Yesterday, when I wrote the blog on clean cut accounting, one of our friends asked me to explain as how the eights basis calculation is done. Let me try to explain it in a simple language.

Let us assume the treaty period is 1st Jan 2024 to 31st Dec 2024. Quarterly accounts to be submitted.

Let us assume, the premium to reinsurer for each quarter is USD 100 million. 1st quarter is from 1st Jan to 31st March. USD 100 million is due to the cession from hundreds of policies underwritten by the cedant during the quarter. Every day of the quarter policies would have been written. The cumulative of all cessions for the quarter are USD 100 million.

We do not know how much premium was ceded on which day. If we knew it, we could have used the 1/365 method. So, we have to make an assumption of one single day on which the entire premium was underwritten and ceded. The most appropriate assumptions are that the entire USD 100 million was underwritten and ceded in the middle of the first quarter- that is on 15th feb.

Treaty ends on 31st Dec 2024. If a policy was written on 15th Feb 2024, it will end on 14th Feb 2025. Current panel of reinsurers should get the premium from 15th Feb 2024 to 31st Dec 2024. The premium from 1st Jan 2025 to 14th Feb 2025 is unexpired premium reserve and has to be transferred to the new panel of reinsurers.

There are 8 half quarters in any year. Hence, unexpired premium reserve is 1/8 of the premium and earned premium is 7/8 of the premium. Hence, out of USD 100 million of first quarter, 1/8 of USD 100 million is unexpired premium reserve. Which is equal to USD 12.5 million.

By same logic, if premium earned in second quarter is USD 100 million,. 3/8 of the premium is unexpired premium reserve. Which is equal to USD 37.5 million.

Third quarter will be 5/8 of USD 100 million. Which will be USD 62.5 million.
Fourth quarter will be 7/8 of USD 100 Million. Which will be USD 87.5 Million.

12.5+37.5+62.5+87.5 = USD 200 million. Which is 50% of the ceded premium for the treaty period.

Change the numbers to USD 200 million, 100 million, 50 million, and 50 million, then the unexpired premium reserve will be

25+ 37.5+ 31.25 + 43.75 = USD 137.5 million.

Blog by Atmaram Cheruvu