DefTaxLiab shortcut

[Bballry1234]

I ended up getting nowhere in my studying today because I couldn't figure out the "future timing differences" lingo in Atkinson Dallas for problem 9.6. It didn't seem to match up to my understanding of the timing difference (SolvencyResInc-TaxResInc). Anywho, I figured out a cute little shortcut if the SOA changes future tax rates on us and wants new provisions or liabilities:

DefTaxLiab(t) = - [DefTaxProv(i)] from i=t+1 to n, where DefTaxLiab(n) = 0, and DefTaxProv(t) = AccruedTax(t) - TaxonEarning(t).

Here is how it works:

DefTaxLiab(n-2) = DefTaxLiab(n-1) - DefTaxProv(n-1)
= DefTaxLiab(n) - DefTaxProv(n) - DefTaxProv(n-1)
= - (DefTaxProv(n-1)+DefTaxProv(n))

Give this a shot with 9.6. It should help you out, and if anyone actually does take the time to read this and my logic ends up being complete nonsense, let me know. So far, it seems like a pretty solid way to approach problems with changing tax rates.

[Dahlia]

Thanks. I'll check it out.

[cube_monkey]

DefTaxLiab(n-2) = DefTaxLiab(n-1) - DefTaxProv(n-1)
= DefTaxLiab(n) - DefTaxProv(n) - DefTaxProv(n-1)
= - (DefTaxProv(n-1)+DefTaxProv(n))

What happened to the DefTaxLiab(n) in the formula?

[cube_monkey]

Ahh, nevermind I see that you say where DefTaxLiab(n) = 0
Seems like solid logic.

[Bballry1234]

bump

[surdahl]

Here's my solution, and I've checked this against the LIPF Exercise 9.6, so hopefully it makes sense and I believe it is correct. The best way to check this is in a spreadsheet to see that the formulas hold up regardless of if the tax rate has changed or not, you should still get the same answer.

In the beginning, when no tax changes are expected:

(1) DefTaxProv(t) = -(TaxEarn(t) - StockEarn(t)) * Current Tax Rate
(2) DefTaxLiab(t) = DefTaxLiab(t-1) + DefTaxProv(t)


Once a tax change has been announced, you must reflect the change in the current year's DefTaxLiab, which means DefTaxLiab(t) should be calculated FIRST and the DefTaxProv(t) should be backed into so that changes are reflected immediately:

If tax rate is changing and will change again (and again) AND these changes are known then:

(3) DefTaxLiab(t) = [TaxEarn(t+1) - StockEarn(t+1)] * TaxRate(t+1) + ... + [TaxEarn(n) - StockEarn(n)] * TaxRate(n), where n is the last year of your projection. (You could use the SumProduct function here if setting this up in Excel)

(4) DefTaxProv(t) = DefTaxLiab(t) - DefTaxLiab(t-1)

If tax rate is changing and will remain at the same rate, then a simplified version of formula (3) above is:

(5) DefTaxLiab(t) = [Sum(TaxEarn(t+1):TaxEarn(n)) - Sum(StockEarn(t+1):StockEarn(n)] * New Tax Rate


For all years going forward, until any NEW changes occur (changes not already reflected in calculations), DefTaxProv(t) and DefTaxLiab(t) can be calculated using the simpler formulas (1) & (2). But you could still continue to use formulas (3) and (4) and should still get the same answer. Note, however, that you should use formulas (1) and (2) UNTIL the change is known. If you use formulas (3) and (4) before the change is known you will not get the right answer* (I know that doesn't make any sense theoretically, but say a problem said you find out in year 5 that a change is going to occur, then do NOT change the formula until year 5. Years 1-4 should use formulas (1) and (2)).

*One caveat: You could use formulas (3) and (4) from the start and you will get the right answer, but as soon as you change the tax rate in year 5 then if years 1-4 used formulas (3) & (4), the values will no longer be correct. This is all assuming you are using a spreadsheet and you have tried to automate your formulas, which is why I suggest using formulas (1) and (2) in ALL years other than the year in which a change is being acknowledged.

[surdahl]

Originally Posted by Bballry1234

I ended up getting nowhere in my studying today because I couldn't figure out the "future timing differences" lingo in Atkinson Dallas for problem 9.6. It didn't seem to match up to my understanding of the timing difference (SolvencyResInc-TaxResInc).

So glad someone else got a bit turned around by this as well! I started questioning my understanding of Solvency Earnings vs. Taxable Earnings, which is reflected by TIMING DIFFERENCES and permanent differences. Then they throw us for a loop and call the differences between Stockholder earnings and taxable earnings timing differences as well! Just not right!!

This confusion once again reflects what my boss always says "all those exams are just a hazing process, weeding out the weak!" Oy!!