Hard McKinsey math

Question

Here’s a math prompt I’m stuck on. The answer is 20%..can someone explain how they got this?

Q: In Florida, Liberty (client) is interested in raising their monthly premiums above $1000 per month, but knows that increasing the premium cost will change the segmentation of customers who purchase healthcare plans. For every 1% increase in premiums, Liberty Healthcare’s customer segmentation will change from the baseline in the given chart by increasing the percentage of ‘unhealthy customers’ by one percentage point, and decreasing the percentage of ‘young and healthy customers’ by one percentage point. The ‘old and healthy segment’ will be unchanged.

For example, raising rates by 1% will change the expected customer segmentation to 65% young and healthy (-1% from baseline), 17% old and healthy, and 18% unhealthy (+1% from baseline).
How high could our client raise premiums before they are no longer charging enough in premiums to pay for expected medical costs?

Answer 1

Hi there,

You need to setup a breakeven equation!

Essentially it's $35,000x + $1,000y = $12,000x + $12,000y

Then, compare the current state to what future state would result in the LHS (Annual Costs) to be < the RHS (Annual Income)