Math logic with % calculations help

Question

The question asks to calculate the impact of introducing a new counterfeit tracking system for pharmaceuticals.

average annual revenue of pharmaceuticals manufacturers is USD 5 M
share of illegal goods in circulation will fall from 20% to 10%, resulting in an equivalent growth in legal sales

Answer: New rev = 5.625M

Can someone explain why we need to find the percentage increase in legal goods i.e 90% (which is new share of legal goods) - 80% (which is old share of legal goods) / 80% = 12.5%..we then take a 12.5% increase of 5M

My question is why can't we deal with this as percentage points increase i.e 20% to 10% so a 10 percentage point increase in legal goods and then apply this 10% to 5M?

Answer 1

Hi there,

This is indeed an interesting question which is probably relevant for quite a lot of users, so I am happy to provide my perspective on it:

The reason is very simple: Without any further information, you need to assume that the total amount of goods in circulation stays the same.
As such, the initial share of legal goods in circulation is 80% which also is the basis for the calculation. A total increase of 10% on the basis of just 80% is 10% / 80% = 12.5%. The 100% + 12.5% = 112.5% of $5M is then $5.625M.

In case you want a more detailed discussion on how to solve this type of quantitative questions, please feel free to contact me directly.

I hope this helps,

Hagen

Answer 2

Yes, you can apply percentage points - but you must note the 10% and 20% refer to the total goods in circulation, not to the 5M of “legal” goods.

So if 80% of the goods are legal and are 5M, then 100% of total goods are 5M/80%=6.25M

If you now only have 10% of illegal, then you have: 6.25 * 90% = 5.625M

Or you can use the % as they did:

10%/80%=12.5% (10% of total goods is the same as 12.5% of legal goods).

5M * (1+12.5%) = 5,625M

Answer 3

Hi there,

Honestly you can take both approaches as long as you do the math/logic right.

Percent increase and percentage point increase need to be multiplied differently…setup the math and do it yourself and you'll see that both can get the same result!