Examiners Report – March 2018 – Question 1

@chrisj1 said:
Question:
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 its sales increases by 15%?

Answer: B 26
In order to calculate the operating profit, the total cost must be calculated first. As sales are
$100m and profit is $20m, the total cost will be $80m. Given the operational gearing is 33.33%, the fixed cost to variable cost will be in the ratio of 1:3. The fixed cost can be calculated as ¼ x $80m=$20m and the variable cost will be $60m. Contribution will be $40m before the increase in sales. After the 15% increase in sales the new contribution will be 1.15 x $40m= $46m and the new operating profit will be $46m – $20m (FC)= $26m

How do they go from 1:3 to 1/4. Please could someone explain the answer.

Hi Chris,

The ratio of fixed costs to variable costs is 1:3 so that means for every one part of fixed costs there are three variable costs parts. Therefore, there are a total of four parts, where one part related to fixed costs and three parts relate to variable costs. So if you know total costs are 80 million then the amount relating to fixed costs is 80 million x 1/4 = 20 million.
To show that this works note that this means fixed costs = 20 and variable costs = 20 x 3 = 60, so the total costs still = 80 million.

Hope that helps.

how do they get 1: 3 first?

The operating gearing (leverage) ratio is the relationship between fixed cost (FC) and variable costs (VC). For example:
Company A: FC = $20k, VC = $40k gives ratio 1: 2 – i.e. half (50%) and FC is 1/3rd of TOTAL cost (20+40 = 60)
Company B: FC = $20k, VC = $60k gives ratio 1: 3 – i.e. a third (33 1/3%) and FC is 1/4 of TOTAL cost
Company C: FC = $20k, VC = $80k gives ratio 1: 4 – i.e. a quarter (25%) and FC is 1/5th of TOTAL cost

I have a question about the same question.

The question is saying that the sales were increased by 15%.

So why are we taking the 15% increase both on Sales and VC please?