Larkspur Foods: Unequal-Life Packaging Machines
Larkspur Foods must choose between two packaging machines. Machine A costs $420,000, has a four-year life, produces after-tax operating cash inflows of $150,000 per year, and can be sold for $40,000 at the end of four years. Machine B costs $680,000, has a six-year life, produces after-tax inflows of $175,000 per year, and has a $60,000 salvage value. Both machines can be replaced with identical units, and demand is expected to continue indefinitely. The appropriate discount rate is 9%. The capital budget is tight, but the CFO insists that the comparison be made on a comparable-life basis rather than by picking the project with the higher IRR. The production manager notes that B is more automated, has higher maintenance risk, and would consume most of the $700,000 available this year. The sales forecast is uncertain, and a 10% shortfall in B's annual inflows is plausible.
1. Compute the NPV of each machine. Show the annuity factors and salvage discount factors.
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NPV_A = −$420,000 + $150,000 × PVIFA(9%,4) + $40,000/(1.09)^4. PVIFA = [1 − (1.09)^−4]/0.09 = 3.2397. PV inflows = $485,955; PV salvage = $28,337; NPV = $94,292. NPV_B = −$680,000 + $175,000 × PVIFA(9%,6) + $60,000/(1.09)^6. PVIFA = 4.4859; PV inflows = $785,033; PV salvage = $35,776; NPV = $140,809. B has the higher NPV, but the raw comparison is incomplete because B lasts two years longer. The NPVs are not directly comparable unless the projects are put on the same time horizon. That is why the CFO's instruction to use a comparable-life method is correct.
2. Compute the equivalent annual annuity (EAA) for each machine and make the recommendation. Why is IRR misleading here?
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EAA = NPV/PVIFA. EAA_A = $94,292/3.2397 = $29,105. EAA_B = $140,809/4.4859 = $31,389. B has higher EAA, so it is the better choice if the projects can be repeated indefinitely and the risk is comparable. Using NPV alone would also favor B ($140,809 > $94,292), but that comparison is misleading because B lasts two years longer. EAA converts each NPV into a level annual equivalent, making the lives comparable. IRR would favor A because A's cash-flow stream is shorter and its IRR is higher; that is exactly the wrong criterion for mutually exclusive projects with different lives. IRR ignores scale and timing, and the reinvestment-rate assumption is not appropriate for ranking here.
3. Assess the sensitivity of the decision to a 10% shortfall in B's inflows and to the tight capital budget. What qualitative factors could overturn the EAA ranking?
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B's EAA advantage is only about $2,284 per year, or 7.3% of A's EAA. If B's annual inflow falls 10% to $157,500, its NPV becomes −$680,000 + $157,500 × 4.4859 + $35,776 = $62,305; EAA = $13,889, far below A. The break-even annual inflow for B is about $172,700 (required NPV = $29,105 × 4.4859 = $130,555; required PV inflows = $810,555; minus salvage $35,776 = $774,779; /4.4859 = $172,700). That is only 1.3% below the forecast, so B is fragile. Qualitatively, B consumes $680,000 of the $700,000 budget, leaving little slack; A preserves $280,000 for other projects or contingencies. If demand is uncertain or capital is rationed, A's lower commitment and earlier replacement option may be worth the lower EAA. Choose B only if the sales forecast is robust and maintenance risk is manageable.