Crossover Point/Rate: Packard Electronics Corp. is evaluating the two mutually exclusive projects shown below.
Boundless Corp.
Project A
Project B
Period
Cash Flows
Cash Flows
0
$ (100,000)
$ (150,000)
1
50,000
15,000
2
40,000
30,000
3
30,000
50,000
4
20,000
70,000
5
10,000
80,000
What is the "crossover rate" of the two projects? (Round off to the nearest (0.01%)

Question

Quizplus · Accepted Answer

The crossover rate is the discount rate at which the NPV of both projects is equal. To find the crossover rate, we can use the following formula:Crossover rate = (PV of Project A - PV of Project B) / (Initial investment of Project A - Initial investment of Project B)PV of Project A = -100,000 + 50,000/(1+r) + 40,000/(1+r)^2 + 30,000/(1+r)^3 + 20,000/(1+r)^4 + 10,000/(1+r)^5PV of Project B = -150,000 + 15,000/(1+r) + 30,000/(1+r)^2 + 50,000/(1+r)^3 + 70,000/(1+r)^4 + 80,000/(1+r)^5Substituting the values, we get:Crossover rate = (-100,000 + 50,000/(1+r) + 40,000/(1+r)^2 + 30,000/(1+r)^3 + 20,000/(1+r)^4 + 10,000/(1+r)^5) - (-150,000 + 15,000/(1+r) + 30,000/(1+r)^2 + 50,000/(1+r)^3 + 70,000/(1+r)^4 + 80,000/(1+r)^5) / (-100,000 - (-150,000))Solving for r, we get:Crossover rate = 10.82%