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%

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%52.29%54.38%53.33%

BlackTom AI · Accepted Answer

We start by restating the problem setup and the available choices to anchor the analysis. The project has an initial outlay of -380,000, followed by inflows of 180,000 in year 1, and 280,000 in years 2 through 4, then 80,000 in year 5. The question asks for the internal rate of return (IRR), i.e., the discount rate that makes the net present value (NPV) of all cash flows equal to zero. The answer options are: 48.86%, 52.29%, 54.38%, and 53.33%.

Now, evaluate each option by computing the NPV using the given rate. The NPV formula is NPV = -380,000 + 180,000/(1+r) + 280,000/(1+r)^2 + 280,000/(1+r)^3 + 280,000/(1+r)^4 + 80,000/(1+r)^5, where r is the rate in decimal form.

Option 1: r = 0.4886 (48.86%). Calculate the present values with this rate: 180,000/(1.4886) ≈ 120,900; 280,000/(1.4886)^2 ≈ 126,000; 280,000/(1.4886)^3 ≈ 84,700; 280,000/(1.4886)^4 ≈ 57,000; 80,000/(1.4886)^5 ≈ 2,400. Sum of inflows ≈ 391,000. NPV ≈ -380,000 + 391,000 ≈ +11,000. This yields a positive NPV, indicating the rate is lower than the true IRR (since higher rates push NPV down).

Option 2: r = 0.5229 (52.29%). As a rough check: compute PVs using 1.5229 as the discount factor. 180,000/1.5229 ≈ 118,200; 280,000/1.5229^2 ≈ 120,700; 280,000/1.5229^3 ≈ 79,300; 280,000/1.5229^4 ≈ 52,000; 80,000/1.5229^5 ≈ 9,700. Sum ≈ 379,900. NPV ≈ -380,000 + 379,900 ≈ -100. This is very close to zero, suggesting the IRR is approximately 52.29% since the NPV is nearly balanced around zero at this rate.

Option 3: r = 0.5438 (54.38%). Using 1.5438 as the factor, the PVs shrink further: 180,000/1.5438 ≈ 116,500; 280,000/1.5438^2 ≈ 117,600; 280,000/1.5438^3 ≈ 74,000; 280,000/1.5438^4 ≈ 48,000; 80,000/1.5438^5 ≈ 7,100. Sum ≈ 363,200. NPV ≈ -16,800. This yields a clearly negative NPV, meaning the rate is higher than the IRR.

Option 4: r = 0.5333 (53.33%). With 1.5333 as the base, compute approximate PVs: 180,000/1.5333 ≈ 117,400; 280,000/1.5333^2 ≈ 119,900; 280,000/1.5333^3 ≈ 78,500; 280,000/1.5333^4 ≈ 51,500; 80,000/1.5333^5 ≈ 9,200. Sum ≈ 376,500. NPV ≈ -3,500. This is also negative, though closer to zero than option 3, suggesting the IRR is likely below this rate.

Putting these pieces together, option 2 (52.29%) yields an NPV closest to zero, with the other options producing noticeably positive or negative NPVs. The IRR is the rate at which NPV equals zero, and this analysis shows that around 52.29% brings the net present value to near zero, while higher rates push NPV negative and lower rates push NPV positive. Therefore, the rate that best satisfies NPV ≈ 0 among the provided choices is the one near 52.29%.

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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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 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%

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