Practice Question 27.8 - "Basic elements of the revenue account"

[David]

Under the "Basic elements of the revenue account" heading of the solution it gives the following:


The constant business volumes and constant 5% increase in premiums means that Written Premium has increased by 5% each year

Earned Premium = (1800/2) + (1800/1.05/2) = 1757.1429

This assumes that risk and policies written are uniform over each year

Claims incurred (undiscounted) = 0.7 * 1757.1429 = 1230

Pattern of claim payments are given in nominal terms. We can use the patterns of claim development to see the amounts of claim payment at each point. (We have completed the table only for those numbers used)

Oldest: -, -, -, 106.25
Previous: -, -, 223.23, 111.56
Last: -, 351.43, 234.29, 117.14
Current: 492, 369, 246, 123


I understand how we calculate the numbers in the current row (i.e. Incurred Claims * Pattern % in that year) For example, 492 = 1230 * 40%

I can't seem to calculate the rest of this table however. Can you please help me understand how these numbers are calculated.

 

[David]

Just as I posted this I think I found out how to do it. May be worth answering incase anyone else is stuck on it.

My confusion was in trying to find the previous years premium by doing 1800 * 0.5 instead of 1800 * (1.05)^-1 (i.e. 1800/1.05) ... ignoring the dividing by 2


I am confused however as to how, further into this section of the question, the amounts of 450 for commission and 89.85 for other expenses were derived.

 

[Darren Michaels]

The total expenses paid are a balancing item between earned premiums, claims incurred, increase in DAC and the underwriting loss given in the question - that gives 539.85. Since acquisition costs are 25% of WP (of 1800) they must be 450, which means non-acquisition expenses are the balance, ie 89.85.