Question

Consider a 9-year project with the following information: initial fixed asset investment = $430,000; straight-line depreciation...

Consider a 9-year project with the following information: initial fixed asset investment = $430,000; straight-line depreciation to zero over the 9-year life; zero salvage value; price = $32; variable costs = $17; fixed costs = $167,700; quantity sold = 98,943 units; tax rate = 33 percent. How sensitive is OCF to changes in quantity sold?

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Answer #1
Initial Investment $430,000.00
Selling Price $32.00
Variable Cost $17.00
Fixed Cost $167,700.00
Quantity Sold 98943 units
Tax Rate 33.00%
Depreciation = $430,000/9 $47,777.78
OCF = ((SP-VC) x Q -FC) x (1-T) + (T x D)
OCF = ((32-17) x 98943 -167,700) x (1-33%) + (33% x $47,777.78) $897,784.82
NPV=-Initial Outlay + OCF (PVIFA10%, 9) + Salvage value
NPV=- 430000 + 897784.82 (PVIFA10%, 9) + 0 $4,740,364.14
Quantity Sold OCF NPV
Base Case 98,943 $897,784.82 $4,740,364.14
Optimistic + 10% 108,837 987,563 $5,257,400.56
Pessimistic - 10% 89,049 808,006 $4,223,327.73
Sensitivity = ?OCF/?Q = ($897,784 - $987,563)/(98943-108,837) 9.07
Sensitivity = ?NPV/?Q = ($4740364 - $5257400)/(98943-108,837) $52.26
For every additional unit sold, OCF goes up by $9.07 and NPV by $52.26
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