We are evaluating a project that costs $1,180,000, has a ten-year life, and has

Question

We are evaluating a project that costs $1,180,000, 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 66,000 units per year. Price per unit is $45, variable cost per unit is $25, and fixed costs are $750,000 per year. The tax rate is 35 percent, and we require a return of 15 percent on this project. a-1 Calculate the accounting break-even point. (Do not round intermediate calculations. Round your answer to the nearest whole number, e.g., 32.) Break-even point units a-2 What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations. Round your answer to 3 decimal places, e.g., 32.161.) DOL b-1 Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your cash flow answer to the nearest whole number, e.g., 32. Round your NPV answer to 2 decimal places, e.g., 32.16.) Cash flow $ NPV $ b-2 What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV/Q $ c. What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest whole number, e.g., 32. ) OCF/VC $

Explanation / Answer

Answer: a-1. Here it is given that the total sales = 66000 units Price per unit = $45 variable cost per unit = $25 Fixed cost = $750,000 Break Even point = Fixed costs / contribution per unit Contribution per unit = Revenues per unit - Variable costs per unit = $45 -$25 = $20 Therefore accounting break even point = $750000/$20 = 37500 units a-2. Degree of operating leverage = (sales - variable costs) / (sales - variable cost - fixed costs) Here the break even point is = 37500 units Therefore Degree of operating leverage at break even point (at 37500 units) = ($45*37500 - $25*37500) / ($45*37500 - $25*37500 - $750000) or DOL = $750000/$0 = infinite b-1. Base case cash flow are calculated as under: Year-0 Year-1 Year-2 Year-3 Year-4 Year-5 Year-6 Year-7 Year-8 Year-9 Year-10 Revenues 2970000 2970000 2970000 2970000 2970000 2970000 2970000 2970000 2970000 2970000 Fixed costs 750000 750000 750000 750000 750000 750000 750000 750000 750000 750000 Variable costs 1650000 1650000 1650000 1650000 1650000 1650000 1650000 1650000 1650000 1650000 Depreciation 118000 118000 118000 118000 118000 118000 118000 118000 118000 118000 Total Costs 2518000 2518000 2518000 2518000 2518000 2518000 2518000 2518000 2518000 2518000 EBT 452000 452000 452000 452000 452000 452000 452000 452000 452000 452000 Taxes(35%) 158200 158200 158200 158200 158200 158200 158200 158200 158200 158200 Net income 293800 293800 293800 293800 293800 293800 293800 293800 293800 293800 OCF 411800 411800 411800 411800 411800 411800 411800 411800 411800 411800 Capital Spending 1180000 Net Cash flows -1180000 411800 411800 411800 411800 411800 411800 411800 411800 411800 411800 Now the NPV is calculated a discount rate of 15% NPV = $886,728.92 b-2. Sensitivity of NPV to changes in sales figure is calculated by finding new OCF at new sales figy=ure and then calculating its NPV Then the required sensitivity of NPV = change in NPV / change in sales Now lets change the revenue figures to 70000 units and calculate the net cash flows like this: Year-0 Year-1 Year-2 Year-3 Year-4 Year-5 Year-6 Year-7 Year-8 Year-9 Year-10 Revenues 3150000 3150000 3150000 3150000 3150000 3150000 3150000 3150000 3150000 3150000 Fixed costs 750000 750000 750000 750000 750000 750000 750000 750000 750000 750000 Variable costs 1750000 1750000 1750000 1750000 1750000 1750000 1750000 1750000 1750000 1750000 Depreciation 118000 118000 118000 118000 118000 118000 118000 118000 118000 118000 Total Costs 2618000 2618000 2618000 2618000 2618000 2618000 2618000 2618000 2618000 2618000 EBT 532000 532000 532000 532000 532000 532000 532000 532000 532000 532000 Taxes(35%) 186200 186200 186200 186200 186200 186200 186200 186200 186200 186200 Net income 345800 345800 345800 345800 345800 345800 345800 345800 345800 345800 OCF 463800 463800 463800 463800 463800 463800 463800 463800 463800 463800 Capital Spending 1180000 New Net Cash flows -1180000 463800 463800 463800 463800 463800 463800 463800 463800 463800 463800 These are the new cash flows and the new NPV = $1,147,704.89 Therefore change in NPV = $1147704.89 - $886728.92 = $260,975.97 and change in sales = 70000 units - 66000 units = 4000 units Therefore required sensitivity = $260975.97/4000= $65.24 it means by increasing the sales by one unit NPV increases by $65.24 c. Now we have to calculate the snesitivity of OCF to changes in variable cost. for this we need to calculate the OCF at new variable cost suppose the new variable cost is $25 Therefore the new OCF will be calculated like this: Year-0 Year-1 Year-2 Year-3 Year-4 Year-5 Year-6 Year-7 Year-8 Year-9 Year-10 Revenues 2970000 2970000 2970000 2970000 2970000 2970000 2970000 2970000 2970000 2970000 Fixed costs 750000 750000 750000 750000 750000 750000 750000 750000 750000 750000 Variable costs 1584000 1584000 1584000 1584000 1584000 1584000 1584000 1584000 1584000 1584000 Depreciation 118000 118000 118000 118000 118000 118000 118000 118000 118000 118000 Total Costs 2452000 2452000 2452000 2452000 2452000 2452000 2452000 2452000 2452000 2452000 EBT 518000 518000 518000 518000 518000 518000 518000 518000 518000 518000 Taxes(35%) 181300 181300 181300 181300 181300 181300 181300 181300 181300 181300 Net income 336700 336700 336700 336700 336700 336700 336700 336700 336700 336700 OCF 454700 454700 454700 454700 454700 454700 454700 454700 454700 454700 Capital Spending 1180000 Net Cash flows -1180000 454700 454700 454700 454700 454700 454700 454700 454700 454700 454700 New OCF = $454700 Old OCF = $411800 Hence change in OCF = $411800 - $454700= -$42,900.00 ans change in variable cost = $25 - $24 = $1 So required sensitivity = change in OCF / change in variable cost per unit = -42900.00

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