A project for a mining company is partly illustrated with the cash flows provided in the nearby table. The initial investment is $42.0 million. The firm’s beta is 1.56, while the current yield on a 1-year Treasury is 3.8%. The firm’s investment bank recommends a market risk premium of 7.0%. What are the two IRRs for this project?

TIME NET CASH FLOW

0

$(42,000,000)
1 $41,000,000
2 $45,000,000
3 $45,000,000
4 $45,000,000
5 $45,000,000
6 $(200,000,000)

Question

A project for a mining company is partly illustrated with the cash flows provided in the nearby table. The initial investment is $42.0 million. The firm’s beta is 1.56, while the current yield on a 1-year Treasury is 3.8%. The firm’s investment bank recommends a market risk premium of 7.0%. What are the two IRRs for this project?

TIME	NET CASH FLOW

0

$(42,000,000)
1	$41,000,000
2	$45,000,000
3	$45,000,000
4	$45,000,000
5	$45,000,000
6	$(200,000,000)

BlackTom AI · Accepted Answer

Question restatement: A mining project has the following cash flows: initial investment of -$42.0 million at time 0, then +$41.0 million at year 1, +$45.0 million at years 2–5, and -$200.0 million at year 6. The task is to determine the two IRRs for this project.

Step-by-step analysis of the cash-flow pattern: The sequence of cash flows changes sign three times: from initial outflow to inflow (− to +), and later from inflows to a large outflow (positive to negative) at year 6. In standard IRR analysis, each sign change in the cash-flow stream can indicate an additional IRR. Since there are two sign changes (at t=0→1 and at t=5→6), the project can possess up to two IRRs.

Option evaluation approach (without given MC options): Normally, one would solve for the discount rate r in the equation NPV = 0, i.e.,
-42,000,000 + 41,000,000/(1+r) + 45,000,000/(1+r)^2 + 45,000,000/(1+r)^3 + 45,000,000/(1+ r)^4 + 45,000,000/(1+ r)^5 - 200,000,000/(1+r)^6 = 0.

Because the cash-flow sequence contains both a modest early inflow burst and a very large negative cash flow at the end, the NPV function as a function of r can cross zero at two distinct r values. This makes multiple IRRs plausible for this project.

Reasoning about the two reported IRRs (5.07% and 88.88%):
- The lower IRR around 5% typically arises from the more moderate portion of the cash flows (the early years with +41 and +45 million) being overwhelmed by the large final outflow at year 6 only when discounting is relatively small. In other words, at low discount rates, the present value of the -$200 million at year 6 is large in present terms, requiring a small r to balance against the earlier positive cash flows to reach net zero.
- The extremely high IRR near 89% is a characteristic artifact of a large late negative cash flow creating a second crossing of the NPV curve with the horizontal axis when the discount rate is very large. At such a high rate, the present value of the year-6 -$200 million is heavily suppressed, allowing the sum of the earlier positive cash inflows to offset it at a steeply discounted level, producing a second root.

Important conceptual notes:
- Two IRRs exist because of the pattern of cash flows with more than one sign change. In such cases, the IRR rule can be ambiguous for decision-making unless you also consider the project's NPV at the firm’s cost of capital or use alternative decision criteria (e.g., NPV at a given discount rate, or MIRR).
- The provided result of 5.07% and 88.88% is plausible given the described cash-flow structure, but in practice one should verify with a solver (or financial calculator) to ensure the roots are accurate, and also check for potential numerical artifacts near extreme discount rates.

If you had multiple-choice options, you would typically compare the two IRRs against the required return or capital budgeting thresholds, but here the focus is on understanding why a project with this pattern yields two IRRs and why they span from a modest to a very high percentage.

FA25-BL-BUS-F370-8099 LC #3

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