To calculate the sensitivity of Operating Cash Flow (OCF) to changes in quantity sold, we need to calculate the OCF for the initial quantity sold and then calculate the OCF for a different quantity sold. The formula for OCF is as follows:
OCF = (Quantity Sold x (Selling Price - Variable Cost)) - Fixed Costs - Tax
1. Calculate OCF for the initial quantity sold:
Quantity Sold = 150,000 units
Selling Price = $39
Variable Cost = $20
Fixed Costs = $210,000
Tax Rate = 31%
OCF = (150,000 x ($39 - $20)) - $210,000 - (31% x ((150,000 x ($39 - $20)) - $210,000))
OCF = (150,000 x $19) - $210,000 - (0.31 x (150,000 x $19 - $210,000))
OCF = $2,850,000 - $210,000 - (0.31 x ($2,850,000 - $210,000))
OCF = $2,850,000 - $210,000 - (0.31 x $2,640,000)
OCF = $2,850,000 - $210,000 - $817,440
OCF = $1,822,560
2. Calculate OCF for a different quantity sold (let's say 180,000 units):
Quantity Sold = 180,000 units
OCF = (180,000 x ($39 - $20)) - $210,000 - (31% x ((180,000 x ($39 - $20)) - $210,000))
OCF = (180,000 x $19) - $210,000 - (0.31 x (180,000 x $19 - $210,000))
OCF = $3,420,000 - $210,000 - (0.31 x ($3,420,000 - $210,000))
OCF = $3,420,000 - $210,000 - (0.31 x $3,210,000)
OCF = $3,420,000 - $210,000 - $993,900
OCF = $2,216,100
3. Calculate the sensitivity of OCF to changes in quantity sold:
ΔOCF = OCF for different quantity sold - OCF for initial quantity sold
ΔOCF = $2,216,100 - $1,822,560
ΔOCF = $393,540
Therefore, the Operating Cash Flow (OCF) is sensitive to changes in quantity sold, with a sensitivity of $393,540.