How to Calculate Pro Rata Return

[liquidsilver]

Hi,

I have a business insurance policy that was cancelled midterm. There was one premium bearing endorsement during the term reducing premium. The policy terms state that any return from a cancellation requested by the insured during the term will be pro rata (no additional details). However, the return premium after cancellation is not what I expected. To try and simplify this, I did change the figures (I inflated them to make the difference more meaningful). I made 1 year equal to 360 days so that each month is equal to 30 days. I would like to know if the insurer's method is correct, or if my method is correct. (U.S.)

I would also like to know why the two methods don't produce the same results.


Method 1, the way I calculated the return premium after cancellation:
======================
Let one year = 360 days. Each month is 30 days.
Policy term is 1 year (360 days)
Original annual premium is $25,000.

Effective day 31 of 360, a location accounting for $22,000 of the original premium is deleted. (Effective 12:01AM)
$22,000 ÷ 12 × 11 = $20,166.67 (Return Premium; amount refunded)
Revised premium paid for the year = $25,000 - $20,166.67 = $4,833.33

Entire policy is then cancelled effective day 181 (cancels at 12:01 AM).
Return premium calculation after cancellation = $4,834 ÷ 360 × 180 = $2,417


Method 2, the way the insurance company calculated the return premium:
======================
Let one year = 360 days. Each month is 30 days.
Policy term is 1 year (360 days)
Original annual premium is $25,000.

Effective day 31 of 360, a location accounting for $22,000 of the original premium is deleted.
$22,000 ÷ 12 × 11 = $20,166.67 (Return Premium; amount refunded)
Revised premium paid for the year = $25,000 - $20,166.67 = $4,833.33

Entire policy is then cancelled effective day 181 (cancels at 12:01 AM).
To determine return premium the insurance company
1) Determines the new "annualized" premium, which is what the annual premium would be if the policy ran for a year after the endorsement was processed.: $25,000 - $22,000 = $3,000

2) Calculates a pro-rated return premium based on the new annualized premium: $3,000 × (180 ÷ 360) = $1,500

 

[stapel]

...a business insurance policy...was cancelled midterm. There was one premium bearing endorsement during the term reducing premium.

Does this mean that, during the term of the policy (perhaps the calendar year?), you and the insurer agreed to one change in the rules of the policy, and this change resulted in a lowering of the (monthly?) payment(s) for the policy? (We can help with the math, but we may need help on the industry-specific lingo for your area of study.)

The policy terms state that any return from a cancellation requested by the insured during the term will be pro rata (no additional details).

How does your textbook define the term "pro rata"? Is it something similar to what is explained here?

Method 2, the way the insurance company calculated the return premium:...

The "right" method is whatever method is outlined in the contract. What rules were you given?

Thank you!

 

[liquidsilver]

Does this mean that, during the term of the policy (perhaps the calendar year?), you and the insurer agreed to one change in the rules of the policy ...

Not a change in rules, but a reduction in coverage. Consider a business that initially asked for coverage of $300,000 to insure the contents of their office building, where $300,000 is estimated replacement cost. They later ask to endorse the policy during the term to adjust the coverage limit to $50,000 after downsizing. Then a few months after, the business closes and cancels the policy midterm.

How does your textbook define the term "pro rata"? Is it something similar to what is explained here?

The policy doesn't define the term. I believe that IRMI would be a standard reference, though.

The "right" method is whatever method is outlined in the contract. What rules were you given?

The term isn't defined in the contract; I've searched. It just says that if insured cancels during the term that "refund will be pro rata." Perhaps the answer is whatever is standard in the field. I do know that their method matches mine if such an endorsement is processed effective the first day of the policy, but not if it's processed effective midterm. But I also wouldn't rule out the possibility that their computer programmers used a faulty algorithm that failed to take into account such a scenario.

 

[Ishuda]

Hi,

I have a business insurance policy that was cancelled midterm. There was one premium bearing endorsement during the term reducing premium. The policy terms state that any return from a cancellation requested by the insured during the term will be pro rata (no additional details). However, the return premium after cancellation is not what I expected. To try and simplify this, I did change the figures (I inflated them to make the difference more meaningful). I made 1 year equal to 360 days so that each month is equal to 30 days. I would like to know if the insurer's method is correct, or if my method is correct. (U.S.)

I would also like to know why the two methods don't produce the same results.


Method 1, the way I calculated the return premium after cancellation:
======================
Let one year = 360 days. Each month is 30 days.
Policy term is 1 year (360 days)
Original annual premium is $25,000.

Effective day 31 of 360, a location accounting for $22,000 of the original premium is deleted. (Effective 12:01AM)
$22,000 ÷ 12 × 11 = $20,166.67 (Return Premium; amount refunded)
Revised premium paid for the year = $25,000 - $20,166.67 = $4,833.33

Entire policy is then cancelled effective day 181 (cancels at 12:01 AM).
Return premium calculation after cancellation = $4,834 ÷ 360 × 180 = $2,417


Method 2, the way the insurance company calculated the return premium:
======================
Let one year = 360 days. Each month is 30 days.
Policy term is 1 year (360 days)
Original annual premium is $25,000.

Effective day 31 of 360, a location accounting for $22,000 of the original premium is deleted.
$22,000 ÷ 12 × 11 = $20,166.67 (Return Premium; amount refunded)
Revised premium paid for the year = $25,000 - $20,166.67 = $4,833.33

Entire policy is then cancelled effective day 181 (cancels at 12:01 AM).
To determine return premium the insurance company
1) Determines the new "annualized" premium, which is what the annual premium would be if the policy ran for a year after the endorsement was processed.: $25,000 - $22,000 = $3,000

2) Calculates a pro-rated return premium based on the new annualized premium: $3,000 × (180 ÷ 360) = $1,500

As staple said, we would need to know what the contract says. However, the way I would do it is:
Item(s) 1: $3000 premium for the year = $250/month
Item 2: $22000 premium for year = $1833.333/month

Item 2 insurance canceled after 1 month means 11 months refunded so
Refund=$20166.67

Item(s) 1 insurance canceled after 6 months so 6 months refunded
Refund = $750

Your Method 1 calculations have not included the fact that out of that $4,833.33 paid for the year you need to pay for both Item(s) 1 AND Item 2. The Item 2 insurance for the year is $1833.33.

 

[liquidsilver]

Your Method 1 calculations have not included the fact that out of that $4,833.33 paid for the year you need to pay for both Item(s) 1 AND Item 2. The Item 2 insurance for the year is $1833.33.

Hmm...

What Method 1 calculations were intended to do is take the actual amount charged for the year, determine the daily rate, and then multiply by the number of days during the year the policy was not in force. This was my idea of a pro rata return.

 

[Ishuda]

Hmm...

What Method 1 calculations were intended to do is take the actual amount charged for the year, determine the daily rate, and then multiply by the number of days during the year the policy was not in force. This was my idea of a pro rata return.

pro rata is "in proportion". That is if something is charged for a year but you only use it for one month you are charged the proportion 1/12 of the original charge [refunded 11/12 of the original charge]. Thus you should be charged 1 month for Item 2 at $1833.33 and 6 months for Item(s) 1 at $1500 for a total of 3333.33. You paid $25,000 so your refund would be 21666.67. You have already been refunded 20,166.67 so what you still have coming is $1500.

EDIT: You can use Method 1 only if all monthly charges are the same. In your case the first months charge [paid in advance] was 2083.33 while for months 2-6 you were charged $250 per month [paid in advance].