Profitability Analysis Framework, pt 3 - Variable Costs, Cost of Goods Sold

Profitability Analysis Framework Series
[ 1. Overview, 2. Fixed Costs, 3. Variable Costs, 4. Sales, 5. Price ]

Continuing the Profitability Analysis - Framework and Practice series, part 3 will look at variable costs.
Now our graph gets a little more interesting. Variable costs increase with the quantity sold (more resources such as raw material and labour are necessary for each additional unit). Also, we now have the two pieces required to put together a total cost curve (fixed cost + variable cost). Notice now that the fixed cost is the y-intercept and that the derivative (slope) of the variable cost curve (marginal cost) is the same as that of the total cost curve. These are two critical concepts in understanding how to graph and model cost curves.

Variable costs are directly related to costs of goods sold (COGS) including factors such as labour and raw materials. For any individual product line and for any given factor of production, the total product curve takes an S shape. This also implies that the variable cost curve doesn't have to be (and often isn't) perfectly linear (which also emphasizes the points made above about the slope of variable cost being identical to the slope of total cost).

Assuming managers can select the workers for the job from highest margin to lowest (most useful to least), there is an accelerated growth pattern due to economies of scale. However, eventually, the law of diminishing returns is such that marginal utility approaches zero for each additional dollar of value put into the system. If you flip the x and y axis, you now have a basis for adding your variable costs against your fixed costs.

Regarding specific details for variable costs, this includes many factors of production such as materials, resources and labour. Common themes that affect this area include:

• Cost of materials. If there is a change in the price of raw materials required for production or if there are inventory management issues which cause loses in the form of lost productivity. Also, if numbers are too high, this could be an indication of wastage, theft or some other form of inefficiency.
  
• Cost of resources such as computing power, electricity or oil. Consumption of resources at peak demand often results in inefficient and expensive hidden costs. Any ability to offset or time shift demand could dramatically cut costs and reduce systematic stress and dependency. Also if costs are seasonal or otherwise predictable, financial hedges such as oil futures can insulate the company from short term volatility (although not long term changes).
  
• Increased costs for overtime pay. This could be an indication that labour capacity is too low and that there needs to be more hires. This is directly related to the seasonality of your organization and could require you to outsource or hire more workers.

[Case Study] A factory is manufacturing cars and has a policy to pay it's workers 1.5 x for overtime worked above 40 hours. With it's current workforce and equipment, a particular factory line is able to produce a maximum of 20 cars per day. However, with a recent spike in the car model produced by this factory line, the demand requires production to increase to 25 cars per day.

While the automated equipment does not need to be augmented to meet demand (lines can simply run longer), there needs to be more human labour to satisfy demand. Should the factory authorize overtime or hire more staff?

[Solution] Looking at the solution, authorizing overtime would increase the labour component of cost of goods sold by 50% (1.5x pay for overtime). For 5 additional cars (or an increase of 25%), this would result in an increase of 37.5% of the total cost of labour (25% increase @ 1.5x labour cost).

In order to get the same increase in labour from hiring, they would simply need to hire 25% more labour (assuming no diminishing returns) would cost 25% more.

Using this logic, it's obvious that it would be better to hire more people and pay them at the stated rate than pay 1.5x for overtime.

So why not just always hire more people rather than pay 'expensive' overtime? If this demand is seasonal rather than permanent, having extra capacity will be detrimental if the demand doesn't last (if the demand for these cars evaporates). In this case, you are left with having to pay the salary for employees who are idle.

The premium for overtime is justified if 1. the incremental revenue is higher than the marginal cost of overtime labour (profitability of marginal units is positive) 2. the demand is temporary and doesn't justify increasing the permanent labour force.

Profitability Analysis Framework Series
[ 1. Overview, 2. Fixed Costs, 3. Variable Costs, 4. Sales, 5. Price ]