Double Taxation

[islas_del_maiz]

Does anyone find this section of Feldblum's Surplus paper difficult to understand? I just can't make much sense out of the formulas here. It seems the different forumulas to calculate the cost of double taxation don't agree, yet the paper doesn't say anything about whether and why they don't.

Also, why is the adjustment for double taxation done by multiplying capital/premium, what is capital #, and what is premium # used in this calculation?

[REX]

This section is very unclear. I think it is important to remember that Myers/Cohn and Atkinson/Dallas did not create two different double taxation formulas. Myers/Cohn developed the double taxation formula. Atkinson/Dallas took that formula and added in the cost of holding capital. That is the only difference between the formulas. (Note: if you're using CSM, this is not how they presented it and one of the formulas they show is incorrect).

The premium to capital ratio is used to calculate the needed premium margin. The cost of double taxation and holding capital are both a percentage of capital. To calculate how this translates to a percentage of premium you need to change bases. This is where the premium to capital ratio is necessary.

[islas_del_maiz]

Thank you very much. Your explanation helped a lot. It's kind of funny that I wondered for some time whether cost of holding capital means the cost of the action of holding the capital, or the cost of the thing that's called holding capital. But then it would have been called cost of capital held i guess.

On page 12, when he talks about needed margins in premium, he really is saying investors should be compensated for the 35%*10% lost yield due to corporate tax. But what about the 10%*35%*(1-35%)=2.45% number? Why not also build that into the premium margin?

In the next paragrpah on Atkinson&Dallas, in this example the idea seems to be that when you invest in this ins co., you lose 4% for conservative investment approach, and lose another 35%*8% for IRS, prior to personal income tax. The cost of double taxation formula here is not the same as the invest yield*corp tax rate*(1-personal tax rate).


This section is very unclear. I think it is important to remember that Myers/Cohn and Atkinson/Dallas did not create two different double taxation formulas. Myers/Cohn developed the double taxation formula. Atkinson/Dallas took that formula and added in the cost of holding capital. That is the only difference between the formulas. (Note: if you're using CSM, this is not how they presented it and one of the formulas they show is incorrect).

The premium to capital ratio is used to calculate the needed premium margin. The cost of double taxation and holding capital are both a percentage of capital. To calculate how this translates to a percentage of premium you need to change bases. This is where the premium to capital ratio is necessary.

[REX]

2.45% is the cost of double taxation to the policyholder. To make up this 2.45% to the investor, the insurer must increase their yield by 3.5% ( = .0245 / [1 - .35] ) to account for the fact that the increased yield will be taxed before the policyholder receives it. That is why the 3.5% is built into the margin calculations and not the 2.45%.

[cmlarson]

Regarding the end of the double taxation discussion in the paper, I'm comfortable with all but the very last step.

I understand that the margin needed as a percentage of investor supplied capital = investment yield * 53.85%.

The next step confuses me:

margin on premium = [capital * investment yield * 53.85%]/prem

Where does that numerator come from?

[REX]

As you said, the first formula calculates the needed margin, as a percentage of capital. To calculate the margin as a percentage of premium you need to change the bases. That is why you multiply by capital and divide by premium.

[Utopial]

my understanding is:

cost of capital (myers cohn) = yield * Tc
after tax cost of capital (myers cohn) = yield * [(1-Tp) - (1-Tc)(1-Tp)]
ie cost of double taxation

cost of capital (atk-dallas) = stock return - yield * (1-Tc)

Margin = [capital * cost of capital / (1-Tc) ] / [prem * (1+yield)^0.5]

can anyone confirm this?

[carrytheCrøss]

cost of capital (myers cohn) = yield * Tc
after tax cost of capital (myers cohn) = yield * [(1-Tp) - (1-Tc)(1-Tp)]
ie cost of double taxation

Margin = [capital * cost of capital / (1-Tc) ] / [prem * (1+yield)^0.5]


I disagree a bit with your equations; though, in my opinion, the picture Feldblum attempts to paint is sloppy at best, and is bound to lead many into a state of confusion.

