Question

Project A has cash flows of −$50,000, $49,400, $27,200, and $24,500 for Years 0 to 3, respectively. Project B has an initial cost of $50,000 and an annual cash inflow of $18,500 for four years. These are mutually exclusive projects. What is the crossover rate? Can someone show how to do this without an excel sheet? I need to know how to break down the problem to really understand it.

Answer 1

To calculate the crossover rate , first we need to find the Npv equation for both the project. Then we need to equate it and find one equation similar to that of IRR. Then use financial calculator to find IRR. The IRR found is the crossover rate.

The steps are shown below.

Project A

NPV = -50,000 + 49,400/(1+r) + 27,200/(1+r)^2 + 24,500/(1+r)^3

Project B

NPV = -50,000 + 18,500/(1+r) + 18,500/(1+r)^2 + 18,500/ (1+r)^3 + 18,500/(1+r)^4

Equating both the equation

-50,000 + 49,400/(1+r) + 27,200/(1+r)^2 + 24,500/(1+r)^3 = -50,000 + 18,500/(1+r) + 18,500/(1+r)^2 + 18,500/(1+r)^3 + 18,500/(1+r)^4

Solving the equation, we get

30,900/(1+r) + 8,700/(1+r)^2 + 6,000/(1+r)^3 - 18,500/(1+r)^4 = 0

Now, putting these values in financial calculator to find IRR which will be crossover rate.

Inputs: C0 = 0

C1 = 30,900. Frequency= 1

C2 = 8,700. Frequency= 1

C3 = 6,000. Frequency= 1

C4 = -18,500. Frequency= 1

IRR = compute

We get , IRR = 8.7875

This IRR is the Crossover Rate i.e. 8.7875%.

When we use this rate as discount rate in both the projects we get the same Npv.