QA Bank 6.21

[tommo]

Question:

general insurance company has been using undiscounted technical reserves for many
years. On this basis, the key accounting data for one particular year is as follows:
written premium was £1,800 million
loss ratio has been stable at 70% for several years
the underwriting result for the year was a loss of £2 million
acquisition costs (ie commission) were 25%
investment return was 8% on funds invested
brokers hold premiums for 3 months before passing them to the insurer
solvency ratio at the end of the year was 40%
tax at 30% of gross profit is paid on the last day of the year

etc etc...

Question is:
The Tax Paid on pre tax profit is 3/7 * (Change in free Reserves). Why is the pre tax profit calculated as (change in free reserves)/7 ?

Thanks,

 

[Hemant Rupani]

The Tax Paid on pre tax profit is 3/7 * (Change in free Reserves).

From this, Tax:change-in-FR::3:7 i.e. change-in-FR is 70% of pre-tax profit(if we assume that there is no profit appropriation, so all net profit is showed in the Balance sheet)
So pre-tax-profit=(change in FR)/0.7

 

[tommo]

Of course!! I'm such an idiot! Thanks, the penny has dropped - I think I need more coffee.

 

[Darren Michaels]

Hemant is correct.

The question says that there have been no dividends for years so post-tax profit=retained profit=increase in shareholders' funds.

Given tax is 30% of gross profit, then tax will be (30%/70%)*increase in shareholders' funds.

 

[jdx911]

Hi
Please can someone explain how the pattern of emerging claims costs and the table of apportioned claims costs works in the solution?
- I assume the 1st year = 40%, etc means that the Incurred claims during any given accounting year is comprised of claims emerging from the past four accounting years, and in the proportions given?
- In the table, I can see that Current is apportioning the Incurred claims during the current accounting year by the proportions. But why then is the Claims paid in the year = the diagonal? Isn't that saying eg that the 40% of claims that emerged in the first year have been fully paid? What about the tail (question says nothing about a tail?)?
- What's the meaning of Last, Previous and Latest? I can see we are just stepping back the proportions of the Incurred claims by what I presume is claims inflation @5%pa?

Thank you

 

[Darren Michaels]

The pattern of emerging claims costs is telling you what percentage of the ultimate incurred claims cost for a given underwriting year is paid in each year of development, ie 40% will be paid in the year the business is written, 30% in the year after and so on.

So as you say in any given calendar year, the claims will come from 4 different underwriting years, the current one, and the three preceding ones (referred to as Last, Previous and Latest in the solution). It might be easier to think of "oldest" for "latest".

Therefore in a given year the payments are the diagonals as they are the current year at year 1 of development plus the last year at year 2 of development, the previous year at year 3 of development and the latest year at year 4 of development.

The development pattern you have been given adds up to 100% so you don't need to worry about a tail beyond year 4 and can assume that all underwriting years are fully run-off after year 4.

To get the amounts in each row, you need to work out the claims incurred from each underwriting year by applying the 70% (constant) loss ratio to the earned premiums from each year and then apply the payment pattern.

To get the earned premiums for each underwriting year, you need to use the fact that premium rates have increased by 5%pa whilst volumes have remained unchanged, which tells you that written premiums have increased by 5%pa.

It might help you to understand the amounts better if you put actual numbers on the years, so if Current was 2017, Last would be 2016, Previous 2015 and Latest 2014.