Question

Consider a four-year project with the following information: initial fixed asset investment = $476061; straight-line depreciation to zero over the four-year life; zero salvage value; price = $34; variable costs = $24; fixed costs = $194366; quantity sold = 79941 units; tax rate = 31 percent. Calculate the sensitivity of the OCF to changes in the quantity sold. (Do not round intermediate calculations and round your final answer to 2 decimal places. Omit the "$" sign and commas in your response. For example, $1.2345 should be entered as 1.23.)

Answer 1

Initial Investment = $476,061
Useful Life = 4 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $476,061 / 4
Annual Depreciation = $119,015.25

If quantity sold are 79,941:

OCF = [(Price - Variable Costs) * Quantity Sold - Fixed Costs] * (1 - tax) + tax * Depreciation
OCF = [($34 - $24) * 79,941 - $194,366] * (1 - 0.31) + 0.31 * $119,015.25
OCF = $605,044 * 0.69 + 0.31 * $119,015.25
OCF = $454,375.09

If quantity sold are 79,950:

OCF = [(Price - Variable Costs) * Quantity Sold - Fixed Costs] * (1 - tax) + tax * Depreciation
OCF = [($34 - $24) * 79,950 - $194,366] * (1 - 0.31) + 0.31 * $119,015.25
OCF = $605,134 * 0.69 + 0.31 * $119,015.25
OCF = $454,437.19

Sensitivity of OCF = Change in OCF / Change in Quantity Sold
Sensitivity of OCF = ($454,437.18 - $454,375.09) / (79,950 - 79,941)
Sensitivity of OCF = $62.10 / 9
Sensitivity of OCF = $6.90