Question

# Consider a four-year project with the following information: initial fixed asset investment = \$491,731; straight-line depreciation...

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.)

#### Homework Answers

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

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