Suppose an investment will cost $90,000
initially and will generate the following cash
flows:
• Year 1: 132,000
• Year 2: 100,000
• Year 3: -150,000
• The required return is 15%.
• Should we accept or reject the project?
The NPV is positive at a required return of
15%, so you should Accept
If you use the financial calculator, you
would get an IRR of 10.11% which would
tell you to Reject
To determine whether we should accept or reject the project, we need to calculate the net present value (NPV) of the investment. NPV is a financial metric that measures the profitability of an investment by comparing the discounted cash inflows to the initial investment.
Here's how we can calculate the NPV of this project:
1. Determine the cash flows for each year:
Year 0 (initial investment): -$90,000
Year 1: $132,000
Year 2: $100,000
Year 3: -$150,000
2. Calculate the present value (PV) of each cash flow using the required return rate:
PV = Cash Flow / (1 + Required Return Rate) ^ Number of Years
Year 0 PV: -$90,000 / (1 + 0.15) ^ 0 = -$90,000
Year 1 PV: $132,000 / (1 + 0.15) ^ 1 ≈ $114,782.61
Year 2 PV: $100,000 / (1 + 0.15) ^ 2 ≈ $83,478.26
Year 3 PV: -$150,000 / (1 + 0.15) ^ 3 ≈ -$102,608.70
3. Calculate the NPV by summing up the present values:
NPV = Sum of PVs
NPV = -$90,000 + $114,782.61 + $83,478.26 - $102,608.70 ≈ $5,651.17
Now, if the NPV is positive, it indicates that the project is expected to generate more cash inflows than the initial investment and it should be accepted. Conversely, if the NPV is negative, it suggests that the project is expected to result in a net cash outflow, and it should be rejected.
In this case, the NPV is approximately $5,651.17, which is positive. Therefore, based on the calculated NPV, we should accept the project.
To determine whether we should accept or reject the project, we need to calculate the net present value (NPV) of the investment.
Step 1: Calculate the present value factor for each cash flow using the formula:
PV factor = 1 / (1 + required return)^n, where n is the number of years.
The required return is 15%, so the PV factors for each cash flow are:
Year 1: PV factor = 1 / (1 + 0.15)^1 = 1 / 1.15 = 0.8696
Year 2: PV factor = 1 / (1 + 0.15)^2 = 1 / 1.3225 = 0.7561
Year 3: PV factor = 1 / (1 + 0.15)^3 = 1 / 1.520875 = 0.6575
Step 2: Calculate the present value (PV) of each cash flow by multiplying the cash flow by the corresponding PV factor.
Year 1: PV = 132,000 * 0.8696 = $114,643.20
Year 2: PV = 100,000 * 0.7561 = $75,610
Year 3: PV = -150,000 * 0.6575 = -$98,625
Step 3: Calculate the total present value of all cash flows by summing up the individual present values:
Total PV = PV of Year 1 + PV of Year 2 + PV of Year 3
Total PV = $114,643.20 + $75,610 -$98,625 = -$8,371.80
Step 4: Compare the total PV to the initial investment. If the NPV is positive, you should accept the project; if it's negative, you should reject it.
In this case, the NPV is negative (-$8,371.80), which means that the present value of the cash flows is less than the initial investment. Therefore, the project should be rejected.