Question

The NPV and payback period

Suppose you are evaluating a project with the cash inflows shown in the following table. Your boss has asked you to calculate the project’s net present value (NPV). You don’t know the project’s initial cost, but you do know the project’s regular, or conventional, payback period is 2.50 years.

The project's annual cash flows are:

Year	Cash Flow
Year 1	$400,000
Year 2	600,000
Year 3	500,000
Year 4	475,000

If the project’s desired rate of return is 8.00%, the project’s NPV—rounded to the nearest whole dollar—is     .

Which of the following statements indicates a disadvantage of using the regular, or conventional, payback period for capital budgeting decisions? Check all that apply.

The payback period does not take into account the time value of money effects of a project’s cash flows.

The payback period is calculated using net income instead of cash flows.

The payback period does not take into account the cash flows produced over a project’s entire life.

Answer 1

NPV is the sum of present Value of all cash flows

Let Cash Flows for Year n be denoted by CFn

Initial Investment = CF0

Given

CF1 = 400000
CF2 = 600000
CF3 = 500000
CF4 = 475000

Given Payback period is 2.5 years (the non discounted sum of cash flows becomes zero at the payback period)

This indicates that the cumulative cash flows become positive in Year 3

Cumulative Cash Flows till Year 2.5 should be zero

=> CF0 + CF1 + CF2 + 0.5*CF3 = 0

=> X + 400000 + 600000 + 0.5*500000 = 0

=> X = -1250000

Hence, Initial Investment = X = CF0 = 1250000

Given Interest Rate = r = 8%

NPV = Σ CFn/(1+r)ⁿ = -1250000 + 400000/1.08 + 600000/1.08² + 500000/1.08³ + 475000/1.08⁴ = $380828.96

The regular payback method does not discount the future value of cash flows and hence does not take into account the time value of money. Hence, option "The payback period does not take into account the time value of money effects of a project’s cash flows." is the correct choice