Throughout the entire "Double Taxation" section, the author is very loose with the term "tax" and "after-tax." Note the following three costs of holding capital, which follow one after another:

1) The Myers-Cohn cost of holding capital (i.e., cost of double taxation) as defined by Feldblum = investment yield * corporate tax rate * (1 – personal tax rate).
This amount is the after-corporate income tax, after-personal income tax loss to the investors.

2) The Myers-Cohn after-corporate income tax, pre-personal income tax loss to the investors
= investment yield * corporate tax rate * (1 – personal tax rate) / (1 - personal tax rate) = investment yield * corporate tax rate

3) The Myers-Cohn pre-corporate income tax, pre-personal income tax loss to investors (i.e., necessary margin)
= investment yield * corporate tax rate / (1 – corporate tax rate)

To convert 3) into a dollar amount, you would tack on the capital, premium, and (1+yield)^0.5 factors as you have done.

As for this one:
cost of capital (atk-dallas) = stock return - yield * (1-Tc)I agree. Recognize, though, that this is an after-corporate income tax, pre-personal income tax loss to the investors. It is pre-personal income tax since there is no personal income tax term involved.

So, when it comes down to it, the Myers-Cohn and A-D costs of holding capital as defined by Feldblum are slightly mismatched: the Myers-Cohn cost is after-corporate income tax, after-personal income tax while the A-D cost is after-corporate income tax, pre-personal income tax. While this treatment may appear inconsistent, Feldblum makes the treatment consistent by dividing the A-D after-corporate income tax, pre-personal income tax cost of holding capital by (1 - corporate tax rate). In doing this, SF gets back to a pre-corproate income tax, pre-personal income tax figure in the A-D context, directly analogous to the one in the Myers-Cohn context. It is these pre-all taxes figures that are used in computing the necessary margins in both contexts.

Hopefully that's at least somewhat clear! :wall:

[WelcomeToTheSuck]

CarryTheCross should volunteer to become the new Feldblum :-D

Thank you as this is now much more clear. Why is the author so bad at explaining and clarifying these obviously very important distinctions?!!?!?!

[WelcomeToTheSuck]

Guys, has this topic ever been tested on in the past exam questions? I have looked through all past problems in 2007 All 10 and have not found one. If we use history as a reliable record, I may skip this terribly written section (even with CarryCross' sage teaching). If not, can someone please tell me the question number and year where it appears? Thanks

[carrytheCrøss]

Guys, has this topic ever been tested on in the past exam questions? I have looked through all past problems in 2007 All 10 and have not found one. If we use history as a reliable record, I may skip this terribly written section (even with CarryCross' sage teaching). If not, can someone please tell me the question number and year where it appears? ThanksI appreciate that, but I don't believe anything's been asked (at least I saw no questions in the All 10 :shrug:). I'm just trying to prepare for it in case this is the year; but, as always, it definitely may not be tested.

[WelcomeToTheSuck]

Does Myers Theorem always use the risk free rate rather than the corporate investment yield? There was no mention of this earlier but then I am puzzled why Feldblmum on page 13 specifically says Myers Therem and then only uses 5% (risk free rate), then calculates it again with the company's yield.

[hellomath]

3) The Myers-Cohn pre-corporate income tax, pre-personal income tax loss to investors (i.e., necessary margin)
= investment yield * corporate tax rate / (1 – corporate tax rate)

To convert 3) into a dollar amount, you would tack on the capital, premium, and (1+yield)^0.5 factors as you have done.


CTC - I have to disagree with you on the needed margin.

IMO, the needed margin is a after-corporate income tax on bond, pre-corporate income tax on U/W income, pre-personal income tax loss to investors.

Capital*Investment yield*53.85%/premium is a % of premium instead of a $ amount.

Also, Feldblum assumes taxes are paid on average at mid-year, I think he was referring to U/W income taxes only.

