A Levered Expansion: WACC, Sunk Costs, and the Lease Option
Ardent Foods is evaluating a new production line with a five-year life. The line costs $60 million, depreciated straight-line to zero, and is expected to generate incremental revenue of $85 million per year with cash operating costs of $62 million. Working capital of $10 million is required upfront and recovered at the end. The line will use floor space that Ardent currently rents to a third party for $2.5 million per year; the lease can be terminated immediately. An existing packaging machine with a market value of $4 million and a zero tax basis would be scrapped if the project proceeds; it has no other use. Salvage value of the new line is $8 million. Ardent's tax rate is 25%. Management proposes a 40% debt target, a pre-tax cost of debt of 6%, a risk-free rate of 4%, and a market risk premium of 5.5%. A comparable pure-play has an equity beta of 1.2 and a debt-to-equity ratio of 25%. Ardent's own equity beta is 1.5. The CFO wants to use the company's 9.5% WACC and argues the $2.5 million rent should be ignored because “we own the space.”
1. Compute the project WACC using the comparable's unlevered beta and Ardent's target capital structure. Explain why Ardent's own beta is not the right input.
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Unlever the comparable at its 25% debt-to-equity ratio: βu = 1.2 / [1 + (1 − 0.25)(0.25)] = 1.2 / 1.1875 = 1.0105. Relever at Ardent's target 40% debt / 60% equity: βL = 1.0105 × [1 + (1 − 0.25)(40/60)] = 1.0105 × 1.50 = 1.5158. Cost of equity = 4% + 1.5158 × 5.5% = 12.34%. After-tax cost of debt = 6% × (1 − 0.25) = 4.5%. WACC = 0.60 × 12.34% + 0.40 × 4.5% = 7.40% + 1.80% = 9.20%.
Ardent's own beta of 1.5 reflects its current business mix and current leverage, not the new line's risk. If the line is in a different business, the comparable's asset beta is the better estimate of operating risk. Using the company's 9.5% WACC would also embed the wrong capital structure if Ardent is moving to 40% debt. If flotation costs are material-say 3% on new equity-the required return should be adjusted upward, or the initial outlay increased by the flotation cost; otherwise the project looks artificially attractive.
2. Build the incremental after-tax cash flows. Treat the rental space and the old machine correctly, and state whether the $4 million machine is a sunk cost.
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Initial outlay: equipment $60m + working capital $10m + after-tax opportunity cost of the old machine. The old machine is not sunk because it has a market value and is forgone; sale proceeds $4m with zero basis create a $1m tax bill, so the after-tax opportunity cost is $3m. Total t0 outflow = $73m. The $2.5m annual rent is also an opportunity cost: using the space forgoes cash rent, so it is an incremental operating cost, not a sunk cost.
Annual operating cash flow: revenue $85m − cash costs $62m − forgone rent $2.5m − depreciation $12m = EBIT $8.5m. Taxes at 25% = $2.125m; NOPAT = $6.375m; add back depreciation $12m = $18.375m per year. Terminal year adds salvage: $8m proceeds, zero book value, tax at 25% = $2m, so after-tax salvage = $6m; plus working-capital recovery $10m = $16m terminal cash flow. Do not deduct interest expense-it is embedded in the WACC. Do not deduct the $4m machine as a sunk cost; it is an opportunity cost included at t0.
3. Compute NPV at the project WACC. Address the CFO's two claims and give a recommendation with a sensitivity.
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Discount factor annuity at 9.20% for five years: [1 − 1/(1.092)^5] / 0.092. 1.092^5 ≈ 1.553, so the factor is [1 − 0.644] / 0.092 ≈ 3.87. PV of annual cash flows = $18.375m × 3.87 = $71.1m. PV of terminal $16m = $16m / 1.553 = $10.3m. Total PV = $81.4m. NPV = $81.4m − $73m = $8.4m. The project creates value, but the margin is thin-about 11% of the initial outlay.
The CFO's first claim is wrong: the company's 9.5% WACC reflects the current mix and current business risk; the project should use 9.2%. The second claim is also wrong: the $2.5m rent is a real opportunity cost because the space can be leased today. Ignoring it would overstate annual cash flow by $2.5m pre-tax, or $1.875m after tax-about $7.3m of PV. Sensitivity: if revenue falls 5% to $80.75m, EBIT falls to $4.25m, NOPAT to $3.19m, annual cash flow to $15.19m, PV of annual flows to $58.8m, total PV about $69.1m, and NPV turns negative at roughly −$3.9m. Recommendation: proceed only with customer contracts or a price concession that protects the first two years; otherwise the project is too close to breakeven.