Tax benefit pT for primary insurer
I want to confirm that the tax benefit, when the price exceeds the commuted discounted reserve, should be negative for the primary insurer. Because the asset is greater than the liability, and there is higher taxable income. And this is reversed for the reinsurer. There is an old quiz answer attached and it's a little confusing.
Comments
When the price exceeds the commuted discounted reserve, the amount paid for commutation is greater than the amount that liability is reduced by. So, income is reduced, and there is a positive income tax benefit.
I don't see your attachment here.
But for primary insurer, isn't they are receiving the cash payment and increasing their liability (by making ceded reserve as 0 and put all reserve as gross reserve). Since the cash payment is greater than the commuted discounted reserve, the income is actually increased for primary insurer, thus negative income tax benefit. The old quiz answer attached I mentioned in the initial post is actually on the wiki. Below is the original text on Wiki:
Pop Quiz! :-o
Will the quantity
p
T
usually be positive or negative? Explain.
Will the quantity
re
T
usually be positive or negative? Explain.
Pop Quiz Answers! :-D
Revised answer (Apr 9, 2023)
Click for
Klann Pop Quiz Old Answer ------------Here is what I am referring to.
Here's the quick answer: The commuted discounted reserve reduces the primary insurer’s income, while the price increases it. In the case where price is greater than thecommuted discounted reserve, income, and tax on income, increases. The effect is reversed for the reinsurer.
→
p
T should be negative
→
re
T should be positive
Looks like the Wiki agrees the income would increase for primary insurer and the final comment is primary insurer Tax benefit usually be negative. But the attached pop quiz answer has the reversed answer. So pretty confusing. I think I get it, It's just the Wiki is not clear on which one should be the correct one.
Sorry, I confused the direction of commutation. The wiki answers seem to be the wrong way around. We will get back to you on this.
The pop quiz answer you quote above says pT should be negative, which is right.
Thank you for confirmation.
Sure, good luck.