Tax Benefit Confusion
Hi -
I am wondering why in the sections for Tax Effect of a Commutation, the primary insurer ends up with a positive change to taxable income and the reinsurer ends up with a negative change (in the examples)- but then in the Pricing a Commutation section, it's discussed that the Primary insurer should have a tax benefit: "The primary insurer's tax benefit pT should be positive. In a commutation, the primary insurer is taking back a group of claims. That causes a shift in their balance sheet from assets to liabilities, which is a shift from taxable to non-taxable income." This would make me think that the primary insurer should have a negative change to taxable income in the Tax Effect of a Commutation section.
Is there an explanation to connect these concepts?
Comments
Could you point me to exactly where you see the sentences you quote?
For "Tax Effect of a Commutation" I am referring to the PDF examples that solve for the change in taxable income. Sample answer (easy version):
Insurer taxable income increases while reinsurer taxable income decreases.
This seems to contradict what is stated in a following section.
The quoted sentence is the answer to the pop quiz in the "Pricing a Commutation" section of Klann.ReinsComm
We are looking into this and will let you know soon.
Hi - do you have an update? Thanks.
We are working on a rewording of the Pop Quiz Answer and will let you know soon. Sorry about the wait.
Here is the link to the revised answer:
so p_T is really just (change in taxable income for primary) x (tax rate for primary)? it seems odd to add p_T to (price - ceded reserves), and then flip the equation for change in taxable income for primary. Would it be wrong to just say:
Price - (economic-discounted primary's ceded reserves prior to commuation) - (p_T), where
p_T = (tax rate) x [(commutation price) - (statutory-discounted loss reserves)]
This would make the equations directly in line with the concepts from the previous section where,
change in taxable income for primary insurer = price - [(ceded reserves) x d1].
Algebraically, it all works since I'm changing the signs and then changing the order of the equation, but I guess I am wondering why it was flipped in the first place.
p_T is as you define it above.
primary insurer benefit = price - (economic-discounted primary's ceded reserves prior to commuation) +(p_T)
I don't follow what you mean by "flipping the equation."
I am just defining p_T as the increase in taxes paid for the primary and then subtracting it off from the mutual benefit equation. Where BattleActs is defining p_T as the decrease in taxes paid for the primary and then adding it to the mutual benefit equation which was throwing me for a loop for a bit. Just to clarify on the flipped equation:
My p_T = (primary tax rate)x[P - (ceded reserves) x (d_1)]
BA's p_T = (primary tax rate)x[(ceded reservers) x (d_1) - P]
I am getting the BA's version of p_T from BattleActs' re-formatted example of Spring 2016 #27. I also see the examiner's report shows it the same way as BattleActs, it was just confusing me at first to call it a tax benefit.
p_T, the tax benefit of commutation for primary, is the negative of (change in taxable income for primary) x (tax rate for primary). That's why it is added in primary's benefit expression.
Yes, your way, with your definition of p_T, works too. But yours is keeping track of the increase in tax, which is not a "benefit" of commutation. That's why it was not preferred in the wiki treatment.
the formula for mutual price seem confused when it comes to decrease to tax benefit. Can we define it more simple this way: (Economic Discounted + Tax rate* Change in taxable income) For insurer< Mutual price<(Economic Discounted - Tax rate* Change in taxable income ) For reinsurer. I think it will go along with the formular for change in taxable income in the Wiki
I don't see the Wiki having an explicit formula for mutual price. Rather, it is solved for in the solution. Your formula appears to work. Feel free to use it.