*13500=	$        10,663.33
3	$ 13,500.00	1/(1+0.125176224326535)^3=	0.702002017	0.702002017025695*13500=	$          9,477.03
				NPV = Sum of all Discounted CF	$              248.47

Project B:

Year	CF	Discount Factor	Discounted CF
0	$-39,000.00	1/(1+0.125176224326535)^0=	1	1*-39000=	-39,000.00
1	$ 13,720.00	1/(1+0.125176224326535)^1=	0.888749672	0.888749671722349*13720=	12,193.65
2	$ 11,500.00	1/(1+0.125176224326535)^2=	0.789875979	0.789875978986583*11500=	9,083.57
3	$ 25,600.00	1/(1+0.125176224326535)^3=	0.702002017	0.702002017025695*25600=	17,971.25
				NPV = Sum of all Discounted CF	$              248.47

We need to create an NPV profile to see which project has higher NPV and should thus be selected:

Cost of capital	A	B
0.00%	$     9,500.00	$   11,820.00
12.00%	$         567.58	$         639.30
12.52%	$         247.02	$         247.02
12.53%	$         240.90	$         239.20
12.55%	$         228.66	$         224.23
12.56%	$         222.55	$         216.75
12.57%	$         216.44	$         209.27
12.58%	$         210.33	$         201.80
12.59%	$         204.22	$         194.32
13.00%	$         -44.79	$       -110.14
13.01%	$         -50.83	$       -117.51

So we can see that the NPV is higher for Project A beyond 12.52% so it should be selected.