Tutorial D2 Q3 UPR at the end of year

[SiliLU]

Hi,

For Tutorial day 2 Q3 ActEd question:
It is given that at the start of the year, UPR is 100M. Assuming annual policies are written uniformly over the year, why at the end of the year, UPR is 100M * 2 = 200M?

Many thanks,
Sili

 

[Aman Sehra]

Hi Sili,
Having looked at the question, and the solution, and I can't seem to see where UPR is 200m. Can you confirm where you are seeing this please?

Aman

 

[SiliLU]

Hi Sili,
Having looked at the question, and the solution, and I can't seem to see where UPR is 200m. Can you confirm where you are seeing this please?

Aman

Hi Aman!

The written premium is calculated as:
100 / (1-0.15) × 2 × 1.2

× 1.2 is to count in the premium increase of 15%. Can you please help to explain the rest of the formula? If I understand correctly, 100 / (1-0.15) is the UPR gross of DAC?

Many thanks!

Sili

 

[Aman Sehra]

The UPR at the start of the year was 100, so to get from UPR to WP, we double it.

The whole written premium calculation is: 200/0.85*1.2 = 282.35

Note that the 0.85 is to get from Net to Gross of DAC, and the 1.2 is for the premium increase of 20%.

 

[SiliLU]

The UPR at the start of the year was 100, so to get from UPR to WP, we double it.

The whole written premium calculation is: 200/0.85*1.2 = 282.35

Note that the 0.85 is to get from Net to Gross of DAC, and the 1.2 is for the premium increase of 20%.

Many thanks!
Please can I check with you - why to get from UPR to WR we double it?
This is the part blocking me.

 

[Aman Sehra]

If risks are written evenly over the year, then at the end of the year, there will still be exposure left that is not expired. For example, if i write business on 30th December, then almost a full year of it will still be unexpired on the 31st December. I suggest revisiting SP7 course material for further information on this.
Thanks

 

[SiliLU]

Thanks I think I get it!
In the beginning of the year, there are 100 premium of exposure not yet earned. There are 100 premium of exposure already earned through the second half of last year. So in total 200 premium written during one year.

 

[SiliLU]

And a follow up question regarding the end of year balance sheet:
Shareholders funds should be equal to funds brought forward + retained profit, ie 779.7-667.5 =100.0+12.2
Why the funds brought forward is 100?

 

[Darren Michaels]

And a follow up question regarding the end of year balance sheet:
Shareholders funds should be equal to funds brought forward + retained profit, ie 779.7-667.5 =100.0+12.2
Why the funds brought forward is 100?

You are correct SHF b/f (ie at the start of the year = that at the end of the previous year) is 100 and SHF c/f (ie at the end of the year) = 112.2

 

[Darren Michaels]

Thanks I think I get it!
In the beginning of the year, there are 100 premium of exposure not yet earned. There are 100 premium of exposure already earned through the second half of last year. So in total 200 premium written during one year.

Almost - but don't forget that the 100 is net of DAC - the UPR gross of DAC is 100/0.85=117.65, hence WP in previous year is 2*UPR gross of DAC = 235.3, hence WP for year in question (allowing for the 20% growth) is 282.35