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log co has an operating gearing ratio of 33.33%. Its sales are currently 100m and its operating profit is 20m. Operating gearing is calculated by dividing fixed costs by variable costs.
What will its operating profit be if its sales increase by 15%
I calculated the sales to be 100*1.15 = 115
Variable costs 66.67/100*115 = 76.6705
Fixed costs 33.33/100*100 = 33.33
Operating profit 115-76.6705-33.33=4.9995
Where have I went wrongFixed costs divided by variable costs = 33.33% or 1/3.
Therefore for every $1 of fixed costs the variable costs are $3, and the total costs are $1 + $3 = $4.
At the moment the operating profit is $20 and so the total costs are 100 – 20 = $80.
Of these $80, the fixed costs are 1/4 x $80 = $20, and the variable costs are 3/4 x $80 = $60.
The sales increase to 100 x 1.15 = $115
The variable costs increase to 60 x 1.15 = $69
The fixed costs, by definition, remain at $20.Therefore the new operating profit = 115 – 69 – 20 = $26M
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