Ace_The_Case_2nd_Ed

Question:

Estimate the number of rubber tyres in the world

This question appears near impossible to get anywhere near an accurate answer as the world is so large and diverse. The key to impressing the interviewer is therefore thinking out loud about possible variables, usage patterns etc. You may not even come out with a final number. After

some discussion you find out a bit more regarding the question in that you are to consider motorised vehicle tyres only (i.e. not bicycles or toys) and further only whole tyres, i.e. broken tyres are out of scope.

Possible Solution:

The first step in such a question may be to brainstorm some variables or things that need to at least be considered. This may take about 5 or so minutes and might involve some interaction with the interviewer. Below is such a list.

Motorised vehicles and rubber tyres have been around since at least the 1930’s

Many used tyres go into landfill, others are dumped, abandoned or burned whilst some are recycled

The worlds population is over 6 billion people however only a fraction have the wealth to even own cars

New tyres are being produced every year

New tyres exist in organisations inventory

Cars actually have 5 tyres because generally speaking they should all carry at least one spare tyre.

Lifespan of a tyre ranges from 1 year to 3 years

Motorised vehicles with tyres include private cars, motor bikes, trucks, buses, taxis, courier vans, race cars, aeroplanes, military vehicles, construction vehicles, trailers etc.

Now you could spend hours trying to accurately quantify everything above, however in limited time you are best off just creating percentages and whole numbers based on gut feel and intuition to at least finish the question. Below is a table assigning some values to the ideas and variables outlined above:

From this data we can formulate an equation; however it will be impossible to calculate without the use of a calculator. A rough set of preliminary calculations will therefore look something like below:

Tyres currently in use

=[(W x A x O) + (W x A x O) x B] x 6

=[(6 billion x 20% x 25%) + (6 billion x 20% x 25%) x 50%] x 6

=[300 million + 150 million] x 6

=450 million x 6 = 2.7 billion tyres

Tyres produced this year

=Tyres in use x 1/ lifespan

=2.7 billion x 1/3

=900 million

Tyres currently kept in inventories

=Tyres produced each year x 5%

=900 million x 5%

=45 Million

Tyres disposed this year

=tyres produced – growth factor

=900 million – 2.5%

=877.5 million

Tyres in landfill and abandoned this year

=tyres disposed x (landfill % + abandon %)

=877.5 million x (50% + 10%)

=877.5 million x 60%

=530 million (rounded up)

Using some of these figures and the 2.5% growth rate we can estimate how many tyres exist out there in the world considering they have existed since the 1930’s. The interviewer may tell you not to bother since by now you have already performed enough calculations and made many assumptions. However if asked, it would look something like this:

2.7 billion + 45 Million + ∑530 + 530*0.975+ 516*0.975.........

= 21 billion tyres

Question:

Estimate the number of cigarettes consumed per day in Canada

The popularity of tobacco in westernized nations has marginally declined in recent years due to research results and extensive health warnings. With population growth however, the sale of cigarettes still slightly increases each year in many of these countries. Canada however has seen a downward trend in cigarette consumption. This question therefore simply asks for a single estimate of unit

consumption of cigarettes in one day for the entire nation of Canada.

Possible Solution:

For those who don’t know, the population of Canada is just over 30 million. Now cigarettes are classified as a fast moving consumer good and therefore huge numbers of them are consumed each day. Regular smokers may go through a pack per day, however not everyone who smokes goes through this many cigarettes. This question is therefore all about estimating reasonable percentages.

See the diagram on the next page for the possible solution:

Method 1: Capacity

By making some assumptions we can determine a maximum capacity figure through understanding how many taxis can actually fit onto the streets.

Method 2: Demand

By working top-down, starting from the population of Manhattan, we can estimate the demand for taxis if we make enough assumptions.

Triangulating an answer:

As discussed earlier in this guide, approaching an ambiguous problem from multiple directions allows you to sensibly check two or more answers against each other to hopefully find a more accurate middle ground. The concept of triangulation helps to achieve this and can assist in verifying one or more answers to the problem by having an additional basis for comparison.

The concept of triangulation comes from the world of geometry, in particular trigonometry, in which the distance to an object can be determined by knowing distances and angles of two other reference points, thus forming a triangle. The term is often borrowed by the business world and management consultants when solving ambiguous business problems which often require a degree of estimation. If more than one technique is used and the estimates align then a greater level of confidence in methodology can be assumed. This also works in reverse however.

For example this is often done by investment banks and consulting firms during financial valuations, whereby a time consuming and detailed discounted cash flow (DCF) valuation model is constructed and compared against a more simplified calculation of the value using a price to earnings multiple approach or some other valuation methodology for the purpose of sense checking

In this problem, looking at both methods used above, the answers are very close to one another. You can therefore have a greater degree of confidence that you are on the right track in estimating a final answer. You can be confident in presenting a final answer to the interviewer knowing that the two calculation methodologies resulted in similar answers. Taking a simple average of the two answers results in a final estimate of 11,500 yellow taxis in Manhattan, this seems reasonable and agrees with the two values calculated above. You should now explain to the interviewer in relative confidence your final estimate to the problem – “I estimate there to be approximately 11,500 yellow taxi cabs in Manhattan on any one day”.