Question

recent project nominated for consideration at your company has a four-year cash flow of $20,000; $25,000; $30,000; and $50,000. the cost of the project is $75,000. what would the npv of the above project be if the inflation rate was expected to be 4% in each of the next four years?

Answer 1

To calculate the NPV of the given project with a 4% inflation rate, the cash flows of each year are discounted to present value and summed up, and then the initial cost of the project is subtracted. The NPV comes out to approximately $36,783.54.

Step-by-step explanation:

To calculate the Net Present Value (NPV) of a project when considering inflation, we must discount each year's cash flow to present value using the inflation rate as the discount rate. Since the inflation rate is provided at 4%, we will use this rate to discount the project's future cash flows.

Here's how we can calculate the NPV:

• Year 1 Cash Flow: $20,000/(1+0.04)¹ = $20,000/1.04 = $19,230.77
• Year 2 Cash Flow: $25,000/(1+0.04)² = $25,000/1.08 ≈ $23,148.15
• Year 3 Cash Flow: $30,000/(1+0.04)³ ≈ $30,000/1.1249 ≈ $26,668.69
• Year 4 Cash Flow: $50,000/(1+0.04)⁴ ≈ $50,000/1.1699 ≈ $42,735.93

Summing these up yields a total present value of the cash flows of ≈ $111,783.54. Since the cost of the project is $75,000, subtracting this cost from the total present value gives us:

NPV = Total Present Value - Project Cost ≈ $111,783.54 - $75,000 = $36,783.54