Stanton, Inc. wants to analyze the NPV profile for a five-year project that is considered to be very risky

Question

The project's initial outlay or cost is $80,000 and it has respective cash inflows for years 1, 2, 3, 4 and 5 of $15,000, $25,000, $35,000, $45,000 and $55,000. Stanton wants to know how the NPV will change for the following required rates of returns: 9%, 14%, 19%, 24%, and 29%. From the NPV profile, at about what rate will the NPV be equal to zero?
What will be an ideal response?

Answer 1

Answer: Let us first compute the NPV for 9%. We have:
NPV = -CF0 + + + + +
= -$80,000 + + + + +
= -$80,000 + $13,761.47 + $21,042.00 + $27,026.42 + $31,879.13 + $35,746.23
= -$80,000 + $129,455.25 = $49,455.25.
In a similar fashion, for 14%, 19%, 24% and 29%, we get respective NPVs of $31,227.48, $16,516.53, $4,507.67, and -$5,398.55. Thus, we can see the rate of return where the NPV is zero will be between 24% and 29%. Using an Excel spreadsheet, one can compute a break-even rate of return (called IRR in the next section) of about 26.16% (26.159675%, which will give a zero negative present value to two decimal points). Beginning with a rate of 24%, the rule of thumb when trying various rates is to increase the rate of return until the NPV becomes zero. If it becomes negative, then one decreases the rate.