Question

102. Consider a 6-year project with the following information: initial fixed asset investment = $460,000; straight-line depreciation to zero over the 6-year life; zero salvage value; price = $34; variable costs = $19; fixed costs = $188,600; quantity sold = 90,528 units; tax rate = 32 percent. What is the sensitivity of OCF to changes in quantity sold? A. $10.20 per unit B. $11.16 per unit C. $11.38 per unit D. $12.33 per unit E. $12.54 per unit OCF = [($34 - $19) × 90,528 - 188,600][1 - 0.32] + [($460,000/6) × 0.32] = $819,670.93 Using 91,528 units: (You can use any amount as the second level of quantity sold as the sensitivity will be the same.) OCF = [($34 - $19) × 91,528 - 188,600][1 - 0.32] + [($460,000/6) × 0.32] = $829,870.93 Sensitivity = ($829,870.93 - $819,670.93)/(91,528 - 90,528) = $10.20 where 91528 comes from???

Answer 1

Initial Investment = $460,000
Useful Life = 6 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $460,000 / 6
Annual Depreciation = $76,666.67

If number of units sold is 90,528:

OCF = [(Selling Price-Variable Cost)*Sales Volume - Fixed Costs]*(1-tax) + Annual Depreciation*tax
OCF = [($34-$19)*90,528 - $188,600]*(1-0.32) + $76,666.67*0.32
OCF = $819,670.93

Let us assume that number of units sold increases to 91,528 units:

OCF = [(Selling Price-Variable Cost)*Sales Volume - Fixed Costs]*(1-tax) + Annual Depreciation*tax
OCF = [($34-$19)*91,528 - $188,600]*(1-0.32) + $76,666.67*0.32
OCF = $820,870.93

Sensitivity of OCF = Change in OCF / Change in Sales Volume
Sensitivity of OCF = ($820,870.93 - $819,670.93) / (91,528 - 90,528)
Sensitivity of OCF = $1.20 per unit.