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which of the following statements is correct? assume that the project b…

Question

which of the following statements is correct? assume that the project being considered has normal cash flows, with one cash outflow at t = 0 followed by a series of positive cash flows. a projects mirr is always greater than its regular irr. a projects mirr is always less than its regular irr. if a projects irr is greater than its wacc, then its mirr will be greater than the irr. to find a projects mirr, we compound cash inflows at the regular irr and then find the discount rate that causes the pv of the terminal value to equal the initial cost. to find a projects mirr, the textbook procedure compounds cash inflows at the wacc and then finds the discount rate that causes the pv of the terminal value to equal the initial cost.

Explanation:

Brief Explanations
  1. Analyze Option A: For normal cash flows (one outflow at t=0, then inflows), MIRR is not always greater than IRR. IRR assumes reinvestment at IRR, MIRR at WACC (or other rate). If cash inflows are reinvested at a rate lower than IRR (like WACC < IRR), MIRR is less than IRR. So A is wrong.
  2. Analyze Option B: MIRR is not always less than IRR. If reinvestment rate (e.g., WACC) is higher than IRR, MIRR could be higher. But for normal cash flows with typical WACC < IRR, MIRR is less than IRR. Wait, no—wait, let's recall: MIRR formula. The regular IRR assumes reinvestment at IRR, MIRR (textbook method) reinvests at WACC. So if WACC < IRR, then the terminal value (TV) of inflows when reinvested at WACC is less than TV when reinvested at IRR. Then, MIRR (the rate that makes PV(TV) = initial cost) will be less than IRR. So B says "always less"—is that true? Wait, no—if WACC > IRR, then TV (reinvested at WACC) is higher than TV (reinvested at IRR), so MIRR would be higher than IRR. But the problem states "normal cash flows" (one outflow, then inflows). So in most cases, WACC is less than IRR for a profitable project. But the option says "always"—but maybe in the context of normal cash flows (and typical WACC < IRR), but let's check other options.
  3. Analyze Option C: If IRR > WACC, then reinvesting at WACC (for MIRR) gives a lower TV than reinvesting at IRR. So MIRR would be less than IRR, not greater. So C is wrong.
  4. Analyze Option D: The MIRR calculation (textbook? No, the "reinvestment rate" for MIRR—some methods use WACC, some IRR. But the standard textbook procedure for MIRR (to address reinvestment rate assumption flaw of IRR) compounds cash inflows at WACC, not IRR. So D is wrong (it says compound at IRR).
  5. Analyze Option E: The textbook procedure for MIRR: compound cash inflows at the WACC (to reflect realistic reinvestment rate) to get the terminal value (TV), then find the discount rate (MIRR) that makes PV(TV) = initial cost (outflow at t=0). This matches the definition. Let's confirm: MIRR steps (textbook): 1. Compound each cash inflow at WACC to t = n (terminal value). 2. Find the rate (MIRR) where PV(TV) = initial investment (CF0). So E is correct.

Wait, let's recheck Option B: "A project’s MIRR is always less than its regular IRR." Is that always true? No, because if WACC > IRR, then compounding at WACC (higher than IRR) would give a higher TV, so MIRR would be higher than IRR. But the problem states "normal cash flows" (one outflow, then inflows). So in cases where WACC > IRR, MIRR could be higher. But maybe in the context of the question, with normal cash flows (and the project is profitable, so IRR > WACC? No, a project could have IRR < WACC (unprofitable). But the options: let's re-express.

Wait, the correct answer is E? Wait, no—wait, let's check the options again.

Wait, Option E: "To find a project’s MIRR, the textbook procedure compounds cash inflows at the WACC and then finds the discount rate that causes the PV of the terminal value to equal the initial cost." Yes, that's the textbook MIRR method. Let's check other options:

Option A: MIRR always > IRR? No. For example, if WACC is 10%, IRR is 15%. Compounding inflows at 10% (lower than 15%) gives a lower TV, so MIRR (rate to make PV(TV)=CF0) is less than IRR. So A is wrong.

Option B: "always less"—but if WACC > IRR, MIRR could be higher. So B is wrong (not always).

Option C: If IRR > WACC, then MIRR > IRR? No, because compounding at WACC (lower than IRR) gives lower TV, so MIRR is less than IRR. So C is wrong.

Option D: "compound cash inflows at the regula…

Answer:

E. To find a project's MIRR, the textbook procedure compounds cash inflows at the WACC and then finds the discount rate that causes the PV of the terminal value to equal the initial cost.