Children vaccine

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Problem Definition

Beyer, one of the biggest pharmaceutical companies in the world, just invented a very reliable vaccine against Chickenpox, a disease that affects children in the age from 2 to 16 years.

Beyer came to you wondering what their potential sales in Europe in the first year would be if they launched this product next year. They are only interested in the overall sales revenue as they already know that the vaccine can be sold for a profit. This is more meant to show them how big the volume they have to supply is and what the revenue would be.


This is an interesting example of substitute product produced by the client (in many cases the client has to react to a substitute that competitors bring to the market).

A good interviewee would achieve a good estimate of the potential market and then make the appropriate considerations to realistically estimate sales (defining what market share the new product will gain and under what conditions).

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.

The following structure would be a good approach:

Suggested approach

I. Potential market

Here the interviewee should investigate the potential market size:

Information that can be shared on the interviewee’s inquiry:
  • The theoretical potential market is made up of all children between 2 and 16 years in Europe.
  • In order to estimate the number of people in a certain age-span it is common practice to consider the population distribution as uniform (i.e. there are as many 8-year-old people as, for instance, 55-year-old people).
    With this assumption, the number of people in the age-span is proportional to the number of years comprised in the age-span. For example, in a population of 100 million people with a life expectancy of 100 years, there will be 10 million people between 50 and 59 (age span of 10 years).
  • However, to make this case more challenging, the age distribution is not considered uniform.
  • Europe can be divided in two segments: countries with a decreasing population and countries with a growing population.

  • Share Diagram 2 and 3 if the interviewee inquires information about the age distribution.
  • Share Diagram 4 if the interviewee inquires information about the population.
  • Share Table 1 with an overview of the probability of the disease and the treatment costs for the different age spans if the interviewee inquires information about Chickenpox.

In order to calculate x and y from Diagram 2 and 3 we can set up the following simple equations:

4x + 4*(1.5x) = 300
10x = 300 -> x = 30 m

5y + 3*(1.66 y) = 200
10y = 200 -> y = 20 m

Now we can approximate the number of 2 – 16 year-old children in both the growing and declining populations. The age span from 2 to 16 years is exactly 15 years.

Calculation for countries with growing population:

Number of people per 10-years age span:

=1.5 * x

Number of children from 2 – 16 years (15 years age span):

Calculation for countries with declining population:

Number of people per 10-years age span:

=1.0 * y

Number of children from 2 – 16 years (15 years age span):

Main conclusions:

The total potential market size is about 100 million children.

II. Forecast for 1st year

Now that we know that 100 million children could theoretically be customers of the new vaccine in Europe, we should determine:

  • Competitors with a similar product
  • Size of customers willing to buy vaccine

Information that can be shared on the interviewee’s inquiry:
  • There are no competitors to the newly invented vaccine.
  • For the analysis of the customers in Europe it will be assumed that the willingness to pay is equal in whole Europe (although there are differences in buying power in reality).
  • The vaccine needs to be administered in 3 doses, with six-month intervals between them. If only 2 vaccines are administered, they do not have any effect.
  • The market price will be in sum €100 for three doses (≈€33 per dose). Each dose is only paid when given to the child.

Share Table 2 if the interviewee inquires information about the treatment costs.

Main conclusions

From Table 2, we can conclude that many parents will be likely to buy the vaccine for their children from 2 - 6 years – as they have to spend on average €75 with the alternative treatment.

However, for children between from 7 – 11 years only some rich parents would buy the vaccine, as the treatment has much lower expected costs and the probability of disease is lower.

There is almost no likelihood that parents of children from 12 - 16 years would buy the vaccine (as the incidence is just 5%).

So we could estimate the real market as:

This is an estimate, there are no right/wrong numbers: For simplicity we are taking 50% and 30%, those numbers coincidentally equal the percentage of children getting sick. However, any other reasonable number should be fine.

50% of children between 2 and 6 (because parents are likely to want to buy the vaccine)

30% of children between 7 and 11 (because only some rich parents want to buy the vaccine)

0% of children between 12 and 16 (because most parents will take their chances that the kids don't get sick anymore)

The total is then around 26.67 million children, which will pay €2.667 billion in total for the vaccines.

However, (and this is a tricky detail in the case), in the first year only two of the three doses are administered (since they are applied 3 times every 6 months).
Therefore the market in the first year will actually be 2/3 of €2.667 billion, that is, €1.778 billion.

The overall number of vaccinations needed is 53.34 million in the first year.

=26.67m * 2 vacc. administered = 53.34 million

III. Conclusion

Here the candidate should be able to succinctly summarize the findings made in the two previous steps and make a sound conclusion.

One possibility would be as follows:

The first-year sales for the new vaccine are very promising and expected to be around €1.778 billion.

To arrive at this number, we first estimated the theoretical potential market of the vaccine in 100 million children. However, due to the lower incidence for older children and to the high price of the vaccine, we figured out that only the parents of about 26.67 million children would buy the vaccine. Since only two of the three doses are administered in the first year, the expected sales would be of about €1.778 billion.

However, it is very important to mention that, since the vaccine prevents the disease for the entire life, only during the release children of different ages will be treated with it.

After the first couple of years, older children will have already been vaccinated. The consequence is then that only children at age 2 will be likely to be vaccinated in the future (if parents want to vaccinate their children, it’s logical that they do it the earliest possible).

Using the same logic as above, we suppose that 50% of the parents will buy the vaccine for their 2-year-old children. There are every year around 6.67 million children that reach the age of 2 years.

Therefore, after some years, when the market stabilizes, there will be about 3.3 million vaccines bought per year, that is €333 million (50% * 3.3 million vaccinated children per year * €100).

= 0.5 * 6.67 m * €100 = €330 m

Here we assumed that the birth rate will remain the same.

The problem of only two doses administered in the first year does not apply here, as the third dose will be administered the following year.
Therefore after the year of introduction of the vaccine it will always be in some sense three vaccinations per year (2/3 of the new vaccinations of the year and 1/3 from the previous year).

Difficult Questions

What other ideas would you pursue to try to maximize the profit with the new vaccine?

Suggested answer:

I would try to obtain a government subsidy for the payment of the vaccines as it is clear that they will save a lot of money by not having to treat children that got the new vaccine and never will get ill.

A similar agreement could be conceived along with private health insurances. They could help patients buy the vaccine. In this case the number of parents buying the vaccine would be much greater.

More questions to be added by you, interviewer!

At the end of the case, you will have the opportunity to suggest challenging questions about this case (to be asked for instance if the next interviewees solve the case very fast).

Questions on this case
2 How do I get the final answer?

The actual kids who will take your vaccine is ~26m The vaccine needs 3 does to work - 1 every 6 months. But in a year they can only take 2 does. So, 26 * 2 = 53 units of vaccine Now 3 vaccin... (more)

3 Market size: Alternative approach
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I don't get the inital system of equations: shouldn't be x=1.5y? Best, Luca

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Case exhibits

Case structure

Age distribution in countries with increasing population

Age distribution in countries with declining population

Demography in Europe

Information about Chickenpox

Until now, there are no other known vaccines for Chickenpox.

Comparison of treatment costs

This is the average cost that a child has with Chickenpox treatment. If half of the children get sick and (traditional) treatment costs amount to €150 then on average there is a cost of €75 per child.