Question

Consider a five-year project with the following information: initial fixed asset investment = $402,000; straight-line depreciation to zero over the five-year life; zero salvage value; price = $31/unit; variable costs = $10.40/unit; fixed costs = $147,000 per year; quantity sold = 84,000 units per year; tax rate = 25%. How sensitive is OCF to changes in quantity sold (i.e., how much does OCF change given an increase of one unit sold in a year)? $14.29 $15.45 $16.10 $13.80 $12.88

Answer 1

The correct answer is $15.45

There are two ways of approaching this problem. First way is that you calculate the operating cash flow when the quantity sold is 84,000. Then you again calculate what the OCF would be at a quantity sold of 84001 and then you compute the difference between the two. The more elegant way is to think about all the different quantities or items that are dependent on the amount of quantity sold and then figure out how sensitive are they to changes in quantity sold. Shown below are both these approaches.

First way

Calculate OCF at 84,000 quantity sold:

Calculate OCF at 84001 quantity sold:

The difference between the two is $15.45 (1,207,665.45 - 1,207,650)

Second way

When you take a closer, you can see that the only quantities in the above calculation dependent on the amount of quantity sold are sales, variable costs and incomes taxes (because they are calculated as a percentage of income before tax). The difference between sales price and variable cost per unit is $20.60 ( 31-10.40). So, a unit change in quantity sold would change the OCF by this amount, after adjusting for taxes i.e. 20.60 (1 - 0.25) = $15.45.