CIA.Taxes

One formula (tax effect of discounting). Meaning of formula (pre-payment of taxes). Often combined with an MfAD calculation.   Forum

Pop Quiz

Given the following, calculate: PV(net unpaid) including PfAD for interest rate risk.

Appointed Actuary's Estimates:

net undiscounted unpaid for AY 2016 @ year-end 2016:	79,000
discount rate:	11%
MfAD(inv):	125 bps (basis points)

Calendar Year Payout Pattern:

net paid @ 12 mths	30%
net paid @ 24 mths	50%
net paid @ 36 mths	100%

BattlePlan

Based on past exams, the main things you need to know (in rough order of importance) are:

• how to calculate the estimated effect of discounting the asset for future income taxes
• definition of the asset for future income taxes

Some subparts of the relevant exam questions were from other papers.

Top Questions ← Questions you absolutely need to know!

* Questions held out from Fall 2019 exam: #15. (Skip these now to have a fresh exam to practice on later. For links to these questions, see Exam Summaries.)

* There is a typo in the examiner's report solution to this problem. For an explanation, see this forum discussion.

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #16)	definition: - asset (future taxes)	calculate: - tax discounting effect
E (2017.Spring #16)	definition: - asset (future taxes)	calculate: - tax discounting effect
E (2015.Fall #17)	calculate: - tax discounting effect
E (2014.Fall #17)	calculate MfAD(claims): - see CIA.MfAD	calculate: - tax discounting effect
E (2014.Spring #17)	calculate loss ratio: - discounted & undiscounted - see CIA.MfAD	calculate: - tax discounting effect
E (2013.Fall #22)	definition: - asset (future taxes)	calculate: - tax discounting effect
E (2012.Fall #22)	see CIA.MfAD	see CIA.MfAD	calculate: - tax discounting effect	definition: - asset (future taxes)

In Plain English!

Intro

There are only 2 things you need to know from this reading: (2017.Spring #16ab)

1. defn of the asset for future income taxes:

This asset represents pre-payment of taxes arising since the tax credit taken for losses is less than the ACTUAL B/S losses

2. How to calculate the estimated effect of discounting the asset for future income taxes. (See next section.)

Statement of Problem: 2017.Spring #16b

This question is poorly worded. Take a look at the given information, then I'll explain what I mean.

Appointed Actuary's Estimates:

net undiscounted estimate:	810,000
net discounted estimate including PfADs:	816,200
discount rate including interest MfAD:	5%

Calendar Year Payout Pattern:

Year 1	60%
Year 2	25%
Year 3	10%
Year 4	5%

Other Information:

net claims liabilities carried in the A/R (Annual Return)	820,000
future income tax rate	35%

So, here is the issue I have with the wording: For the appointed actuary's estimates, they don't tell you which accident years are included, or what the evaluation date is.

• Is the unpaid estimate for a single accident year? AY 2016 @ Dec 2016?
• But then how do you apply the payment pattern?
  • Does Year 1 refer to 2016? That's normally the case in problems involving payment patterns - you would rebase Year 2, Year 3, and Year 4 according to the 40% that is still to be paid out.
  • Or does Year 1 refer to 2017? Then you would take the percentages directly from the table without rebasing.

The examiner's report accepts either interpretation, but Alice the Actuary was really steamed because they took no responsibility for their sloppy wording. (And this isn't the first time this has happened.)

Anyway, I'm going to use the first interpretation and rebase the payment pattern because that's normally what's done.

Solution to 2017.Spring #16b

The formula for the effect of discounting the asset for future income taxes is:

discounting effect = ( RR - 95% x min[RR, APV] ) x TaxRate x (1 - PVfctr)

The green items are what we're given. The red items are what we have to calculate.

• RR = Reported Reserve = net claim liability carried in A/R = 820,000
• APV = net discounted estimate with PfADs = 816,200
• TaxRate = 35%
• PVfctr = present value factor

The formula for the PVfctr is:

PVfctr = ( PV + PfAD(int) ) / ( net undiscounted estimate )

• net undiscounted estimate = 810,000 (given)

The last piece is to calculate PV + PfAD(int). If you recall the CIA.MfAD paper, this would be the first step in calculating APV. (Note that the given discount rate of 5% includes MfAD.)

Year	PV Calculation by Year	Result
2	25/40 x 810,000 ÷ 1.05^0.5 =	494,049
3	10/40 x 810,000 ÷ 1.05^1.5 =	188,209
4	5/40 x 810,000 ÷ 1.05^2.5 =	89,623
--	total includes PfAD:	771,881

We now have PVfctr = 771,881 / 810,000 = 0.9529, and the final answer is:

• discounting effect = ( 820,000 - 95% x min(820000, 816200) ) x 35% x (1 - 0.9529) = 735.4

Tax Calculations from Prior Exams You must be logged in or this will not work.

BattleCodes

• Memorize:
  • defn: asset for future income taxes (in the context of discounting for future income tax)

• Conceptual:
  • none

• Calculational:
  • estimated effect of discounting the asset for future income taxes

Full BattleQuiz You must be logged in or this will not work. (opens in a separate window)

  Forum

POP QUIZ ANSWERS

Age	PV Calculation by Year	Result
12-24	2/7 x 79,000 ÷ 1.0975^0.5 =	21,546
24-36	5/7 x 79,000 ÷ 1.0975^1.5 =	49,079
--	total includes PfAD:	70,625