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 −$27,000 −$27,000
1 10,000 18,100
2 10,000 8,000
3 18,000 10,120
multiple choice
a. 11.75%;
b. 17.19%;
c. 18.64%;

* Crossover rate is A.11.75%

* At crossover rate, Project B should be chosen.

Explanation:

* Finding the crossover rate:

Denote x is the crossover rate which is the discount rate at which the net present value (NPV) of the two project is the same. So, we have:

NPV Project A = NPV Project B at X discount rate

<=> -27,000 + 10,000/(1+x) + 10,000/(1+x)^2 + 18,000/(1+x)^3 = -27,000 + 18,100/(1+X) + 8,000/(1+x)^2 + 10,120/(1+x)^3 <=> 1+x = 1.1175 <=> x = 11.75%

* Choosing what project to be taken:

For any required return rate that is above crossover rate, we have the NPV of Project B is higher than the NPV of Project A; so Project B should be chosen.

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