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?
A)40
B)30
C)20
D)10
E)none of the above b) What is this project’s NPV?
A)$380,885
B)$500,000
C)$444,444
D)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?

Answer 1

The payback period for the original project is 10 years, and its NPV is $444,444. Delaying the investment for the new project's technology, even though it offers higher cash flows, results in a negative NPV when considering the time value of money.

Step-by-step explanation:

The question relates to the calculation of the payback period, net present value (NPV), and a decision on investment timing using present value analysis.

a) Accounting Payback Period

The payback period is the time it takes for the project to recover its initial costs from the cash flows it generates. In this case, the project costs $4 million and generates $400,000 annually. Therefore, the payback period is $4 million / $400,000 per year = 10 years. The correct answer is D) 10.

b) Net Present Value (NPV)

The NPV of an investment is the present value of cash flows minus the investment cost. For a perpetual cash flow, the NPV is calculated as Annual Cash Flow / Discount Rate. So, the NPV is $400,000 / 0.09 = $4,444,444. Minus the initial investment of $4 million, the final NPV is $444,444. The correct answer is C) $444,444.

c) Investment Decision

Delaying the investment for the new project yields a perpetual cash flow of $500,000 starting after four years (including the initial three-year wait plus one year after the investment). The present value of these future cash flows at year three using the 9% discount rate would be $500,000 / 0.09. The NPV for the new project at year three, before considering the $5 million cost, is approximately $5,555,556. To compare, we must discount this back to the present value: $5,555,556 / (1+0.09)3 = $4,320,754. Subtracting the cost of $5 million, the NPV at year zero would be around -$679,246. Therefore, the original project is better because it has a positive NPV of $444,444 vs. the negative NPV of the delayed project.