We are evaluating a project that costs $832,000, has an eight-year life, and has
ID: 2654058 • Letter: W
Question
We are evaluating a project that costs $832,000, has an eight-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 40,000 units per year. Price per unit is $40, variable cost per unit is $15, and fixed costs are $700,000 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.
2) What is the degree of operating leverage at the accounting break-even point?
3) Calculate the base-case cash flow and NPV.
4) What is the sensitivity of NPV to changes in the sales figure? (Delta NPV/ Delta Q)
5) What is the sensitivity of OCF to changes in the variable cost figure? (Delta OCF/Delta VC)
We are evaluating a project that costs $832,000, has an eight-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 40,000 units per year. Price per unit is $40, variable cost per unit is $15, and fixed costs are $700,000 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.
2) What is the degree of operating leverage at the accounting break-even point?
3) Calculate the base-case cash flow and NPV.
4) What is the sensitivity of NPV to changes in the sales figure? (Delta NPV/ Delta Q)
5) What is the sensitivity of OCF to changes in the variable cost figure? (Delta OCF/Delta VC)
Explanation / Answer
1. At accounting break even sales, the business generates zero profits.
(It is being assumed that the depreciation amount has been included in the annual fixed costs of $700,000).
Total sales = units sold * price per unit = 40,000 * 40 = 1,600,000. Total variable costs = 40,000*15 = 600,000
Contribution margin = 1,600,000 - 600,000 = 1,000,000. Contribution margin % = 1,000,000/1,600,000 = 62.5%
Fixed costs = 700,000
Break even sales = 700,000/62.5% = $1,120,000. Number of units = 1120000/40 = 28,000 units. (Tax is not considered, as upto the level of breakeven tax is not applicable. Tax is applicable only when profits are earned i.e after break even).
2. degree of operating leverage = (sales - variable costs)/(sales - variable costs - fixed costs)
at break-even, sales = 1,120,000. variable costs = units*variable cost per unit = 28,000*15 = 420,000. fixed costs = 700,000
degree of operating leverage = (1120000 - 420000)/(1120000-420000-700000) = 700,000/0 = undefined and highest.
3. base case operating cash flow:
Operating cash flow = profit after tax+depreciation
depreciation per year = 832,000/8 = 104,000
operating cash flow per year (from year 1 to year 8) = 195,000+104,000 = $299,000
NPV @18%
4. if sales are increased by 10% per year to $1,760,000 then in the model of NPV in excel, NPV will become $1,900,203 i.e an increase of 59%. Thus sensitivity = %change in NPV/% change in sales = 59%/10% = 5.9% change in NPV for every 1% change in sales.
5. current operating cash flow = 299,000. current variable cost = $600,000. If variable costs are increased by 10% to 660,000 then operating cash flow will be: 260,000 (profit after tax = 156,000 and depreciation = 104,000). change in operating cash flow = 299,000 - 260,000 = 39,000. % change = 39,000/299,000 = 13.04%
Thus sensitivity = 13.04%/10% = 1.304% change in OCF for every % change in variable costs.
Year Units sold Price per unit Revenue Variable cost per unit Total variable cost Fixed costs Profit before tax Tax @ 35% Profit after tax 0 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 1 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 2 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 3 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 4 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 5 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 6 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 7 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000 8 40,000 40 1,600,000 15 600,000 700,000 300,000 105,000 195,000Related Questions
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