We are evaluating a project that costs $1,140,000, has a ten-year life, and has

Question

We are evaluating a project that costs $1,140,000, has a ten-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 54,000 units per year. Price per unit is $50, variable cost per unit is $20, and fixed costs are $720,000 per year. The tax rate is 35 percent, and we require a return of 18 percent on this project.

1) Calculate the accounting break-even point. (I got 27800)

2) What is the degree of operating leverage at the accounting break-even point? (I got 7.316)

3) Calculate the base-case cash flow and NPV. (I got 624900 for cash flow)

4) What is the sensitivity of NPV to changes in the sales figure?

5) What is the sensitivity of OCF to changes in the variable cost figure?

Explanation / Answer

Break even point = Fixed cost / Contribution per unit = (720000+114000)/30 = 27800 units

Assumed that 18% is the cost of equity and the firm is unlevered

Degree of operating leverage is calculated as Contribution / EBIT = 1620000/786000 = 2.06

Taking a trail and error method for calculating NPV=0 bu decreasing sales, a sale of $2128870.65 will give an NPV of 0

The percentage difference in sales is (2700000-2128870.65)/2700000*100 = 21%. Sensitivity to sales is 21%

Same as above, a variable cost of $1651129.3 will give a 0 NPV. The sensitivity is (1651129.3-1080000)/1080000*100 = 52.88%

Units Price Value Sales 54000 50 2700000.00 Variable cost 54000 20 1080000.00 Contribution 1620000.00 Fixed cost 720000.00 Depreciation 114000.00 Profit 786000.00 Tax 275100.00 Profit after tax 510900.00 Cashflow 624900.00 PV factor cumulated for 10 years @18% 4.4941 PV of future cash flows 2808363.09 Original Investment 1140000.00 NPV 1668363.09

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