Question

Consider a project with a life of 4 years with the following information: initial fixed asset investment = $380,000; straight-line depreciation to zero over the 4-year life; zero salvage value; price = $28; variable costs = $15; fixed costs = $121,600; quantity sold = 54,720 units; tax rate = 25 percent. How sensitive is OCF to changes in quantity sold?

Answer 1

Solution:
	sensitive of OCF to changes in quantity sold $	9.75
	[Means for 1 unit sales increase, increases OCF by $9.75 ]
Working Notes:
	Operating cash flows at 54720 units
	=((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation)
	=(($28 - $15) x 54720 - 121600 ) x (1- 0.25) + ( 0.25 x (380000/4))
	=($13 x 54720 - 121600 ) x 0.75 +23,750
	=589760 x 0.75 + 23750
	=442320 + 23750
	=$466,070
	lets take units changes to 54,720 units from 54,500 units
	Operating cash flows at 54500 units
	=((price - variable cost) x annual quantity - fixed cost ) x (1- tax rate) +( tax rate x depreciation)
	=(($28 - $15) x 54500 - 121600 ) x (1- 0.25) + ( 0.25 x (380000/4))
	=($13 x 54500 - 121600 ) x 0.75 +23,750
	=586900 x 0.75 + 23750
	=440175 + 23750
	=$463925
	Sensitivity of OCF to changes in the quantity sold = Change in OCF/ Change in units
	=(OCF at 54720 - OCF at 54500)/(54720 -54500)
	=(466070 - 463925)/220
	=9.75
Alternatively we can calculate this by
	Sensitivity of OCF to changes in the quantity sold
	=(price - variable cost ) x (1- tax rate)
	=(28 - 15 ) x (1- 0.25)
	=13 x 0.75
	=9.75
Please feel free to ask if anything about above solution in comment section of the question.