# Calculating Net Present Value (NPV) for a Public Project

A public project is supposed to yield a net benefit of $NBi every year starting with the current year and lasting for 4 more years. Assume that the discount rate is r. The net present value (NPV) of this project is given by the following formula, where NBi denotes the net benefit from the project in year I, with the subscripts denoting the respective year, starting with the current year denoted 0:

## A. NPV = NB0 + NB₄/(1+r)⁴

## B. NPV = NB0/(1+r) + NB₁/(1+r)¹ + NB₂/(1+r)² + NB₃/(1+r)³

## C. NPV = NB0 /(1+r)⁴

## D. NPV = NB0/(1+r)⁰ + NB₁/(1+r)¹ + NB₂/(1+r)² + NB₃/(1+r)³+ NB₄/(1+r)⁴

**Final answer:** The right choice is option D. Each year's net benefit is divided by (1+r) raised to the power of that year, contributing to the NPV calculation. The correct option is D.

**Explanation:** The correct choice for the calculation of the Net Present Value (NPV) given the information about a public project outlined in your question is option D. The NPV is a sum of the net benefits (NBi) for each year, discounted back to their present values using the discount rate 'r'. The discounting acknowledges the time value of money (the future value is worth less than the same amount today).

So, for a project spanning five years (current year is 0, so it goes up to year 4), it can be represented as:

NPV = NB0/(1+r)⁰ + NB₁/(1+r)¹ + NB₂/(1+r)² + NB₃/(1+r)³+ NB₄/(1+r)⁴

As we can see, each year's net benefit is divided by the factor (1+r) raised to the power equivalent to the year number, which plays an integral part in the calculation of NPV.

What is the correct formula for calculating the Net Present Value (NPV) of a public project spanning 5 years with a discount rate 'r'? The correct formula for calculating the NPV of a public project spanning 5 years with a discount rate 'r' is option D: NPV = NB0/(1+r)⁰ + NB₁/(1+r)¹ + NB₂/(1+r)² + NB₃/(1+r)³+ NB₄/(1+r)⁴.