Capital Investment Appraisal under Uncertainty
Kipande Ltd is considering investing in a new production line costing KES 20 million. The project has a expected life of 5 years with no residual value. The company uses straight-line depreciation. Expected annual sales are 30,000 units at a selling price of KES 500 per unit, and variable costs are KES 300 per unit. Fixed costs (excluding depreciation) are KES 2 million per year. The company's cost of capital is 12%. The tax rate is 30%, and tax is paid one year in arrears. The company has a target payback period of 3 years and a minimum accounting rate of return (ARR) of 15%. The finance director is concerned about the uncertainty of sales volume and wants to know the sensitivity of the project's NPV to changes in selling price and variable cost.
1. Calculate the project's NPV, payback period, and ARR. Assess whether the project should be accepted based on all three criteria.
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Calculations:
- Annual sales revenue = 30,000 × KES 500 = KES 15,000,000
- Variable costs = 30,000 × KES 300 = KES 9,000,000
- Contribution = KES 6,000,000
- Fixed costs = KES 2,000,000
- Depreciation = KES 20,000,000 / 5 = KES 4,000,000
- Profit before tax = 6,000,000 - 2,000,000 - 4,000,000 = KES 0
- Tax = 0
- Net cash flow = Profit before tax + Depreciation = KES 4,000,000 (since tax is zero)
Wait, profit before tax is zero, so tax is zero. Annual cash flow = 4,000,000.
NPV: PV of annuity factor at 12% for 5 years = 3.6048 PV of cash flows = 4,000,000 × 3.6048 = KES 14,419,200 NPV = 14,419,200 - 20,000,000 = -KES 5,580,800 (negative)
Payback period: Initial investment = 20,000,000 Annual cash flow = 4,000,000 Payback = 20,000,000 / 4,000,000 = 5 years (exceeds target of 3 years)
ARR: Average annual profit = 0 (since profit before tax is zero) ARR = 0% (below 15% target)
Assessment: All three criteria indicate rejection: negative NPV, payback longer than target, and ARR below minimum. The project should not be accepted.
Note: The above assumes no tax because profit is zero. If tax were considered with tax shield on depreciation, there might be a tax saving, but with zero profit, no tax is payable. Thus cash flow is correct.
2. Calculate the sensitivity of the NPV to a 1% change in selling price and variable cost. Interpret the results and advise management on which variable is more critical to monitor.
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Sensitivity analysis: First, find the base NPV: -KES 5,580,800 (negative).
Selling price sensitivity: A 1% change in selling price = 1% × KES 500 = KES 5 per unit. Change in annual contribution = 30,000 units × KES 5 = KES 150,000. This increases annual cash flow by KES 150,000 (since tax is zero). PV of change = 150,000 × 3.6048 = KES 540,720. So NPV changes by +KES 540,720 for a 1% increase in price. Sensitivity percentage = (NPV / PV of change) × 1%? Actually, sensitivity is the percentage change in variable that makes NPV zero. To make NPV zero, need PV of cash flows = 20,000,000. Current PV = 14,419,200. Shortfall = 5,580,800. Required increase in annual cash flow = 5,580,800 / 3.6048 = KES 1,548,000. As percentage of base cash flow (4,000,000) = 38.7%. So selling price can fall by 38.7% before NPV becomes zero? Wait, that's the sensitivity to cash flow, not price. Better: Sensitivity to selling price = (NPV / PV of change for 1% change) × 1%? Actually, the percentage change in price that makes NPV zero = (NPV / PV of change per 1% change) × 1%. PV of change per 1% change in price = 540,720. So percentage change = (5,580,800 / 540,720) × 1% = 10.32%. Thus, a 10.32% decrease in selling price would make NPV zero.
Variable cost sensitivity: 1% change in variable cost = 1% × KES 300 = KES 3 per unit. Change in annual cash flow = 30,000 × KES 3 = KES 90,000 (increase in cost reduces cash flow). PV of change = 90,000 × 3.6048 = KES 324,432. Percentage change to make NPV zero = (5,580,800 / 324,432) × 1% = 17.20%. So a 17.20% increase in variable cost would make NPV zero.
Interpretation: The project is more sensitive to changes in selling price (10.32% decrease wipes out NPV) than to variable cost (17.20% increase). Therefore, management should monitor selling price more closely, as a relatively small decline in price could make the project unviable. However, both sensitivities are significant, and given the already negative NPV, the project is not viable under current assumptions. Management should consider ways to increase price or reduce costs before proceeding.