A packaging manufacturer's cost per unit has risen 15% in two years. How would you find the cause?
Check volume and mix first, because fixed costs spread over fewer units raise unit cost even if no bill rises. Then split each cost into price and usage. If a $1.00 box now costs $1.15, a 20% volume drop alone explains 5 cents.
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Example answer
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Costs are either fixed or variable, so I'd go through both. I'd split cost per unit into four pieces.
One is materials. That's the price of paper times how much goes into each box.
Two is labor. That's wage rates against output per hour.
Three is overhead. That covers energy, maintenance and depreciation.
Four is volume.
Then I'd look for ways to reduce whichever one went up.
What holds it back
Fixed and variable is a textbook split that doesn't say where to look. The four pieces are listed with no order of attack, volume gets a single word, and it never asks whether volume or the product mix changed.
Two checks first. Has volume changed over the two years? And is the product mix the same, or are there more small custom orders now? I'd split cost per unit into four pieces. Then I'd see how much of the 15% each one explains. One is materials. That's the price of paper times how much goes into each box. Two is labor. That's wage rates against output per hour. Three is overhead. That covers energy, maintenance and depreciation. Here I'd only ask whether the total bill went up. Four is volume and mix. Fixed costs get spread over the units made, so cost per unit rises when volume falls, even if nothing costs more. I'd test volume and mix first. It's quick, and it changes how I read the other three. Then materials, since paper is likely the biggest share of the cost. Do we have cost per unit by category for both years?
Two checks first. Has volume changed over the two years? And is the product mix the same, or are there more small custom orders now? I'll assume they make corrugated boxes, cost per box went from $1.00 to $1.15, and volume fell from 100 million to 80 million. I'd split cost per unit into four pieces. Then I'd see how much of the 15% each one explains. One is materials. That's the price of paper times how much goes into each box. Price is set by the market, and I can compare it with what other buyers pay. Usage is ours, so I'd look at scrap rates and whether the boxes got heavier. Two is labor. That's wage rates against output per hour. Overtime and slower lines would show up here. Three is overhead. That covers energy, maintenance and depreciation. Here I'd only ask whether the total bill went up. Four is volume and mix. Fixed costs get spread over the units made, so cost per unit rises when volume falls, even if nothing costs more. That includes salaried labor. With $20 million of fixed costs, 100 million boxes carry 20 cents each and 80 million carry 25 cents. That's 5 of the 15 cents, a third of the rise, with no bill going up. Mix does it too, because more short custom runs mean more changeovers, so the average box costs more even if each product costs the same. I'd test volume and mix first. It's quick, and it changes how I read the other three. Then materials, since paper is likely the biggest share of the cost. A volume problem is solved by winning orders or closing a line, and no supplier negotiation will touch it. My hypothesis is that lost volume explains about a third and paper prices most of the rest. Can I see cost per box by category for both years, with volume by product?
The numbers, step by step
The volume effect alone, assuming $20 million of fixed costs, volume falling from 100 million boxes to 80 million, and cost per box rising from $1.00 to $1.15.
- Fixed cost per box before$20 million ÷ 100 million boxes
- $0.20
- Fixed cost per box now$20 million ÷ 80 million boxes
- $0.25
- Rise from volume alone$0.25 − $0.20
- $0.05
- Total rise in cost per box$1.00 × 15%
- $0.15
- Share of the rise explained by volume$0.05 ÷ $0.15
- about 33%
What the interviewer listens for
- Do you ask whether volume or product mix changed before blaming a cost line?
- Do you split each cost into a price and a quantity?
- Do you see that fixed costs over fewer units raise cost per unit on their own?
- Do you say which piece you would test first, and why?
- Do you separate what the market did from what the plant did?
Common mistakes
- Looking only at costs that went up in total.Cost per unit also rises when the same fixed costs are spread over fewer units.
- Treating materials as one number.A higher paper price and more scrap are different problems with different fixes.
- Skipping product mix.More short custom runs raise the average cost per unit even when every single product costs the same to make as before.
- Going through all four pieces in order without saying which is checked first or how much of the 15% each might explain.
More case openings
- Your client is a regional grocery chain. Profits are down 20% over two years. How would you structure the problem?
- An airline's profits are falling even though it is carrying more passengers. What is going on?
- A software company is growing 40% a year and still losing money. How would you assess whether that is a problem?
- A clothing retailer needs to cut costs by 10% without hurting sales. Where would you look?
- One of your client's three divisions is losing money. Should they fix it, sell it or close it?
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