The Expansion Decision at Riverside Foods: NPV, Payback and the Cost of Capital
Riverside Foods is considering a second production line costing Tk 4,000,000, payable immediately. Expected incremental cash inflows are Tk 1,300,000 a year for five years, after all operating costs but before tax. The line will be depreciated straight-line to nil over five years for accounting purposes. Riverside pays tax at 25%, one year in arrears. The company's existing capital is Tk 6,000,000 of equity, on which shareholders require 16%, and Tk 4,000,000 of debt carrying 10% interest. The finance director proposes to appraise the project at the 10% debt rate because 'that is the rate we will actually pay to fund it'. The managing director wants the money back within three years and says the project should be rejected if payback is longer. A consultant has offered a lease alternative at Tk 950,000 a year for five years, payable in advance.
1. Compute the appropriate discount rate and evaluate the finance director's proposal to use the debt rate.
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Weighted average cost of capital. Market values are equity Tk 6,000,000 and debt Tk 4,000,000, total Tk 10,000,000, so weights are 60% and 40%.
WACC = (0.60 x 16%) + (0.40 x 10%) = 9.6% + 4.0% = 13.6%.
If interest is tax-deductible, the after-tax cost of debt is 10% x (1 - 0.25) = 7.5%, giving WACC = 9.6% + (0.40 x 7.5%) = 9.6% + 3.0% = 12.6%. The correct figure depends on whether the 10% is already stated pre-tax; the analysis should state the assumption explicitly. Using 12.6% is standard where interest is deductible.
Why the debt rate is wrong. The debt rate measures the return lenders require for bearing low risk, secured against specific assets. The project's cash flows are operating and uncertain, and they accrue to shareholders who bear residual risk. Discounting at 10% would value the project as if it were as safe as a secured loan and would systematically accept projects that do not cover the shareholders' required return. It also ignores the 60% of the funding that is equity.
The deeper error. Funding mix and project risk are separate questions. Even if the line were 100% debt-financed, the correct rate would still reflect the risk of the cash flows, not the instrument used to finance them. The finance director is confusing the source of funds with the cost of capital.
Judgement. Use 12.6% (or 13.6% if interest is not deductible), disclose the assumption, and test sensitivity at both. The gap between them is small enough that the decision should not turn on it, which is itself a useful finding.
2. Compute the project's relevant cash flows, net present value at 12.6%, and payback. State the decision.
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Step 1: incremental cash flows.
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Operating inflow | 1,300,000 | 1,300,000 | 1,300,000 | 1,300,000 | 1,300,000 | |
| Tax at 25%, one year in arrears | (325,000) | (325,000) | (325,000) | (325,000) | ||
| Tax on year 5 inflow | ||||||
| Capital spend | (4,000,000) | |||||
| Net cash flow | (4,000,000) | 1,300,000 | 975,000 | 975,000 | 975,000 | 975,000 |
A final tax payment of Tk 325,000 falls in year 6 and must be included in a complete appraisal; it is shown below as a year-6 outflow.
Step 2: discount at 12.6%. Discount factors: year 1 = 0.888, year 2 = 0.789, year 3 = 0.700, year 4 = 0.622, year 5 = 0.552, year 6 = 0.491.
- Year 1: 1,300,000 x 0.888 = 1,154,400
- Year 2: 975,000 x 0.789 = 769,275
- Year 3: 975,000 x 0.700 = 682,500
- Year 4: 975,000 x 0.622 = 606,450
- Year 5: 975,000 x 0.552 = 538,200
- Year 6: (325,000) x 0.491 = (159,575)
Present value of inflows = 3,591,250. Less initial outlay 4,000,000 gives NPV = approximately (Tk 409,000), negative.
Step 3: payback. Cumulative flows: year 1 1,300,000; year 2 2,275,000; year 3 3,250,000; year 4 4,225,000. Payback = 3 + (750,000 / 975,000) = 3.77 years.
Decision. Reject on NPV at 12.6%. The project destroys value. Note that the tax lag is decisive: ignoring it would give a positive NPV, so the timing of tax is a material appraisal issue, not a technicality.
Caveat. The figures are sensitive to the discount rate. At 10% the NPV would be positive, which is exactly why the finance director's proposal must be resisted: the choice of rate, not the cash flows, would determine the answer.
3. Evaluate the managing director's payback rule and compare the lease alternative qualitatively.
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The payback rule. Payback of 3.77 years fails the three-year test, so the managing director's rule and the NPV rule agree here. That agreement is coincidental, not a validation of the rule.
Payback has three defects. It ignores all cash flows after the cut-off, so it cannot distinguish a project that dies in year four from one that generates cash for a decade. It ignores the time value of money within the payback period. And the three-year threshold is arbitrary: it is not derived from the cost of capital or from the company's strategic needs. Its real merit is as a liquidity and risk screen, which matters for a company with limited reserves, but it should sit alongside NPV, not replace it.
Here the rule gives the right answer for the wrong reason: it rejects the project because cash returns slowly, not because the project fails to earn its cost of capital.
The lease alternative. At Tk 950,000 a year in advance, total nominal payments are Tk 4,750,000 over five years, which looks more expensive than the Tk 4,000,000 purchase. But the comparison is not like for like:
- Timing. Lease payments start immediately, so the first is undiscounted; the discounted cost at 12.6% is roughly 950,000 x (1 + 0.888 + 0.789 + 0.700 + 0.622) = approximately Tk 3,800,000.
- Tax. Lease rentals are typically deductible in full, giving a tax shield of 25% x 950,000 = Tk 237,500 a year, one year in arrears, which the purchase option does not give in the same form.
- Risk and flexibility. The lease transfers residual value risk and technology obsolescence to the lessor and preserves Tk 4,000,000 of capital for working capital in a low-margin food business.
- Control. The lease may restrict modification of the line and creates a five-year commitment that is harder to exit than owned assets.
Conclusion. The lease is worth appraising properly on a discounted, after-tax basis rather than dismissing it on nominal cost. The decision should be made on the lower present value of cost, adjusted for risk transfer and flexibility, not on which option has the smaller headline number.