Appraising a Project with Unequal Lives and a Capital Ration
Dunmore Engineering has $500,000 of capital available and is considering two mutually exclusive projects plus a smaller one. Project X costs $400,000, has a five-year life and expected annual net cash inflows of $120,000. Project Y costs $300,000, has a three-year life and inflows of $130,000 per year. Project Z costs $100,000, has a four-year life and inflows of $32,000 per year. The company's cost of capital is 10%. The finance manager has ranked the projects by payback period, which favours Y, and proposes funding Y and Z together. Annuity factors at 10%: 3 years 2.487, 4 years 3.170, 5 years 3.791.
1. Calculate NPV for each project and critique the payback ranking.
Read the worked answer
X: $120,000 x 3.791 = $454,920, NPV $54,920. Y: $130,000 x 2.487 = $323,310, NPV $23,310. Z: $32,000 x 3.170 = $101,440, NPV $1,440. Payback ignores the time value of money and cash flows after payback, and it cannot compare projects of different lives fairly. Ranking by NPV favours X, not Y. The manager's proposal of Y plus Z uses $400,000 and yields combined NPV of $24,750, which is less than X alone at $54,920 while leaving $100,000 idle. The recommendation should be based on NPV and on how the capital budget is used.
2. Because the projects have unequal lives, the manager asks whether a replacement-chain comparison changes the answer. Advise, showing an equivalent annual annuity.
Read the worked answer
Equivalent annual annuity converts each NPV to a level annual amount over its life: EAA = NPV / annuity factor. X: $54,920 / 3.791 = $14,487. Y: $23,310 / 2.487 = $9,373. Z: $1,440 / 3.170 = $454. On a repeatable basis X still wins, so the unequal lives do not overturn the ranking. The assumption is that each project can be repeated on the same terms, which should be checked. If capital is rationed to $500,000, the best combination is X plus Z at $500,000, giving combined NPV of $56,360, which beats X alone. The judgement is to rank by NPV or EAA for mutually exclusive options, but by profitability index when the capital limit binds and projects are divisible.