A company is considering two mutually exclusive projects Adept and Boffo.Project Adept requires an initial investment of $100,000 and is expected to generate after-tax cash flows of $45,000 per year for three years.Project Boffo requires an initial investment of $150,000 and is expected to generate after-tax cash flows of $50,000 per year for four years.The appropriate discount rate is 10%.What is the crossover rate for projects Adept and Boffo?

Question

Quizplus · Accepted Answer

To find the crossover rate, we need to find the discount rate at which the net present value (NPV) of both projects is equal.

NPV for Project Adept: 
Year 1: $45,000/(1+10%)^1 = $40,909
Year 2: $45,000/(1+10%)^2 = $37,172
Year 3: $45,000/(1+10%)^3 = $33,793
NPV = -$100,000 + $40,909 + $37,172 + $33,793 = $11,874

NPV for Project Boffo:
Year 1: $50,000/(1+10%)^1 = $45,455
Year 2: $50,000/(1+10%)^2 = $41,322
Year 3: $50,000/(1+10%)^3 = $37,566
Year 4: $50,000/(1+10%)^4 = $34,155
NPV = -$150,000 + $45,455 + $41,322 + $37,566 + $34,155 = $8,498

We can use a financial calculator or excel to find the discount rate at which the NPVs of both projects are equal. The crossover rate is approximately 7.77%.

Therefore, Project Boffo is the best choice since it has a higher NPV and generates more cash flows over a longer period of time.

A Company Is Considering Two Mutually Exclusive Projects Adept and Boffo.Project