Why don't we differentiate between fixed and variable costs ?

Question

Hi everyone,

I have a clarification question regarding the cost structure in this case.

We are given the following cost breakdown (in $m):

Labor: 11
COGS: 18
SG&A: 3
R&D: 1
Marketing: 2

From this, I understood that:

COGS (18m) represents variable costs
The rest (Labor, SG&A, R&D, Marketing) are fixed costs
→ So fixed costs = 17m
→ Variable costs = 18m

Since the company currently sells 50m units, this would imply:

Variable cost per unit = 18 / 50 = 0.36

So current profit would be:

Revenue = 1 × 50 = 50
Total costs = 17 (fixed) + 0.36 × 50 = 35
Profit = 15

If we reduce the price to 0.9 and assume 75m units sold (100% market share):

Revenue = 0.9 × 75 = 67.5
Variable costs = 0.36 × 75 = 27
Total costs = 27 + 17 = 44
Profit = 23.5

However, in the solution, they assume a stable unit cost of 0.7.

I don’t understand why we would assume a constant unit cost of 0.7 when the case clearly distinguishes between fixed and variable costs.

Thanks in advance!

Answer 1

Hi!

Yes, you’re right - COGS typically are variable and others are fixed. But case gives “unit cost 0.7” explicitly, overriding breakdown.

Why solution uses 0.7 (not your split)?
Case convention “Unit cost 0.7” may mean fully loaded unit cost (variable COGS + allocated fixed). So, Labor/SG&A/etc already baked into 0.7 - no need to re-split.

Answer 2

This is a really insightful question, and you're spot on for thinking about cost differentiation – it's crucial for understanding profitability. Your breakdown of fixed and variable costs is perfectly logical from an economic standpoint.

Here's why the solution likely simplifies it to a stable unit cost: In many case interviews, especially when not explicitly prompted to perform a detailed fixed vs. variable cost analysis, the default assumption is to derive a fully-loaded average cost per unit from the initial data. In your example, total costs are $35m (11+18+3+1+2) for 50m units, which gives a $0.70 per unit cost ($35m / 50m units). This approach streamlines calculations and assumes that, for the relevant range of volume changes in the case, those 'fixed' costs (like a base level of SG&A or R&D) are effectively absorbed into the per-unit cost for simplicity, or that there's a semi-variable component that isn't worth modeling out explicitly under time pressure.

It's not that your method is wrong, but rather that the case is testing your ability to derive and apply a reasonable simplified metric quickly. Unless a question specifically asks you to analyze the impact of scale on fixed costs, or if the volume changes are truly extreme (e.g., from 50m units to 1m units, where fixed costs would obviously be a massive burden per unit), stick with the simplest valid calculation that uses all provided cost data. If you have a choice between deriving a total unit cost or performing a detailed fixed/variable split, and the latter requires more assumptions or isn't explicitly requested, the former is usually safer and faster.

Hope this clarifies things for future cases!