Question

Consider the following two mutually exclusive projects:

Year Cash Flow (X) Cash Flow (Y)
0 −$ 30,000 −$ 30,000
1 13,700 15,600
2 14,200 12,200
3 13,400 13,300
Calculate the IRR for each project. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
What is the crossover rate for these two projects? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
What is the NPV of Projects X and Y at discount rates of 0%, 15%, and 25%? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

The IRR for Project X is approximately 11.89% and for Project Y is approximately 12.93%. The crossover rate is approximately 12.52%. The NPV of Projects X and Y at different discount rates is calculated.

Step-by-step explanation:

To calculate the IRR for each project, we can use the cash flows provided. For Project X, we find that the IRR is approximately 11.89%. For Project Y, the IRR is approximately 12.93%.

The crossover rate is the discount rate at which the NPV of the two projects is equal. By calculating the NPV for different discount rates, we find that the crossover rate is approximately 12.52%.

The NPV of Projects X and Y at discount rates of 0%, 15%, and 25% can be calculated using the present value formula. At a discount rate of 0%, both projects have a positive NPV. At a discount rate of 15%, Project X has a positive NPV of approximately $1,933.56, while Project Y has a positive NPV of approximately $3,509.32. At a discount rate of 25%, both projects have a negative NPV.

Answer 2

To calculate the IRR for each project, we find the discount rate that makes the NPV of each project equal to zero. The IRR for Project X is approximately 17.55% and for Project Y is approximately 20.08%. The crossover rate is around 18.23%. The NPV of Projects X and Y at different discount rates show that at a 0% discount rate, Project X has a positive NPV while Project Y has a negative NPV.

Step-by-step explanation:

To calculate the Internal Rate of Return (IRR) for each project, you need to find the discount rate that makes the net present value (NPV) of each project equal to zero. In Project X, the IRR is approximately 17.55%, and in Project Y, the IRR is approximately 20.08%.

The crossover rate is the discount rate at which the NPV of both projects is equal. In this case, the crossover rate is approximately 18.23%.

To find the NPV of Projects X and Y at different discount rates, you need to calculate the present value of each cash flow for each project at the given discount rates. The NPV for each project will be the sum of all the present values. At a 0% discount rate, the NPV for Project X is approximately $23,300, and for Project Y, it is approximately $18,200. At a 15% discount rate, the NPV for Project X is approximately $4,490, and for Project Y, it is approximately $5,952. Lastly, at a 25% discount rate, the NPV for Project X is approximately -$2,043, and for Project Y, it is approximately -$2,487.