You start an insurance company as your first entrepreneurial venture after gradu

Question

You start an insurance company as your first entrepreneurial venture after graduation. Your main product line is malpractice insurance for dentists.  After exhaustive research, you learn that settling malpractice claims against careful dentists costs $2,000 and settling malpractice claims against reckless dentists costs $7,500.  Individual dentists know whether they are reckless or careful, and your research shows that approximately 20% of dentists are reckless.

How much do should you charge for malpractice insurance to break even? Why?

Explanation / Answer

First off you already stated 20% of dentists will be reckless, so we have the probability of malpractice. You have one real piece of the puzzle, which is the average amount that claims are expected to cost ($2,000 + $7,500 = $9,500). The second piece is how many claims are anticipated for the year. You state that 20% of dentists are reckless (I'm assuming that's per year), but 20% of 10 means you'll be expecting two claims per year, 20% of 10,000 means you're expecting 2,000 claims per year. Number of claims times anticipated payout equals the amount in claims you're paying out in the year. If we assume there are 10,000 dentists then 9,500 x 2,000 = $19,000,000 is the anticipated claims cost. Now we need to know how many policyholders we anticipate we have or will have. If we're the only dental malpractice insurer in the market, then we can assume all 10,000 dentists will be insured with us. Therefore $19,000,000/10,000 = $1,900, which is the amount you need to charge each client assuming no administrative costs, no profit margin and no buffer in case you have a bad year.

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