# Operating Gearing and Marginal Analysis

If you have an activity, and it has high fixed costs compared to it’s variable costs, then that activity has high operating gearing.

When operating gearing (OG) is high, a small change in sales will have a much bigger effect on profit, so you can say that profits are more sensitive to activity volume when OG is high.

## Marginal analysis

If you need to make a decision that involves a limited time, and small changes to existing practice, you mostly care about the variable costs. (Variable costs are the same thing as marginal costs). Variable costs change depending on the outcome of the decision, making them a relevant cost.

In the same vein, fixed costs are irrelevant because the decision won’t affect them. Marginal analysis is what you use to make short term decisions.

So what are some decisions marginal analysis might be used on? It’s normally used in these four ‘key decision areas’:

• Acception / rejection of special contracts
• Determining the most efficient way to use limited resources
• Decisions on making or buying something (aka outsourcing decisions)
• Closing or continuation decisions

We’ll go through each of the decision types in turn, with examples to explain.

## Acception / rejection of special contracts

If you remember the company that made llamas from the last post, they have a spare capacity to make more llamas. A company overseas has offered to buy 300 llamas at £13 each (normal selling price is £14). As before, the fixed costs are £500 and the variable cost per unit is £12. Should they accept the offer?

There isn’t really a right answer to this. By my calculations, they’ll make 300 × £13 = £3,900 in revenue, and the cost will be 300 × £12 =  £3600. You don’t need to include fixed costs, as they’re being paid out regardless of whether this decision is made.

There are more factors than money to consider here though. Should they be selling off the capacity for that price, or for more? What if other customers who have paid the higher price complain? But the buyer is from overseas, maybe this purchase will help them enter a new market.

So there isn’t a definite right answer here!

## Determining the most efficient way to use limited resources

There’s a company that makes 3 different products: Chalk, cheese and benzoylmethylecgonine. Here’s some more info about the products:

Machine time is limited to 148 hours / week. So what combination of products should be manufactured for the highest profit?

So in this case, the machine time is the limited resource. The first thing to do is calculate how much profit each product makes per unit. This is just revenue – variable costs, so gives us:

• Chalk: £15
• Cheese: £12
• Benzoylmethylecgonine: £11

Now divide the profit by the machine time to work out how much profit each product makes in an hour of machine time:

• Chalk: £3.75
• Cheese: £4
• Benzoylmethylecgonine: £2.75

So now we have everything we need to solve the problem. Obviously we want to make as many units of cheese as possible as it brings in the most profit, so let’s have the machine make 20 units of cheese (to fill the weekly demand, any more will be a waste of resources). As it has a machine time of 3 hours, making 20 units of cheese will take up 60 of the machines 148 hours, leaving 88 hours.

The next most profitable product is chalk, so we want to make as much of that as we can. To fulfil the demand of 25 units would take 100 machine hours though, so we can’t completely fulfil the demand. Therefore we should just use all of the remaining 88 hours to make 22 units of chalk.

20 units of cheese and 22 units of chalk is the most profitable way of using the machine.

## Decisions on making or buying something (aka outsourcing decisions)

Another example. A company needs to acquire a chip for one of its products. They can subcontract the production of it, costing £35 per chip, or produce it themselves for total variable costs of £28 per unit.

The problem is, the company doesn’t have any spare capacity, so they’ll have to reduce the output of something else (call it product B) in order to make the new one. Product B makes a contribution of £15.

What decision do they take?

What are the relevant costs here? It will cost £28 per unit, plus the £15 they ‘lose’ from being unable to make Product B. That gives a total of £43. Therefore they should subcontract it, as the cost to them is less.

There are a couple of other factors to consider though. Outsourcing means the company loses control over the quality of it, and there could be problems with the supply down the line.

## Closing or continuation decisions

I need to get a copy of the textbook to fill in an example for this, but basically apply the same logic that’s been used in the previous areas!

## Weaknesses of break even analysis

### Non-linear relationships

The relationship between output and costs (or revenue) might not be a straight line. However, as break even analysis is based on forecasting and nothing concrete, it usually doesn’t mean it’s a serious weakness.

### Stepped fixed costs

The previous post explained stepped fixed costs. It is difficult to include these in the analysis, as the steps are more often than not at different points.