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Fixed cost per tonne at different utilization rates

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.

Tessaline Chemicals (a fictional company) runs a polyethylene plant with capacity of 1.5 million tonnes a year and fixed costs of USD 180 million a year. What is the fixed cost per tonne at 90 percent utilization and at 70 percent?

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.

Step 1: At 90 percent
What a strong candidate does: Output 1.35 million tonnes.
Fixed cost at 90 percent (USD per tonne): 180 ÷ (1.5 × 0.9) = 133
Step 2: At 70 percent
What a strong candidate does: Output 1.05 million tonnes.
Fixed cost at 70 percent (USD per tonne): 180 ÷ (1.5 × 0.7) = 171
Step 3: Difference
What a strong candidate does: Extra fixed cost carried by each tonne.
Increase in fixed cost (USD per tonne): 180 ÷ (1.5 × 0.7) - 180 ÷ (1.5 × 0.9) = 38.1

The recommendation to listen for

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

Tessaline should make utilization its first priority, because falling from 90 to 70 percent adds about USD 38 of fixed cost to every tonne, from about USD 133 to USD 171. First, the USD 180 million of fixed costs is spread over fewer tonnes. Second, in a business where the spread may be only a few hundred dollars per tonne, this means a USD 38 increase is large. The risk is new industry capacity pushing everyone's utilization down. As a next step, check industry capacity additions against our order book.

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.