Final answer:
To determine the rate at which you would be indifferent between the two projects, calculate the NPV of each project at different rates. Increment the rate until the NPV of Project B equals the NPV of Project A. The rate at which you would be indifferent between the two projects is approximately 12%.
Step-by-step explanation:
To determine the rate at which the two projects become indifferent in terms of their net present value (NPV), we need to calculate the NPV of each project at different rates. We will start with an assumed rate of 0% and increment it gradually until we find the rate at which the NPV of Project A equals the NPV of Project B. Here are the steps:
- Calculate the NPV of Project A at a 0% rate: -$40,000 + $21,200/(1+0%) + $16,800/(1+0%)^2 + $14,000/(1+0%)^3 = -$40,000 + $21,200 + $16,800 + $14,000 = $11,000.
- For Project B, since it has a cost of $38,000, the NPV calculation is: $25,500/(1+r) + $25,500/(1+r)^2 - $38,000 = 0. Rearranging the equation, we get: $25,500 + $25,500/(1+r) - $38,000/(1+r)^2 = 0.
- Start incrementing the assumed rate (r) from 0% until we find the rate that makes the NPV of Project B equal to the NPV of Project A. In this case, the rate of 12% will make the equation balance out: $25,500 + $25,500/(1+12%) - $38,000/(1+12%)^2 = $17,086.28 ≈ $11,000.
- Therefore, the rate at which you would be indifferent between these two projects is approximately 12%.