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

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

BlackTom AI · Accepted Answer

To determine the NPV, we must discount each of the project's cash inflows at the cost of capital (9%) and then subtract the initial outlay.
First, note the cash flows: Year 0 = -300,000; Year 1 = 250,000; Year 2 = 90,000; Year 3 = 90,000; Year 4 = 100,000; Year 5 = 110,000.
Option A: 228,454.01. If we incorrectly treat Year 1 cash flow as fully worth its face value without discounting it or apply an inconsistent discounting pattern, we could land near this figure. However, the correct PV of Year 1 should be 250,000 divided by 1.09, which is about 229,358, not 228,454.01, and we still need to discount the later years.
Option B: 216,940.48. This is very close to the precise NPV after performing all proper discounting and summing, then subtracting the initial outlay. It suggests careful discounting of each cash flow to present value and a final net figure around 216.9k.
Option C: 205,873.92. This would arise if several cash inflows were discounted more aggressively or if one or more inflows were undervalued, such as discounting inflows at a higher rate than 9% or using a wrong year alignment.
Option D: 234,156.78. This would correspond to overestimating the present value of inflows—perhaps by using too small a discount factor or misplacing the year of one of the cash flows.
Now, let us verify by calculating each component carefully:
- PV of Year 1: 250,000 / 1.09 ≈ 229,358
- PV of Year 2: 90,000 / (1.09)^2 ≈ 90,000 / 1.1881 ≈ 75,732
- PV of Year 3: 90,000 / (1.09)^3 ≈ 90,000 / 1.295029 ≈ 69,492
- PV of Year 4: 100,000 / (1.09)^4 ≈ 100,000 / 1.411582 ≈ 70,844
- PV of Year 5: 110,000 / (1.09)^5 ≈ 110,000 / 1.538624 ≈ 71,519
Sum of PV inflows ≈ 229,358 + 75,732 + 69,492 + 70,844 + 71,519 ≈ 516,945
Subtract the initial outlay: 516,945 − 300,000 ≈ 216,945
This result aligns most closely with the value 216,940.48 among the provided options, indicating a precise calculation would yield that figure.
If you compare the other options to the step-by-step PV calculations: the first option diverges from the Year 1 PV by a noticeable margin, suggesting a misapplication of the discount rate or a misalignment of cash flows; the third option underestimates by combining discounted inflows in a way that lowers the total; the fourth option overstates the PV of inflows, likely from an under-discounting error or incorrect year framing.
In summary, the correct approach uses discounting at 9% for each future cash flow and aggregates them before subtracting the initial investment, yielding an NPV around 216,940.48. The stray figures arise from common mistakes in discount application or arithmetic, not from the proper present-value methodology.

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单项选择题

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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]$205,873.92$216,940.48$234,156.78$228,454.01

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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