Prudence Margin in reserving

[Tushar Gora]

A company uses an investment return assumption of 5.5% for profit testing. The risk discount
rate is same as well. During a profit testing exercise, the company decided to increase the
prudence margin in reserving from 10% to 12.5%. The NPV of future profits at the inception
of the contracts:
(a) Will increase by 2.5%
(b) Will decrease by 2.5%
(c) Will remain unchanged
(d) Will increase by 0.15%

The correct answer is (c). I want to know the logic behind this.
Wouldn't the profit vector change by changing the prudence margin, which should change the NPV.

 

[Joe Hook]

Hi Tushar,

I'm not sure where this question has come from but if I understand it correctly:

Typically we expect to earn lower investment returns on reserves than on free assets due to constraints on the assets that we can hold to back reserves ie we generally choose safer assets. This would lead to a lower investment return than risk discount rate. By increasing the prudence of reserves we tie up our money in reserves for longer and so defer profit until later and therefore reduce the NPV.

However, in the case above the investment return is 5.5% and the risk discount rate is 5.5%. Imagine we now had to hold £200k more in reserves for 2 years. Setting up that reserve costs £200k. We earn interest on that reserve of 5.5% per annum so in 2 years it would be worth £222,605 and would be released. The present value of the money released is 222,605 / (1.055^2) = £200k. So the present value of the reserve set up equals the present value of the reserve released and so has no impact on the Net present value.

Another way to think about it is that we'd expect to earn 5.5% on any free assets ie any profit released. As this is the same rate we can earn on our reserves it makes no difference to us whether we release as profit now and invest at 5.5% or whether we put that money into the reserves.

Hope this helps. Let me know if I've misunderstood the scenario in any way.

Thanks
Joe

 

[Tushar Gora]

Hi Joe,

Thank you so much for replying.

The question is from IAI April, 2021.

I think your explanation fits.

Many Thanks
Tushar

 

[padasala]

@Joe Hook would the settlement patterns change the answer? If the claims are short tail in nature, would this have an impact of lowering the NPV (since you end up dipping into the prudence margins?

 

[Joe Hook]

No I don't think settlement patterns would have any impact here either. You can pay the claims via your reserves or your free assets, and both are able to benefit from 5.5% pa returns. So if you weren't dipping into your prudent reserve you'd be paying it out of some kind of retained profits and in either case the cashflow impact on you would be the same (a negative cashflow and the loss of future interest)

Basically in this scenario you're indifferent as a company as to whether you set up these reserves or retain profits because they both earn the same rate of interest. You can imagine having two bank accounts which earn the same rate of interest and then consider whether you'd care which account you took the money from to pay a bill? Now in reality, if we were setting aside a reserve we'd want to put that money somewhere safe because we've set it aside for the purposes of meeting some future liabilities. Safe assets tend to have a lower return, and so the interest earned on our reserves will be lower than that earned on profit. Setting that money aside at a lower interest rate will reduce our NPV but we'd then want to pay our claims out from that pot of money so that we continue to earn good returns on our retained profits. But in this case the investment returns are the same so we're happy to pay out from either pot.