We are evaluating a project that costs $832,000, has an eight-year life, and has
ID: 2764033 • 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.
What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
What is the sensitivity of OCF to changes in the variable cost figure? (Do not round intermediate calculations. A negative answer should be indicated by a minus sign.)
b-2
What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
Explanation / Answer
Answer:
b. NPV, when Sales = 40,000 x $ 40 = $ 1,600,000 is equal to [{$1,600,000 (sales) - $ 15 x 40,000(variable cost) - $ 700,000 (fixed cost) - $ 832,000/8 (depreciation) - $ 67,600 (tax@35% on 196,000) + $ 104,000 (depreciation add back)} x PVAF @18% for 8 years - $ 832,000] = $ 232,400 x 4.0775 - $ 832,000 = $ 115,611
and,
NPV, when Sales = 30,000 x $ 40 = $ 1,200,000 is equal to [{$1,200,000 (sales) - $ 15 x 30,000(variable cost) - $ 700,000 (fixed cost) - $ 832,000/8 (depreciation) + $ 18,900 (tax saving@35% on - $ 54,000) + $ 104,000 (depreciation add back)} x PVAF @18% for 8 years - $ 832,000] = $ 68,900 x 4.0775 - $ 832,000 = - $ 551,060.25
therefore, change in NPV due to change in Sales = {$ 115,611 - (-$ 551,060.25)} / (40,000 - 30,000) = 66.6671 per unit change in sales quantity. That is, for every 1 unit change in sales quantity, the NPV shall change by $ 66.6671 in the direction of change in sales quantity.
c. Calculation of change in Operating Cash Flow with respect to change in Variable Cost;
When Variable cost is $ 15 per unit that is $ 600,000 then Operating Cash Flow = $ 232,400
and when Variable Cost id $ 10 per unit that is $ 400,000 then Opearting Cash Flow = $ 1,600,000 - $ 400,000 - $ 700,000 - $ 104,000 - $ 138,600 + $ 104,000 = $ 361,400;
therefore, for every $ 1 change in Variable Cost per unit, the Operating Cash Flow shall change by $ 232,400 - $ 361,400 / $ 15 - $ 10 = $ 25,800 per $ change in Variable Cost in the opposite direction of Variable Cost Change.
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