Which of the following is the correct equation to solve for the NPV of the project that has an initial outlay of $30,000, followed by three years of $20,000 in incremental cash inflow? Assume a discount rate of 10%.
A) NPV = -30,000 + (3 × 20,000)/(1.10)3
B) NPV = -$30,000 + $20,000/(1.10)1 + $20,000/(1.10)2 + $20,000/(1.10)3
C) NPV = -$30,000 + $20,000/(1.01).10 + $20,000/(1.02).10 + $20,000/(1.03).10
D) NPV = -$30,000 + $20,000/(1.1).10 + $20,000(1.2).10 + $20,000(1.3).10

Question

Quizplus · Accepted Answer

The correct equation for calculating the NPV of a project with an initial outlay and incremental cash inflows is to discount each cash flow separately and then sum them up. This can be represented by the equation NPV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + ... + CFn/(1+r)^n, where CF represents the cash flow in each period, r represents the discount rate, and n represents the total number of periods.

In this case, the initial outlay is a cash outflow, so it is represented as a negative value (-$30,000). The incremental cash inflows are $20,000 per year and start in year 1. Therefore, the correct equation for calculating the NPV is:

NPV = -$30,000 + $20,000/(1.10)^1 + $20,000/(1.10)^2 + $20,000/(1.10)^3

Simplifying this equation gives us:

NPV = -$30,000 + $18,181.82 + $16,528.93 + $15,025.39 = $19,735.14

Therefore, the best choice is B.

Which of the Following Is the Correct Equation to Solve