Replacement Press with Working Capital and Tax
Halden Engineering is evaluating a five-year replacement press. The new press costs $1,000,000 and requires $100,000 installation; it will be depreciated straight-line to zero over five years. It is expected to reduce cash operating costs by $380,000 per year. At the end of year 5 it can be sold for $150,000. The old press can be sold now for $90,000; its book value is $40,000. The company needs $120,000 of additional working capital immediately, recoverable at the end. The tax rate is 25%, tax is paid in the same year, and the after-tax discount rate is 10%. The CFO wants to use a 7% real rate instead, leave out working capital because it comes back, and treat the installation cost as an expense. The board wants a clear NPV and a critique of those assumptions before approving the project.
1. Calculate the initial outlay, annual incremental after-tax cash flow, terminal cash flow, and NPV at 10%. State whether the project should be accepted.
Read the worked answer
Initial outlay: new press and installation are capitalized, $1,000,000 + $100,000 = $1,100,000. Sale of old press: gain = $90,000 − $40,000 = $50,000; tax = $12,500; net proceeds = $77,500. Working capital = $120,000. Net initial cash flow = −$1,100,000 + $77,500 − $120,000 = −$1,142,500. Annual depreciation = $1,100,000/5 = $220,000. After-tax cost savings = $380,000 × 75% = $285,000. Depreciation tax shield = $220,000 × 25% = $55,000. Annual cash flow years 1–5 = $340,000. Terminal flow: salvage $150,000; tax on gain $150,000 × 25% = $37,500; net salvage = $112,500; plus working capital recovery $120,000 = $232,500. NPV = −$1,142,500 + $340,000 × 3.7908 + $232,500 × 0.6209 = −$1,142,500 + $1,288,872 + $144,359 = $290,731. The NPV is positive, so accept the project, subject to qualitative review.
2. Critique the CFO's three assumptions: use a 7% real rate, omit working capital, and expense installation.
Read the worked answer
The 7% real rate is not comparable with the cash flows as presented, which are nominal and include tax depreciation based on historical cost. Mixing a real discount rate with nominal cash flows overstates NPV. Either discount nominal cash flows at a nominal rate, or convert all cash flows to real terms and use the real rate consistently. Omitting working capital is wrong: $120,000 is committed at the start, has an opportunity cost, and is recovered only at the end. Its timing affects NPV even though the principal returns. Expensing installation would reduce the depreciable basis and change the tax shield: capitalizing $100,000 creates additional depreciation of $20,000 per year and a tax shield of $5,000 per year. Expensing may accelerate the tax benefit, but it does not make the cost irrelevant. The analysis should also ignore any sunk cost on the old press and include its forgone sale proceeds as an opportunity cost, which the calculation does.