Question

Assume that the project is expected to return monetary benefits of $20,000 the first year, and increasing benefits of $5,000 until the end of project life (year 1 = $20,000, year 2 = $25,000, year 3 = $30,000). The project also has one-time costs of $30,000, and fixed recurring costs of $10,000 until the end of project life. The project has a discount rate of 8% and a three-year time horizon.

Calculate overall net present value (NPV) of the project at the end of project life.

Answer 1

CF0 = One time cost = -30,000

CF1 = Benefit - fixed recurring costs = 20,000 - 10,000 = 10,000

CF2 = Benefit - fixed recurring costs = 25,000 - 10,000 = 15,000

CF3 = Benefit - fixed recurring costs = 30,000 - 10,000 = 20,000

We need to find the NPV at year 3

NPV = -CF0 * (1 + r)^3 + CF1 * (1 + r)^2 + CF2 * (1 + r)^1 + CF3

NPV = -30,000 * (1 + 0.08)^3 + 10,000 * (1 + 0.08)^2 + 15,000 * (1 + 0.08)^1 + 20,000

NPV = -37,791.36 + 11,664 + 16,200 + 20,000

NPV = $10,072.64