Question at position 2 You have just been hired as a senior financial manager of the XYZ Inc. by the eccentric CEO, Elon Tusk. Elon is considering the following potential projects (all cash flows happen at the end of the year). Assume the cost of capital for XYZ Inc. is 14%. [table]
Year | Project A | Project B | Project C
0 | -200,000 | -480,000 | -680,000 1 | 150,000 | 280,000 | -100,000 2 | 80,000 | 280,000 | 350,000 3 | 90,000 | 280,000 | 350,000 4 | 100,000 | 280,000 | 750,000 5 | 110,000 | 280,000 | 650,000
[/table] What is the IRR for Project B?50.87%48.7%61.5%33.4%

Question

Question at position 2 You have just been hired as a senior financial manager of the XYZ Inc. by the eccentric CEO, Elon Tusk. Elon is considering the following potential projects (all cash flows happen at the end of the year). Assume the cost of capital for XYZ Inc. is 14%. [table]
Year | Project A | Project B | Project C
0 | -200,000 | -480,000 | -680,000 1 | 150,000 | 280,000 | -100,000 2 | 80,000 | 280,000 | 350,000 3 | 90,000 | 280,000 | 350,000 4 | 100,000 | 280,000 | 750,000 5 | 110,000 | 280,000 | 650,000
[/table] What is the IRR for Project B?50.87%48.7%61.5%33.4%

BlackTom AI · Accepted Answer

We start by restating the problem and options to ensure clarity.
Question: You are evaluating Project B, which has an initial outlay of -480,000 (year 0) and a series of end-of-year cash inflows of 280,000 from year 1 through year 5. The cost of capital is 14%, and you are asked to find the IRR for Project B. Answer choices: 50.87%, 48.7%, 61.5%, 33.4%.

Option 1: 50.87%
To check IRR, set the net present value (NPV) to zero using r = IRR and solve -480,000 + 280,000/(1+r) + 280,000/(1+r)^2 + 280,000/(1+r)^3 + 280,000/(1+r)^4 + 280,000/(1+r)^5 = 0. If r ≈ 0.5087, the sum of the discounted inflows should be about 480,000, offsetting the initial outlay. The computation shows that an IRR near 50.8% makes the present value of the inflows ≈ 480,000, yielding NPV ≈ 0, which aligns with this option.

Option 2: 48.7%
This would require a slightly larger present value of inflows relative to the outlay than at 50.87%. However, the discounting at 48.7% still yields a high PV of inflows relative to 480k, producing a positive NPV (likely well above zero), so it would not zero out exactly. In short, 48.7% undervalues the required discount rate to bring NPV to zero compared to the precise IRR.

Option 3: 61.5%
Discounting at 61.5% reduces the present value of each yearly inflow quite aggressively. The sum of discounted inflows would be significantly less than 480,000, producing a negative NPV. This would not solve the equation to zero and thus is not the IRR.

Option 4: 33.4%
At 33.4%, the inflows are discounted less heavily, yielding a PV well above the initial outlay of 480,000. The NPV would be strongly positive, not zero, so 33.4% cannot be the IRR.

Now, integrating these observations: IRR is the discount rate that makes NPV zero. Since solving the equation numerically shows that a rate around 50.8% brings the PV of five 280,000 inflows to roughly 480,000, the IRR is closest to 50.87%. The other options either under- or over-discount the cash inflows relative to this balance, leading to NPVs not equal to zero. Therefore, the most accurate IRR given the cash flows is around 50.87%.

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