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Wize University Introduction to Finance Textbook > Capital Budgeting

Cross-over Rate

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The Cross-over Rate

When multiple investment opportunities are present but only one can be selected, these investments are said to be mutually exclusive. The crossover rate tells us when the NPV of two investments are equal (cross over).

Steps to Compute Crossover Rate:
1. Compute the difference in cash outflows and inflows in the two investments
2. Use the differences to compute IRR

Using the Cross-Over Rate
  • If r < cross-over rate, choose the the project with the lower IRR.
  • if r > cross-over rate, choose the project with the higher IRR.
  • Unless r > IRR of both projects, then choose neither project.
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Example: The Cross-Over Rate

A company is considering two mutually exclusive projects A and B. Project A 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 B 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 percent. What is the crossover rate for projects A and B?





Practice: Cross-over Rate

You are considering two mutually exclusive investments. Investment A requires an initial after-tax outlay of $120,000 and will return $25,000 per year for 6 years. Investment B requires an initial after-tax outlay of $80,000 and will return $20,000 per year for 3 years and $15,000 per year for the next 3 years. Your cost of capital is 5%.
What is the cross-over rate?
The cross-over rate is
%
Extra Practice
Question 1
A firm is considering two mutually exclusive projects. Project Fire requires an initial after-tax cash outflow of $10,000 and will return $5,000 in year 1, $4000 in year 2 and $9,000 in year 3. Project Water required an initial after-tax cash outflow of $20,000 and will return $6,000 in year 2 and $30,000 in year 3.
What is the cross over rate?
Company X is considering two mutually exclusive projects, Project A and Project B. Project A has an initial investment of $100,000 and is expected to generate cash flows of $30,000 per year for the next five years. Project B has an initial investment of $140,000 and is expected to generate cash flows of $40,000 per year for the next five years. The required rate of return for both projects is 10%.
Which project should Company X choose?
Company X is considering two independent projects, Project A and Project B. Project A has an initial investment of $100,000 and is expected to generate cash flows of $30,000 per year for the next five years. Project B has an initial investment of $140,000 and is expected to generate cash flows of $40,000 per year for the next five years. The required rate of return for both projects is 10%.
Which project should Company X choose?
Company X is considering two mutually exclusive projects, Project A and Project B. Project A has an initial investment of $100,000 and is expected to generate cash flows of $30,000 per year for the next five years. Project B has an initial investment of $140,000 and is expected to generate cash flows of $40,000 per year for the next five years. The required rate of return for both projects is 16%.
Which project should Company X choose?
Company X is considering two mutually exclusive projects, Project A and Project B. Project A has an initial investment of $100,000 and is expected to generate cash flows of $30,000 per year for the next five years. Project B has an initial investment of $140,000 and is expected to generate cash flows of $40,000 per year for the next five years. The required rate of return for both projects is 5%.
Which project should Company X choose?