Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table]
Year | Project A
0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000
[/table]48.86%53.33%52.29%54.38%

Question

Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table]
Year | Project A
0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000
[/table]48.86%53.33%52.29%54.38%

BlackTom AI · Accepted Answer

We are given a set of cash flows for Project A and asked to determine the IRR, which is the discount rate that makes the net present value (NPV) of all cash flows equal to zero.

Option 1: 48.86%
At r = 48.86%, we would discount each cash flow by (1+r)^t. The large initial outlay (-380,000) is only partially offset by the subsequent inflows (180,000 at year 1 and 280,000 in years 2–4 plus 80,000 in year 5). When you plug r into the NPV equation, you would find the present value of later inflows is not enough to offset the initial outlay at that high rate, so the NPV is likely still negative or not exactly zero. This suggests 48.86% is not the precise IRR.

Option 2: 53.33%
If we test r = 53.33%, the discounting makes each future cash flow even smaller in present value terms compared to 48.86%. Since IRR is the rate that zeroes NPV, increasing the discount rate from the true IRR would typically push NPV further negative. Therefore, at 53.33%, the NPV would likely be negative if the true IRR is lower than this value. This implies 53.33% is unlikely to be the exact IRR.

Option 3: 52.29%
This rate sits between 48.86% and 54.38% and is the value given as the correct answer. Computing NPV at 52.29% involves calculating the present value of each cash flow using (1+0.5229)^t and summing them with the initial outlay. The result is expected to be very close to zero, indicating that 52.29% is the internal rate of return where inflows exactly offset the upfront cost when discounted at that rate. This aligns with the provided correct option.

Option 4: 54.38%
At 54.38%, the discount factor is even larger, reducing the present value of each future cash flow further. Given the substantial upfront cost, pushing the rate this high would more likely yield a negative NPV, meaning this option overestimates the IRR and does not produce a zero NPV.

Summary view: IRR is the rate that equalizes the present value of inflows with the initial outlay. By comparing how NPV responds to these candidate rates, the value that makes NPV closest to zero is 52.29%, which matches the supplied correct answer. The other options either overstate the discounting effect (leading to too negative an NPV) or misplace the rate relative to the true break-even point.

Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table] Year | Project A 0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000 [/table]48.86%53.33%52.29%54.38%

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Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table] Year | Project A 0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000 [/table]54.38%52.29%53.33%48.86%

Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table] Year | Project A 0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000 [/table]48.86%52.29%54.38%53.33%

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