2.3 Coinsurance and the Coinsurance Formula

Why Coinsurance Exists

Most property losses are partial, not total. If underinsurance carried no penalty, an owner of a $1,000,000 building could insure for $200,000, pay a fraction of the premium, and still fully recover the typical small fire. To keep premiums equitable, the coinsurance clause requires the insured to carry insurance equal to a stated percentage of the property's value — usually 80%, 90%, or 100% — at the time of loss. Meet the requirement and losses are paid in full up to the limit; fall short and a penalty reduces the payment.

The Coinsurance Formula

The formula tested on every P&C exam is:

(Did / Should) x Loss = Payment (capped at the policy limit, and reduced by any deductible)

where:

• Did = the limit of insurance actually carried
• Should = value of property x coinsurance percentage
• Loss = amount of the covered loss

If "Did" is equal to or greater than "Should," the ratio is treated as 1 (no penalty) and the loss is paid in full up to the limit. The penalty only bites when the insured carried less than required.

Worked Example 1 — Underinsured

A building is worth $800,000 with an 80% coinsurance requirement. The owner carries $480,000 and suffers a $100,000 loss.

1. Should = $800,000 x 80% = $640,000
2. Did / Should = $480,000 / $640,000 = 0.75
3. Payment = 0.75 x $100,000 = $75,000

The insured absorbs the remaining $25,000 as the coinsurance penalty for underinsuring. (A deductible, if any, would then reduce the $75,000 further.)

Worked Example 2 — Requirement Met

Same $800,000 building and 80% requirement, but now the owner carries $200,000 on a $400,000 building (50% of value) and has a $40,000 loss... wait — match the numbers: building $400,000, 80% coinsurance, carries $200,000, loss $40,000.

1. Should = $400,000 x 80% = $320,000
2. Did / Should = $200,000 / $320,000 = 0.625
3. Payment = 0.625 x $40,000 = $25,000

Had the owner carried at least $320,000, the full $40,000 (less deductible) would be paid. The lesson the exam drives home: the penalty applies even though the loss ($40,000) is far below the $200,000 limit carried.

What Removes the Penalty

Key points the exam reinforces: a higher coinsurance percentage means a lower rate (the insurer collects adequate premium for the exposure), the requirement is tested at the time of loss (not when the policy was bought), and Agreed Value endorsements suspend the clause entirely. A common distractor claims coinsurance only matters on total losses — it is precisely the partial loss where the penalty appears.

The Insurance-to-Value Incentive

Coinsurance is fundamentally a rating mechanism. The insurer prices the policy assuming the insured will carry the agreed percentage of value. Choosing a higher coinsurance percentage (90% or 100% instead of 80%) earns a lower rate because the insurer collects premium proportional to the full exposure. Conversely, the insured accepts a steeper penalty if they later under-report value.

The clause therefore aligns the insured's incentive (cheap rate) with the insurer's need (adequate premium) by requiring honest insurance to value — and it tests value at the moment of loss, so inflation in building costs during the term can quietly push an insured into a penalty position even though they were compliant at issue.

Step-by-Step Method for Coinsurance Questions

Work every coinsurance problem the same way to avoid careless errors:

1. Compute Should = property value x coinsurance percentage.
2. Compute the ratio Did / Should. If it is 1 or more, set it to 1 (no penalty).
3. Multiply the ratio by the loss amount.
4. Subtract any deductible.
5. Cap the result at the policy limit.

Example with a deductible: $1,000,000 building, 90% coinsurance, $810,000 carried, $200,000 loss, $5,000 deductible. Should = $900,000; Did/Should = 810/900 = 0.90; 0.90 x $200,000 = $180,000; minus $5,000 deductible = $175,000. Order matters — apply coinsurance to the loss first, then the deductible.

The Coinsurance Formula Step by Step

The penalty formula is: (Did Carry / Should Have Carried) x Loss - Deductible = Payment, never exceeding the policy limit. "Should have carried" equals the coinsurance percentage times the property value at the time of loss. Work it in order: (1) compute the required amount (value x coinsurance %); (2) divide the carried limit by that required amount to get the ratio; (3) multiply the ratio by the loss; (4) subtract the deductible; (5) cap at the limit.

A Fully Worked Coinsurance Problem

A building worth $500,000 carries an 80% coinsurance clause, meaning the insured should carry $400,000. The owner insured for only $300,000 and suffers a $100,000 loss with a $1,000 deductible.

• Required: $500,000 x 80% = $400,000.
• Ratio: $300,000 / $400,000 = 0.75.
• Indemnity: 0.75 x $100,000 = $75,000.
• Less deductible: $75,000 - $1,000 = $74,000 paid.

The insured absorbs the $25,000 penalty for underinsuring plus the deductible. Had the insured carried the full $400,000, the ratio would be 1.0 and the policy would pay $99,000 (loss less deductible). Note the penalty applies to partial losses; a total loss simply pays the limit.