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 −$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%;

Answer 1

Answer:

* 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.