Question

Consider the following two mutually exclusive projects with their expected Cash Flows ($)

Project C0 C1   C2 C3

A –$100 +$60 +$60 +$60

B –$100 ------ ------ +$208.35

What is the cross-over rate for these two projects?

a. unknown, because the discount rate is unkown

b. 28%

c. 36%

d. 32%

e. 15%

Answer 1

IRR is the rate at which NPV of the project is 0.

Cross-over rate is a rate at which NPVs of both the projects are equal.

NPV is the sum of present value of the cash flows and the initial capital outlay.

PV of cash flow at time n = Cash flow at time n/ ((1+r)^n)

NPV of Project A = -100+ (60/((1+interest rate)^1)) + (60/((1+interest rate)^2)) + (60/((1+interest rate)^3

NPV of Project B  = -100 + (280.35/((1+interest rate)^3

We equate both the NPVs and solve for the interest rate we will get the cross-over rate

-100+ (60/((1+cross-over rate)^1)) + (60/((1+cross-over interest rate)^2)) + (60/((1+cross-over interest rate)^3 = 100 + (280.35/((1+cross-over interest rate)^3

solvinf for cross-over rate, we get cross-over rate = 15%

Hence, Option e is the answer.