Question

Consider a four-year project with the following information: Initial fixed asset investment = $655,000; straight-line depreciation to zero over the four-year life; zero salvage value; price = $28; variable costs = $16; fixed costs = $245,000; quantity sold = 61,000 units; tax rate = 21 percent.

How sensitive is OCF to changes in quantity sold? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The operating cash flow (OCF) for the project increases by $9.48 for each additional unit sold, based on the given costs, price, and tax rate.

Step-by-step explanation:

To calculate how sensitive the operating cash flow (OCF) is to changes in quantity sold, we first need to compute the initial OCF using the provided information. We apply the formula OCF = (Sales - Variable Costs - Fixed Costs)(1 - Tax Rate) + (Depreciation * Tax Rate), where Sales = Price * Quantity, and Depreciation is calculated using the straight-line method. Let's compute the initial OCF and then determine the change in OCF due to a change in quantity sold.

Initial Sales = $28 * 61,000 units = $1,708,000

Initial Variable Costs = $16 * 61,000 units = $976,000

Depreciation = Initial Fixed Asset Investment / Project Life = $655,000 / 4 = $163,750 per year

Initial OCF = (($1,708,000 - $976,000 - $245,000) * (1 - 0.21)) + ($163,750 * 0.21) = ($487,000 * 0.79) + $34,388 = $384,630 + $34,388 = $419,018

Now, let's determine how a change in quantity sold by one unit affects OCF. For one additional unit sold: Change in Sales = $28, Change in Variable Costs = $16, Change in OCF = ($28 - $16)(1 - 0.21) = $12 * 0.79 = $9.48 per unit.

Therefore, the OCF is sensitive to the quantity sold by $9.48 for each additional unit sold.