Question

you are comparing two mutually exclusive projects. both projects have an initial cost of $49,000 . project a has cash inflows of $30,000 , $27,000 , and $24,000 over the next 3 years, respectively. project b has cash inflows of $19,000 , $24,600 and $45,000 over the next 3 years. what is the crossover rate for projects a and b? multiple choice 27.69 percent 28.40 percent 29.16 percent 29.42 percent

Answer 1

The crossover rate for projects A and B is approximately 28.40 percent.

The crossover rate for projects A and B can be calculated by determining the rate at which the net present values of the two projects are equal. To find the crossover rate, we need to calculate the net present values (NPVs) of each project using a common discount rate. The discount rate at which the NPVs are equal is the crossover rate.

Let's assume a discount rate of 10% for both projects:

• Project A:
• $30,000/(1+10%)¹ + $27,000/(1+10%)² + $24,000/(1+10%)³ = $70,397.54
• Project B:
• $19,000/(1+10%)¹ + $24,600/(1+10%)² + $45,000/(1+10%)³ = $78,218.11

At a discount rate of 10%, the NPV of Project B is higher than that of Project A. Therefore, to find the crossover rate, we need to adjust the discount rate until the NPVs of the two projects are equal.

Using trial and error, we find that a discount rate of approximately 28.40% results in the NPVs of both projects being equal. Therefore, the crossover rate for projects A and B is 28.40 percent.