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

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

BlackTom AI · Accepted Answer

We start by identifying the cash flows and discount rate from the problem. Initial outlay (Year 0) = -300,000. The subsequent cash inflows are: Year 1 = 250,000; Year 2 = 90,000; Year 3 = 90,000; Year 4 = 100,000; Year 5 = 110,000. The discount rate is 9% per year.

Next, we compute the present value of each inflow:
- Year 1 PV = 250,000 / 1.09 ≈ 229,357.80
- Year 2 PV = 90,000 / (1.09)^2 ≈ 90,000 / 1.1881 ≈ 75,736.90
- Year 3 PV = 90,000 / (1.09)^3 ≈ 90,000 / 1.295029 ≈ 69,470.80
- Year 4 PV = 100,000 / (1.09)^4 ≈ 100,000 / 1.411581 ≈ 70,880.10
- Year 5 PV = 110,000 / (1.09)^5 ≈ 110,000 / 1.538622 ≈ 71,520.90

Then, sum the PVs of inflows: 229,357.80 + 75,736.90 + 69,470.80 + 70,880.10 + 71,520.90 ≈ 516,966.50.
NPV = Present value of inflows + Present value of outflows (initial investment is already negative, so we add -300,000): NPV ≈ -300,000 + 516,966.50 ≈ 216,966.50.

Now compare with the given options:
- Option 1: $216,940.48. This is very close to the computed NPV (difference due to rounding of intermediate PVs). It aligns with the calculated value when using standard rounding rules for each present value.
- Option 2: $234,156.78. This would imply a higher total PV of inflows, which would occur if one or more discount factors or cash flows were misapplied (for example, using a slightly smaller discount factor for several years or misreading a cash flow amount). It is not consistent with the 9% discounting shown.
- Option 3: $205,873.92. This would result from under-discounting the inflows (or overestimating outflows) in aggregate; it deviates meaningfully from the proper PVs of the individual cash flows.
- Option 4: $228,454.01. This is close to the Year 1 PV alone (or to a partial sum), but neglects the substantial PVs from Years 2–5. It undercounts the later inflows, so it’s not the correct total NPV.

Putting it together, the calculation clearly yields a figure near $216,940.48, which matches Option 1 when rounding is applied. The other options reflect common missteps such as misplacing or omitting later-year cash flows, incorrect discounting, or incorrect aggregation of inflows and outflows.

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

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