[carrytheCrøss]

IMO, the needed margin is a after-corporate income tax on bond, pre-corporate income tax on U/W income, pre-personal income tax loss to investors.

Also, Feldblum assumes taxes are paid on average at mid-year, I think he was referring to U/W income taxes only.You very well may be right, and there's no way that I ever would have thought of it like this. I doubt we have to know this much detail, though, but thanks for looking into this.

[hellomath]

You very well may be right, and there's no way that I ever would have thought of it like this. I doubt we have to know this much detail, though, but thanks for looking into this.

For this exam, I am having a hard time distinguish need-to-know from too-detail.

[Utopial]

my understanding is:

after corp tax cost of capital (myers cohn) = yield * Tc
after corp&pers tax cost of capital (myers cohn) = yield * [(1-Tp) - (1-Tc)(1-Tp)] = yield * Tp * (1-Tp)
ie cost of double taxation

after corp tax cost of capital (atk-dallas) = stock return - yield * (1-Tc)

Margin = [capital * after corp tax cost of capital / (1-Tc) ] / [prem * (1+yield)^0.5]

can anyone confirm this?



CtC i think we have the same definitions, i just defined mine poorly. ive added extra details above

[Malcolm]

CTC - I have to disagree with you on the needed margin.

IMO, the needed margin is a after-corporate income tax on bond, pre-corporate income tax on U/W income, pre-personal income tax loss to investors.

Capital*Investment yield*53.85%/premium is a % of premium instead of a $ amount.

Also, Feldblum assumes taxes are paid on average at mid-year, I think he was referring to U/W income taxes only.

heckomath, you are right. the idea is that your investors (let's call them A&D) demand a certain return on their investment - the cost of capital. let's say that's 12%. they could get that by investing directly in stocks expected to return 12%. instead, they decide to invest in your insurance company. they still expect to get 12% back.

now, heckomath insurer can't just go out and invest in those same 12% stocks - for one, you'd have to pay taxes on your returns before paying the investors, and second, they're too risky. so instead you invest in some nice safe 8% bonds that will make the NAIC RBC formula happy. so far, your investors aren't too happy, because they're only getting 65% * 8% = 5.2% return, when they demand 12%. because of your risk-averse investment strategy, they're missing out on 6.8% they could otherwise get.

but you're not just in the business of investing other people's money. you're also going to write insurance policies to insured's and invest their money, too. in addition, you're going to build in a little bit extra in the premium for your trouble. now, A&D say "that's our money, and we want our other 6.8%!" there's no other place to get it other than your policyholders, so that's the profit you have to make off them in order to pay your investors. however, for all this big profit load you're building in, the IRS is going to take its cut. if you just made 6.8% on each policy, you're only going to have 65% * 6.8% = 4.42% to pay A&D. that's not enough. so you gross it up to a pre-tax figure of 6.8% / 65% = 10.46%. of course, this is on a percent of capital basis. in order to figure what you need to make off each policyholder, you convert this to a percent of premium basis, account for the fact that you can invest their premiums for about half a year (on average) before paying taxes on all this u/w profit and voila - you have the margin on premium.

The Myers-Cohn cost of holding capital is just the cost of double taxation, which I think assumes that investors would otherwise invest in the same types of securities you (the insurer) will invest in, so it doesn't compare your investment strategy to investor demands.

The Myers theorem, which appears out of nowhere in Feldblum's paper after being introduced in an endnote, says that the cost of holding capital does not depend on the particular investment strategy, since the risk-based model of cash flows for risky investments gives the same PV as risk-free investments, so it uses the risk-free rate instead of the insurer's investment yield.

i realize i've probably mangled this explanation, but i hope someone can get something out of this, and maybe untangle it a bit.

[alphaace]

ARGH! I don't get this at all!

