Question at position 1 (3 marks, difficulty level: Easy) What is the NPV of this project? Assume the cost of capital is 9%. [table]
Year | Project A
0 | -300,000 1 | 250,000 2 | 90,000 3 | 90,000 4 | 100,000 5 | 110,000
[/table]$205,873.92$216,940.48$234,156.78$228,454.01

Question

Question at position 1 (3 marks, difficulty level: Easy) What is the NPV of this project? Assume the cost of capital is 9%. [table]
Year | Project A
0 | -300,000 1 | 250,000 2 | 90,000 3 | 90,000 4 | 100,000 5 | 110,000
[/table]$205,873.92$216,940.48$234,156.78$228,454.01

BlackTom AI · Accepted Answer

We start by restating the problem: an initial outlay of 300,000 at year 0, and the annual cash inflows of 250,000 (year 1), 90,000 (year 2), 90,000 (year 3), 100,000 (year 4), and 110,000 (year 5). The discount rate is 9%. The net present value is the sum of the discounted inflows minus the initial outlay.

Option A: 205,873.92
To assess this, discount each cash flow at 9% and sum:
- Year 1: 250,000 / 1.09 ≈ 229,365
- Year 2: 90,000 / 1.09^2 ≈ 75,780
- Year 3: 90,000 / 1.09^3 ≈ 69,500
- Year 4: 100,000 / 1.09^4 ≈ 70,860
- Year 5: 110,000 / 1.09^5 ≈ 71,500
Total inflows ≈ 517,005; NPV ≈ 517,005 − 300,000 ≈ 217,005
The option 205,873.92 is noticeably lower than this approximate NPV, suggesting it undervalues the discounted inflows.

Option B: 216,940.48
This value is very close to the rough calculation above (around 217,000). Since the exact discounting involves precise powers of 1.09, this aligns with the expected sum of discounted inflows minus the initial outlay. Small discrepancies can arise from rounding intermediate steps, but the magnitude matches the calculated range.

Option C: 234,156.78
This figure is higher than the rough aggregate of the discounted cash inflows. To reach such an NPV, either the inflows would need to be larger when discounted, or the initial outlay would need to be smaller. Given the provided cash flows and 9% discount rate, this appears inconsistent with the standard present-value math here.

Option D: 228,454.01
This value sits between the approximate 217k range and the 234k figure, but it still exceeds the straightforward sum of discounted inflows minus 300,000 by about 11k. If one computes with precise powers of 1.09 and more exact arithmetic, this option would typically be outside the expected result for these cash flows.

Key ideas to compare across options:
- The core method is discounting each future cash flow by (1.09)^t and summing, then subtracting 300,000.
- The year-by-year PVs (roughly) are in the 229k, 76k, 69.5k, 70.9k, and 71.5k ranges, producing a total near 517k, and subtracting 300k yields about 217k.
- Any option far from that ~217k mark likely results from rounding differences, misapplication of the discount factor, or arithmetic mistakes.

In summary, based on standard NPV calculation with 9% discounting, the option close to the computed aggregate is the one near 217k, while the others deviate due to either underestimating the discounted inflows or overestimating them. The most plausible match to a correct computation is the option that sits around 216,940.48, with slight variations attributable to rounding at intermediate steps.

Question at position 1 (3 marks, difficulty level: Easy) What is the NPV of this project? Assume the cost of capital is 9%. [table] Year | Project A 0 | -300,000 1 | 250,000 2 | 90,000 3 | 90,000 4 | 100,000 5 | 110,000 [/table]$205,873.92$216,940.48$234,156.78$228,454.01

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Question at position 1 (3 marks, difficulty level: Easy) What is the NPV of this project? Assume the cost of capital is 9%. [table] Year | Project A 0 | -300,000 1 | 250,000 2 | 90,000 3 | 90,000 4 | 100,000 5 | 110,000 [/table]$228,454.01$216,940.48$205,873.92$234,156.78

Question at position 1 (3 marks, difficulty level: Easy) What is the NPV of this project? Assume the cost of capital is 9%. [table] Year | Project A 0 | -300,000 1 | 250,000 2 | 90,000 3 | 90,000 4 | 100,000 5 | 110,000 [/table]$216,940.48$234,156.78$205,873.92$228,454.01

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