Spring 2015 Question 26

Turley36

When calculating Surplus change from the commutation, is there a difference between the total benefit to the insurer and the amount of Surplus change? If this problem would have given us the discounted ceded reserves and the non-discounted ceded reserves, which ones would we use for the change to the surplus?

graham

The benefit to the insurer and the surplus change are the same (at least for this narrow problem.) Surplus equals assets minus liabilities and the commutation is just shifting the assets and liabilities. Assets increase due to the payment from the reinsurer to take back the liabilities but (net) Liabilities also increase at the same time. They don't increase by the same amount though so that's why there's a change in surplus.

The problem is a bit tricky because you have to use both the discounted reserves and undiscounted reserves to get the final answer.

• surplus increases due to the (implied) $600 payment from reinsurer to insurer
• liabilities increase by $1000

Based on this, without considering taxes, there would be a surplus decrease of $400. Ok, now let's figure out the tax implication:

• even though reserves are shown undiscounted on the balance sheet, they must be discounted for tax purposes
• for tax purposes we can only take credit for 0.85 x $1,000 = $850 of reserves
• now take the payment of $600 and subtract the discounted reserves of $850 to get -$250 of taxable income
• since this is negative, the tax burden will decrease, and the amount of decrease is 35% x $250 = 87.5

If you put this al together you get:

• $400 - $87.5 = $312.5

So just to emphasize the answer to your question. You use undiscounted reserves to get the change in surplus without the tax implication. But then you have to use the discounted reserves to calculate the change in taxes. The final step is to put these 2 items together as shown above.

Turley36

Thank you again Graham!

So what is the point of calculating the total benefit to the insurer? What I mean by that is when you discount reserves both economically and for the potion considered the taxation benefit. Is this a GAAP versus SAP difference where you would realize the full benefit in GAAP, but in SAP the discount only affects the taxable portion of the benefit? Potentially because that aligns with the more philosophically conservative nature of SAP? Sorry , my question got a tad murky... Let me know if I need to unpack that a little more clearly...

graham

Let me try to answer your questions in turn, although I may not be answering exactly what you intended to ask:

Why calculate the total benefit?

• This is likely an important piece of information in deciding whether to follow through with the commutation (if it isn't forced.)

SAP vs GAAP

• You cannot discount the reserves either in SAP or in GAAP (with certain limited exceptions that apply to both.) You don't have to use same the discount rate in GAAP as you use in SAP however so that could affect the total benefit. So it isn't the discounting process itself that causes the difference, it's the discount rate that's used.
• The question asked for the change in statutory surplus but you you couldn't calculate the GAAP surplus anyway. You don't have enough information. You would at least need the provision for reinsurance and the value of the DAC asset. So the total benefit in GAAP could be different from SAP when you add in the impact of those other components.
• As for taxes, there isn't a difference in SAP versus GAAP. The taxes owed depend on the tax code but SAP and GAAP are merely different ways of presenting financial statement information.

Let me know if this doesn't properly address your question.

Turley36

That helps!

Sorry, I should have mentioned that I was talking about a theoretical scenario where we would have enough information to calculate the GAAP surplus. I should've elaborated more clearly.

For whatever reason the decision making aspect that you mentioned didn't come to mind. I was trying to wrap my head around the why without that vein of thought, and just confusing myself. This clears up a ton about the topic.

Thanks again.

arch1892

I'm not sure if this has been asked before but is the commutation price received by primary insurer recorded under the balance sheet as an asset? Would this be considered as 'other amounts receivable under reinsurance contracts'?

arch1892

Sorry, I guess it will be treated as an asset under cash received?

Staff - AC

It most likely goes under cash, like premium.

arch1892

Would it also be recorded in the income statement as other income? Income statement will also be impacted by commutation, correct where the incurred losses will increase

Staff - AC

Yes, correct.