Question

Consider the following cash flows for projects A and B.

Year                                                    Project A         Project B

0                                                          -$1000             -$1000

1                                                          375                 900

2                                                          375                 700

3                                                          375                 500

4                                                          375                 -200

5                                                          -100                 200

The cost of capital for both projects is 10%. What is the cross over rate for projects A and B (the rate at which NPV profiles of the projcets intersect each other)?

	1.	There is no cross over rate as the NPV profiles of projects A and B do not cross each other for any rate between 0% and 100%.
	2.	There are multiple cross over rates for projects A and B for rates between 0% and 100%.
	3.	15.61%
	4.	10%

Answer 1

Crossover rate is the cost of capital at which the net present values of two projects are equal.
It is the point at which the NPV profile of one project crosses over (intersects) the NPV profile of the other project.
First step to calculate cross over rate is find the difference between initial investments of both projects and between each periodic cash flows.
Second step is to develop an IRR equation by equating the net present value equation of the resulting differential cash flows to zero.
Year	Project A	Project B	Difference
a	b	c	b-c
0	-$1,000.00	-$1,000.00	$0.00
1	$375.00	$900.00	-$525.00
2	$375.00	$700.00	-$325.00
3	$375.00	$500.00	-$125.00
4	$375.00	-$200.00	$575.00
5	-$100.00	$200.00	-$300.00
IRR of the difference =			#NUM!
As we are unable to find the IRR of the difference , there is no cross over rate between these tow projects.
The answer is Option 1.