The Correct Answer and Explanation is:
To find the crossover rate between the two projects, we need to determine the discount rate at which the net present values (NPVs) of both projects are equal. The key steps involve calculating the incremental cash flows and solving for the discount rate.
Solution:
- Compute Incremental Cash Flows (Project A – Project B):
- Year 0: -1,000 – (-800) = -200
- Year 1: 250 – 150 = 100
- Year 2: 300 – 225 = 75
- Year 3: 300 – 280 = 20
- Year 4: 400 – 325 = 75
- Use the Internal Rate of Return (IRR) Formula:
- The IRR of the incremental cash flows is found using the equation:
0=∑Ct(1+r)t0 = \sum \frac{C_t}{(1+r)^t}
- Applying numerical methods or a financial calculator, the crossover rate is approximately 14.92%.
Explanation:
The crossover rate represents the discount rate where two investment alternatives yield identical NPVs. To derive this, we first compute the difference in cash flows between the projects, resulting in the incremental cash flow series. These incremental values help determine when choosing Project A over Project B becomes beneficial.
By applying the IRR concept, the crossover rate is the discount rate where the sum of discounted incremental cash flows equals zero. This means, at rates below the crossover point, Project A has a higher NPV, while above this rate, Project B is preferable.
The crossover rate is useful in capital budgeting decisions because it informs the preference between mutually exclusive investments depending on the cost of capital. If the required return falls below 14.92%, Project A should be chosen. If the cost of capital exceeds this rate, Project B is more favorable.
This method enables firms to make optimal financial decisions based on project scalability and expected returns.
