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Fixed cost per tonne at two utilization levels

You run the case. Read the prompt, answer questions from the notes below, and share data only when the candidate asks for it or gets stuck. Score at the end.

Case timer

00:00

Target length:

1. Read the prompt aloud

Read it slowly, then pause. Let the candidate ask questions before they structure.

A fictional cement plant has capacity of 5 million tonnes a year and fixed costs (staff, maintenance, insurance, overheads) of USD 75 million a year. What is the fixed cost per tonne at 80 percent and at 60 percent utilization?

2. Answers to clarifying questions

This case has no scripted clarifying answers. Answer from the prompt, and say "assume what you think is reasonable" if the prompt does not cover it.

3. A model structure

Compare the candidate's structure with this one. A different split can be just as good if it is clean and fits the problem.

  • Fixed cost per tonne = fixed costs divided by tonnes produced
    • Tonnes produced = capacity x utilization

4. The working, step by step

Each step shows how a strong candidate works it out. Share a new fact from it only when the candidate asks or is stuck, and let them do the math: the result in the dark box is what they should reach.

  1. Step 1: At 80 percent

    What a strong candidate does: Output 4 million tonnes.

    Fixed cost at 80 percent (USD per tonne): 75 ÷ (5 × 0.8) = 18.75

  2. Step 2: At 60 percent

    What a strong candidate does: Output 3 million tonnes.

    Fixed cost at 60 percent (USD per tonne): 75 ÷ (5 × 0.6) = 25

  3. Step 3: Difference

    What a strong candidate does: Extra fixed cost carried by each tonne.

    Increase in fixed cost (USD per tonne): 75 ÷ (5 × 0.6) - 75 ÷ (5 × 0.8) = 6.25

The recommendation to listen for

At the end, say: "The CEO walks in. What is your recommendation?"

The plant should treat volume as its first lever, because falling from 80 to 60 percent utilization adds about USD 6 of fixed cost to every tonne. First, the same USD 75 million is spread over 3 million tonnes instead of 4 million. Second, against EBITDA of perhaps USD 10 to 15 a tonne, this means a slump in volume can wipe out half the profit. The risk is that chasing volume with price cuts starts a price war that hurts every plant in the region. As a next step, map regional capacity and demand to see whether the slump is ours or the whole market's.

Score the candidate

Score each criterion from 1 to 5. A 2 or a 4 sits between the descriptions.

This case has no exhibit. Score Exhibit reading on how the candidate used the data you gave them: did they pick out the number that matters and say what it means?

Structuring
1
No clear structure, or a memorized framework that does not fit the problem.
3
A sensible structure, but with some overlap, a gap, or no clear priority.
5
A structure built for this problem, with no overlap and no gaps, a stated hypothesis, and a clear first step.
Math
1
Frequent errors, no units, or needed heavy help to finish.
3
Right answers but slow or messy working, or one error caught late.
5
Accurate and clearly narrated, with units, a sense check, and what the number means.
Exhibit reading
1
Read the chart aloud without finding the number that matters.
3
Found the key number but gave only part of the so-what.
5
Pulled the right number quickly and said what it means for the case.
Synthesis
1
Summarized what was done, with no clear answer.
3
Gave an answer, but with weak reasons or no next step.
5
Answer first, then two or three reasons with numbers, the main risk, and next steps.
Communication
1
Hard to follow: long silences, no signposting.
3
Clear most of the time, with some rambling.
5
Calm and concise, signposted each step, and checked in with the interviewer.

Total

0 out of 25

Score all five criteria to see the band and the feedback template.