Moerdyk & Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the one with the higher IRR will also have the higher NPV, i.e., no conflict will exist.

WACC:

5.50%

0

1

2

3

4

CFS

-$1,025

$650

$450

$250

$50

CFL

-$1,025

$100

$300

$500

$700

Question

Moerdyk & Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the one with the higher IRR will also have the higher NPV, i.e., no conflict will exist.

WACC:

5.50%

0

1

2

3

4

CFS

-$1,025

$650

$450

$250

$50

CFL

-$1,025

$100

$300

$500

$700

BlackTom AI · Accepted Answer

NPV comparison at the WACC determines value; IRR can mislead when cash‑flow timing differs. Here compute the NPV difference (the value forgone if IRR picks the lower‑NPV project).

Relevant concepts:
- NPV using the WACC (5.50%) is the correct measure of value for mutually exclusive projects.
- If IRR ranks projects differently than NPV, choosing by IRR can forgo the NPV difference.
- The forgone value = NPV(L) − NPV(S) = PV of the incremental cash flows (L − S).

Step‑by‑step calculation (using exact fractions from 1.055 = 211/200):
Discount factors: D1 = 1/1.055 = 200/211, D2 = (200/211)^2 = 40,000/44,521, D3 = (200/211)^3 = 8,000,000/9,393,931, D4 = (200/211)^4 = 1,600,000,000/1,982,119,441.

Incremental cash flows (L − S): year0 = 0, year1 = −550, year2 = −150, year3 = +250, year4 = +650.
PV of incremental flows = −550·D1 −150·D2 +250·D3 +650·D4.

Compute each term:
- Term1 = −550*(200/211) = −110,000/211 = −521.326539
- Term2 = −150*(40,000/44,521) = −6,000,000/44,521 = −134.768026
- Term3 = 250*(8,000,000/9,393,931) = 2,000,000,000/9,393,931 = +212.903450
- Term4 = 650*(1,600,000,000/1,982,119,441) = 1,040,000,000,000/1,982,119,441 = +524.690686

Sum: −521.326539 −134.768026 +212.903450 +524.690686 = 81.499571 ≈ $81.50.

Why this is the forgone value: IRR would choose the project with the higher internal rate (project S, because it returns cash earlier and thus has the higher IRR), but the correct NPV ranking at the firm’s 5.50% cost of capital favors project L. Choosing by IRR therefore sacrifices NPV equal to NPV(L) − NPV(S) = $81.50.

Why other choices are incorrect: the other numeric options ($67.64, $84.76, $90.46, $80.68) do not match the precise PV of the incremental cash flows computed above; the exact discounted sum equals $81.50.

Final confirmation: the value forgone by choosing the project with the higher IRR is $81.50, matching the provided answer.

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