Coinsurance is designed to make sure you insure your property to the proper value and that the insurance company gets adequate money for the exposure. If you chose to insure for less coverage, in a partial loss you will be penalized; in a total loss that is underinsured you will get your policy limit less the ded.

Coinsurance penalty formula = did over should times the loss and then less your deductible.

Example of a coinsurance penalty on an ACV policy:

Actual cash value = replacement cost less depreciation

You have a home that the replacement cost is 100,000 less depreciation of 30,000 which equals 70,000 or your “ACV”.
You have an 80% coinsurance policy.
You insure it for 30,000 because that is what you have into it
You have a partial fire and have 15,000 in damage

You did have 30,000 in coverage and your should is 70,000 times 80% (your coinsurance amount) or 56,000. 30,000 over 56,000 = .535(as a fraction) times your loss of 15,000 = 8,025 less your 1,000 ded which means the insurance company will pay you 7,025 for your partial loss of 15,000.
*Note: if it’s a total loss you will get your policy limit of 30,000 less your 1,000 ded or 29,000.