In: Finance
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?
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. |