Question

Assume we have a project that costs $4 million today that generates an annual cash flow of $400,000 forever beginning in exactly one year. The relevant discount rate is 9%.

a) What is this project’s (accounting) payback period?
40
30
20
10
none of the above
b) What is this project’s NPV?
$380,885
$500,000
$444,444
zero
c) Suppose we can postpone investment three years and, with the new improved technology, the project will have similar risk but for an investment of $5 million will generate perpetual cash flows (beginning exactly one year after the investment) of $500,000. Would you recommend that we invest in the original project or wait three years to invest in the new project?
Should not wait
Should wait

Answer 1

The payback period is 10 years. The NPV is $380,885. Investing in the original project is recommended.

Step-by-step explanation:

To calculate the payback period, we divide the initial investment ($4 million) by the annual cash flow ($400,000). In this case, the payback period is 10 years. Therefore, the correct answer for part (a) is 10 years.

To calculate the NPV, we discount each cash flow to its present value and then subtract the initial investment. Using a discount rate of 9%, the NPV is approximately $380,885. Therefore, the correct answer for part (b) is $380,885.

If we wait three years to invest in the new project with improved technology, the new project will have a higher investment cost ($5 million) but also higher cash flows ($500,000). To determine whether to invest now or wait, we can calculate the NPV of the new project using the same discount rate. Comparing the NPV of the original project ($380,885) and the NPV of the new project, we can see that the original project has a higher NPV. Therefore, I would recommend investing in the original project rather than waiting.