I have a question about problem 11 in chapter 4 of Public Finance and Public Pol

Question

I have a question about problem 11 in chapter 4 of Public Finance and Public Policy 5th edition by Jonathan Gruber. The answer on Chegg says that the project should not be undertaken at an discount because the net wealth will always be in the negative. However, when I input 2% into the equation I get a positive value. It is possible that I did not do the equation right on the calculator but any help would be appreciated.

Here is the problem: Consider a project that costs $126,000, provides an income of $70,000 a year for five years, and costs $225,000 to dispose of at the very end of the fifth year. Assume that the first payment comes at the start of the year after the projefct is undertaken. Should the project be undertaken at a 0% discount rate? How about 2%? 5%? 10%?

Here is how I set up the equation for 2%: -126,000+70,000+70,000/(1.02)2+70,000/(1.02)^3+70,000/(1.02)^4-155,000/(1.02)^5

My answer was 1,525.2824

Explanation / Answer

Your answer is correct considering that only first years payment was paid at the start of the year while the rest of the years the payment was made at the end

when assuming that every year the payment was received at the start of the year this should be the equation

-126,000+70,000+70,000/(1.02)+70,000/(1.02)^2+70,000/(1.02)^3+70,000/(1.02)^4-225,000/(1.02)^5

the NPV being +6751

so in anyway the project should be undertaken

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