As far as I can tell:

Cost of double taxation = Myers cost of holding capital = yield * Tc * (1-Tp)
Cost of holding Capital vs Atkinson = ((equity yield - inv yield) + Tc * inv yield)

However then on his example on page 13 he states

"The cost of double taxation using the Myer's Theorem is 185 * .05 * .35) = 3.24M. Why isn't it 185 * .35 * (1 - Tp) whatever Tp is in this case? Why is he using the risk free rate?


Also, in his exmaple above that, he says premium to capital is 1.25. Why does he divide 10% by 1.2 then??

[vitamink]

Let me try here.

1 yield * Tc * (1-Tp) is after personal-tax level. In the calculation 185 * .05 * .35 equals to yield(185*.05) *Tc(.35) is after corp-tax, before personal-tax level.

2 Myers methods uses the risk free rate, Atkinson uses investment yield plus opportunity cost. These are both from the paper, as I remembered.

3 10% yield rate [8%*0.35+(12%-8%)]/(1-35%) (before corp-tax here)is return on equity, since premium/equity(surplus)=1.25:1, so return on premium is 10%/1.25.

Hope it helps. Let me know if there is any errors since I know it's so easy to miss something here

[alphaace]

Shoudn't then, as CtC states a few posts back the Myers after Corporate, pre-personal tax simply be Inv Yield * Corporate Taxes?

In the article, there is a line "The cost of double taxation using the company's investment yield is 185 * 8%*35%". So I take this to be PreTax cost of capital. Why is the sentence before that using the risk free rate then?

[WelcomeToTheSuck]

Shoudn't then, as CtC states a few posts back the Myers after Corporate, pre-personal tax simply be Inv Yield * Corporate Taxes?

In the article, there is a line "The cost of double taxation using the company's investment yield is 185 * 8%*35%". So I take this to be PreTax cost of capital. Why is the sentence before that using the risk free rate then?

That's how I thought it should be. I have no idea why the example is using the risk free rate. In the unlikely event that we're tested on this topic, I don't see how they could fault us for using the company investment yield since it clearly states to use this in the paper.

[Malcolm]

That's how I thought it should be. I have no idea why the example is using the risk free rate. In the unlikely event that we're tested on this topic, I don't see how they could fault us for using the company investment yield since it clearly states to use this in the paper.

I agree. The risk free rate calculation is the Myers Theorem (not to be confused with Myers-Cohn, though it's probably the same Myers). Although Feldblum mentions the Myers Theorem a few times toward the end of the paper, he only introduces & explains it in an endnote.

The two methods he explains in the body of the paper are Myers-Cohn and Atkinson-Dallas, both of which CtC explained in earlier posts much better than I could do now.

[chicken_po_boy]

Feldblum - surplus

Help! I was doing OK on this paper but I get totally lost on pg 13

Q1. Can someone explain why "The cost of holding capital depends on both the capital explicitly held as surplus and the capital embedded in statutory reserves."

Q2. What is the meaning of "equity in the unearned premium reserve" and why is it equal to UPR x acquisition expense ratio?

Q3. What is the meaning of "equity in the undiscounted loss reserves" and why does it = loss reserves x (1-IRS discount factor)?

Q4. What is meant by "statutory deferred tax asset stemming from the revenue offset"? and why does it = tax rate x 20% x UPR

Q5. What is meant by "statutory deferred tax asset stemming from the loss reserve discounting"? and why does it = tax rate x 25% x 20% x undiscounted reserves

[MountainHawk]

You hold 100% of UEPR as a reserve, however, many acquisition costs are paid at policy outset, so they are being double counted (once as paid expense, once in UEPR). The equity in the UEPR is the expected excess of the reserve over the future loss and expense payments.

Similar idea for the equity in the undiscounted loss reserves, since we does only need to hold the discounted loss reserves to meet the obligation.

[chicken_po_boy]

Thanks!! That helps me totally understand Q1 - Q3. I'm still a bit fuzzy on Q4 and Q5 though.

[MountainHawk]

Don't remember the answers to 4 and 5, sorry.