Question

Diana usually uses a three-year payback period to determine if a project is acceptable. A recent project with uniform yearly savings over a five-year life had a payback period of almost exactly three years, so Diana decided to find the project's present worth to help determine if the project was truly justifiable. However, that calculation didn't help either since the present worth was exactly 0. What interest rate was Diana using to calculate the present worth? The project has no salvage value at the end of its five-year life.

Diana's interest rate was (just input the number...and round to the nearest whole pecent

Answer 1

The way to solve it is as follows:

Let's assume that the CF over the five-year period is 100, i.e., 20 per year

Now since the payback period is 3 years, we can say that initial investment would be equal to teh CF in first three year, i.e., 60

We are told that the PV of teh CF of 100 over 5 years is equal to investment, i.e., 60 (that's why the NPV is zero).

So we need to solve for r in the following expression

20/(1+r)^1 +20/(1+r)^2 +20/(1+r)^3 +20/(1+r)^4 +20/(1+r)^5 = 60

r = 19.8%