Appraising a Plant Upgrade with Uneven Cash Flows
A manufacturer is considering a $600,000 plant upgrade. Expected net cash inflows are $150,000 in year 1, $200,000 in year 2, $220,000 in year 3, $180,000 in year 4 and $120,000 in year 5. The company's cost of capital is 10%. The payback hurdle is 3.5 years. The company can instead invest in a government bond yielding 6% with certainty. The upgrade is financed 70% by debt at 8% pre-tax and 30% by equity; the tax rate is 30%. A director argues that because total inflows ($870,000) exceed the outlay, the project is obviously acceptable.
1. Calculate the payback period and the net present value (NPV) at 10%, and evaluate the director's argument.
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Cumulative cash flows: Y1 150,000; Y2 350,000; Y3 570,000; Y4 750,000. Payback = 3 + (600,000 − 570,000)/180,000 = 3 + 0.167 = 3.17 years, within the 3.5-year hurdle.
NPV at 10% (discount factors):
- Y1: 150,000 × 0.9091 = 136,365
- Y2: 200,000 × 0.8264 = 165,280
- Y3: 220,000 × 0.7513 = 165,286
- Y4: 180,000 × 0.6830 = 122,940
- Y5: 120,000 × 0.6209 = 74,508
- PV inflows ≈ $664,379; NPV = 664,379 − 600,000 = +$64,379
Positive NPV at the 10% cost of capital supports acceptance. The director's reasoning is wrong: undiscounted totals ignore the time value of money and the required return. A project can have inflows exceeding outlay and still destroy value if the return is below the cost of capital.
2. Assess whether the 10% discount rate is appropriate given the financing mix, and discuss one qualitative factor.
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The weighted average cost of capital: debt after tax = 8% × (1 − 0.30) = 5.6%; equity cost is not given, but if we infer it from the 6% bond plus a risk premium, the 10% rate is plausible as a rough WACC. Using 70% debt at 5.6% and 30% equity at, say, 20%, WACC = 0.7×5.6% + 0.3×20% = 3.92% + 6% = 9.92%, close to 10%. So 10% is defensible as a hurdle.
However, the 10% should reflect the project's risk, not just the firm's average. If the upgrade is riskier than existing operations, a higher rate is warranted. Qualitative factors: the 6% bond is a low-risk alternative, so the project must earn a risk premium; technology obsolescence over five years; and whether the cash flow forecasts are reliable. Sensitivity analysis on the year 5 inflow is advisable given its weight.