Question

In: Finance

Consider a 3-year project with the following information: initial fixed asset investment = $420,000; straight-line depreciation...

Consider a 3-year project with the following information: initial fixed asset investment = $420,000; straight-line depreciation to zero over the 3-year life; zero salvage value; price = $29; variable costs = $16; fixed costs = $197,400; quantity sold = 78,960 units; tax rate = 35 percent. How sensitive is OCF to changes in quantity sold? (Do not round your intermediate calculations.)

A) $6.00

B) $0.12

C) $10.90

D) $9.63

E) $8.45

Solutions

Expert Solution

First, we calculate the OCF at 78,960 units as below :

depreciation per year = initial investment / 3

income before tax = revenue - VC - FC - Depreciation

OCF = Income before tax - taxes

Year Investment Revenue Variable Cost Fixed Cost Depreciation Income before taxes Taxes OCF
0 ($420,000.00)
1 $2,289,840.00 ($1,263,360.00) ($197,400.00) ($140,000.00) $689,080.00 ($241,178.00) $447,902.00
2 $2,289,840.00 ($1,263,360.00) ($197,400.00) ($140,000.00) $689,080.00 ($241,178.00) $447,902.00
3 $2,289,840.00 ($1,263,360.00) ($197,400.00) ($140,000.00) $689,080.00 ($241,178.00) $447,902.00

OCF at 78,960 output is $447,902

Next, we calculate the OCF at 79,961 units of output :

Year Investment Revenue Variable Cost Fixed Cost Depreciation Income before taxes Taxes OCF
0 ($420,000.00)
1 $2,289,869.00 ($1,263,376.00) ($197,400.00) ($140,000.00) $689,093.00 ($241,182.55) $447,910.45
2 $2,289,869.00 ($1,263,376.00) ($197,400.00) ($140,000.00) $689,093.00 ($241,182.55) $447,910.45
3 $2,289,869.00 ($1,263,376.00) ($197,400.00) ($140,000.00) $689,093.00 ($241,182.55) $447,910.45

OCF at 78,961 output is $447,910.45

sensitivity of OCF to changes in output = change in OCF / change in output = (447,910.45 - 447,902) /1 ==> 8.45

The answer is E


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