Ahoy, Black Gold!

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Problem Definition

Do you remember that one friend in school that always asked you to help him out with homework? Well, things never change and as this friend learnt that you are a consultant now, you receive a call. The friend’s grandfather, who was a captain, passed away and left an oil tanker behind. As your friend wants to be sure for tax reasons, exactly how much worth the tanker is, your help is needed – again!

Short Solution (Expand)

Detailed Solution

Paragraphs highlighted in green indicate diagrams or tables that can be shared in the “Case exhibits” section.

Paragraphs highlighted in blue can be verbally communicated to the interviewee.

Paragraphs highlighted in orange indicate hints for you how to guide the interviewee through the case.

I. Understanding the Case & Structure

Share diagram 1 with the interviewee.

There are mainly three classes of tankers in the world, within their class they're identical: Large, medium and small. Share table 1 with the interviewee.

Now that the interviewee knows the supply side, the interviewee should ask about the demand.

Upon request:

  • You can tell the interviewee that oil demand is fixed at 50m m³ per year and fully inelastic in this analysis. It shall be regarded as stable for an infinite amount of time.
  • Your friend's tanker is of medium size.
  • As for costs, the interviewee can assume that any other transportation costs are fully incorporated in the oil price and can be neglected.
  • Due to overcapacity in the last years, the market is highly fragmented and therefore competitive, but supply is regarded stable infinitely as well.
  • The discount rate is 10%.

II. Equilibrium Price and Profit Calculation

We would now need to draw conclusions from the given data and develop a valuation model.

We know that the market is competitive, hence the market clearing price will be the equilibrium price. The equilibrium price will be set by the participation price of the marginal capacity: below that price the marginal capacity will not offer their service/product (=tanker) and demand cannot be fulfilled. Thus the price rises until it meets the costs of the marginal capacity.

So, what is the marginal capacity?
Large tankers have the lowest cost per m³, hence all capacity can be used (as they can offer the lowest price – theoretically. In practice they cannot set the price.) Large tankers will be able to transport 400,000 m³* 100 = 40m m³ of oil.

Medium tankers will need to cover the remaining 10,000,000 m³ which is possible by contracting half of the available tankers (100/2 = 50; 50* 200,000 m³ = 10m m³). As those tankers will not operate for anything less than the operating cost, the market clearing price will be $75,000 per 100,000 m³ oil (one medium tanker can carry 200,000 m³ of oil and costs $150,000 to operate = $ 75,000 per 100,000 m³)

We can calculate the profits for each tanker class.

Large tankers: Profit = Revenue - Cost = (Capacity * price / 100,000 m³) - $200,000 = 400,000 m³ * $75,000 / 100,000 m³ - $200,000 = $ 100,000
Medium tankers: Profit = Revenue - Cost = (Capacity * price / 100,000 m³) - $150,000 = 200,000 m³ * $75,000 / 100,000 m³ - $150,000 = $ 0
Small tankers: Profit = Revenue - Cost = (Capacity * price / 100,000 m³) - $100,000 = 100,000 m³ * $75,000 / 100,000 m³ - $100,000 = $ -75,000

While large tankers will make a profit of $ 100,000 per year, medium tankers earn 0 and no small tanker would operate as they are incurring losses of $75,000 every year.

III. Calculation of value

To calculate the value, we can use the Discounted Cash Flow method.

You can share diagram 2 with the interviewee if necessary. At latest when the interviewee starts using the first formula, indicate that since cashflows are the same in every period and T=infinite, we can use the second formula.

Large tankers are worth $ 100,000 / 0.1 = $1m each. Medium tankers and small tankers have zero worth (or, alternatively, scrap value only).

IV. Conclusion

As we have calculated, the equilibrium price will be the one that clears the market. As not all of the capacity can be covered by large tankers, the price that compensates for the operating cost of the marginal capacity, i.e. medium tankers (like your friend's), will be paid for all actors on the market. While large tankers due to their lower operating cost are still making a profit, medium sized tankers don't. Their only value is the scrap value, just as the small tankers' value.

If the interviewee was very fast, you can repeat the exercise, but with a fixed demand of 65m m³ ceteris paribus.


Market clearing price will be $100,000 per 100,000 m³ oil.

Large tankers: Profit = Revenue - Cost = (Capacity * price / 100,000 m³) - $200,000 = 400,000 m³ * $100,000 / 100,000 m³ - $200,000 = $ 200,000
Medium tankers: Profit = Revenue - Cost = (Capacity * price / 100,000 m³) - $150,000 = 200,000 m³ * $100,000 / 100,000 m³ - $150,000 = $ 50,000
Small tankers: Profit = Revenue - Cost = (Capacity * price / 100,000 m³) - $100,000 = 100,000 m³ * $100,000 / 100,000 m³ - $100,000 = $ 0

Large tankers: $2m
Medium tanker: $0.5m
Small tanker: $0 or scrap value only.

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