Question

In: Finance

Consider a project with a life of 4 years with the following information: initial fixed asset...

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?

Solutions

Expert Solution

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.

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