Question

Consider a four-year project with the following information: initial fixed asset investment = $491,731; straight-line depreciation to zero over the four-year life; zero salvage value; price = $33; variable costs = $24; fixed costs = $195,602; quantity sold = 79,813 units; tax rate = 36 percent. Calculate the sensitivity of the OCF to changes in the quantity sold.

[Hint: Think of this as, "How much does OCF change if we can sell one more unit each year?"]

(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 = $491,731
Useful Life = 4 years

Annual Depreciation = Initial Investment / Useful Life
Annual Depreciation = $491,731 / 4
Annual Depreciation = $122,932.75

If quantity sold is 79,813:

OCF = [(Price - Variable Costs) * Quantity Sold - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
OCF = [($33.00 - $24.00) * 79,813 - $195,602] * (1 - 0.36) + 0.36 * $122,932.75
OCF = $522,715 * 0.64 + 0.36 * $122,932.75
OCF = $378,793.39

If quantity sold is 79,814:

OCF = [(Price - Variable Costs) * Quantity Sold - Fixed Costs] * (1 - Tax Rate) + Tax Rate * Depreciation
OCF = [($33.00 - $24.00) * 79,814 - $195,602] * (1 - 0.36) + 0.36 * $122,932.75
OCF = $522,724 * 0.64 + 0.36 * $122,932.75
OCF = $378,799.15

Sensitivity of OCF = Change in OCF / Change in Quantity Sold
Sensitivity of OCF = ($378,799.15 - $378,793.39) / (79,814 - 79,813)
Sensitivity of OCF = $5.76