Feldblum.Surplus - Old Version

This reading by Feldblum, Statutory Surplus: Computation, Pricing and Valuation,” CAS Study Note, June 2003 explains the difference between statutory surplus & invested capital. It also discusses the subsequent implications for pricing & reserving.

  Forum

Study Tips

You can gain valuable insights by carefully studying Feldblum's paper, but that would take a few days. There's lots there. (Normally I like Feldblum's writing, but I struggled to make sense out of some it, especially the section on double-taxation.) The topics that seem more likely to be on the exam are shown below. Note that there is significant overlap between Odomirok.6-7-BS and Odomirok.8-9-IS, so you can skip the first 10 pages and start with the section on double-taxation. That leaves only the last 4 pages, but it's a dense 4 pages.

Some of the first 10 pages of Feldblum's paper requires that you've had a proper accounting course and are familiar with double-entry bookkeeping. In particular you have to be familiar with the concept of a debit and a credit. If you haven't had an accounting course, this won't make any sense to you. I seriously doubt any of that would appear on the exam anyway.

Estimated study time: 3 hours (not including subsequent review time.)

BattleTable

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

• Problem Type: how to calculate whether to liquidate or continue operations - uses invested capital, PV(future income)
• Problem Type: margin required to offset double-taxation
• miscellaneous items from related chapters (see footnotes to BattleTable)

reference	part (a)	part (b)	part (c)	part (d)
E (2018.Spring #12)	invested capital: - calculate	PV(future income): - calculate	shareholder preference: - liquidation/continuance
E (2017.Spring #15)	surplus: - calculate 3	impact on surplus/income: - ABs 2 → 90 days past due
E (2015.Spring #12)	statutory income: - calculate 1	reserve adequacy: - supporting exhibits

¹ This is a good review of the statutory net income material from chapters 8 & 9 of Odomirok.

² AB's refers to: uncollected premiums and Agents’ Balances in the course of collection

³ Recall from chapter 6 of Odomirok that another way to calculate surplus is to calculate assets MINUS liabilities. But this means you have to be good at recognizing which line items are assets MINUS liabilities and which are neither. (You can learn this by practicing the location quiz from quiz #2 available here).

Full BattleQuiz You must be logged in or this will not work.

  Forum

In Plain English!

I coded 2 practice templates for this reading but they are easier than many of the others. The one on double-taxation looks like a good potential question.

Problem Type: Margin Required to Offset Double-Taxation (Basic Version)

This section befuddled poor Ian-the-Intern so Alice had to step in to help him make sense of it. The first order of business is defining more concise notation:

y	% yield on investment that an investor requires
TC	corporate tax rate (historically 35%, but as of 2018 it is 21%)
TP	personal tax rate (varies by person)

First, we'll describe the concept and lay out the formulas.

Question: what does Feldblum mean by double-taxation

Double-taxation happens when you invest money in a company and then the company reinvests the money elsewhere.

• the company pays taxes on its investment gain (corporate tax)
• the company pays you dividends
• you pay taxes on the dividends (personal tax)

==> The original investment gain is taxed twice (corporate & personal)

Question: how can you avoid double-taxation

• You can avoid double-taxation by investing your money directly into stocks or bonds (or something else that pays you directly without going through a "corporate middleman".)

Numerical Example: if y = 10%, TC = 35%, TP = 30%, calculate the cost of double-taxation (as a percentage of your dollar investment)

• tax on direct investment

   = ( investment yield ) x ( your personal tax rate )

   = y x T_P

   = 10% x 30%

   = 3%

• tax on indirect investment (through a company that reinvests your money as described above)

   = y x [ T_C + (1 - T_C) x T_P ]    ← take a moment to think through why this formula is true

   = 10% x [ 35% + (1 - 35%) x 30% ]

   = 5.45%

==> cost of double-taxation

   = ( tax on indirect investment ) – ( tax on direct investment )

   = 5.45% – 3%

   = 2.45%

Question: what are the implications of double-taxation for the investor, insurer, and policyholders

• the investor must get a higher rate of return (through their dividend payments) if investing indirectly through an insurer
• the insurer must pay a higher rate of return than the investor could get through a direct investment
• the policyholder must foot the cost of this higher return in the form of a margin added to their premium (specifically to offset the effect of double-taxation for the investor)

I suppose it seems kind of unfair to saddle the policyholder with this extra cost, but there isn't any other place to get it. Without it, the investor would simply go elsewhere, either to a different insurer or to a direct investment.

Question: calculate the margin on premium that the policyholders must pay to offset double-taxation for the investor

First, do the algebra using the above equations to get an expression for the cost of double-taxation:

==> cost of double-taxation

   = ( tax on indirect investment ) – ( tax on direct investment )

   = y x [ T_C + (1 - T_C) x T_P ]    –    y x T_P

   = y ⋅ T_C(1 - T_P)

Now back out both the personal and corporate tax:

==> cost of double-taxation (prior to tax)

   = y ⋅ T_C(1 - T_P) / [ (1 - T_C) ⋅ ( 1 - T_P) ]

   = y ⋅ T_C / (1 - T_C)

Using the numbers from the example, we can calculate:

==> cost of double-taxation (prior to tax)

   = 10% x 35% / (1 - 35%)

   = 5.38%

This means: For every dollar of capital invested, each written premium dollar pays an added margin of 5.38%.

But we're not quite done for 2 reasons:

• there may not be a 1-1 correspondence between capital invested and written premium so the capital-to-premium ratio must be factored in
• if premiums are paid at the beginning of the year but taxes are not due until the middle of the year, we have to account for the time value of money

Final(ish) Premium Margin Formula:    (capital / premium)    x    y ⋅ TC / (1 - TC)    x    (1 + y)-(1/2)

• The reason this is only the final-ish version of the margin formula is that it assumes there are no restrictions on the types of investments an insurer can seek. We'll look at this in the next section.

mini BattleQuiz 1 You must be logged in or this will not work.

Problem Type: Margin Required to Offset Double-Taxation (Atkinson & Dallas Modification)

The reason the margin formula from the previous section is only the final-ish version is that it assumes no restrictions on the types of investments an insurer can seek. In reality, however, there are restrictions regarding the level of risk an insurer is permitted to accept, and this in turns restricts the yield y.

For example, an insurer may want to invest in a financial instrument with a return of y = 12% but regulators may consider the investment too risky. (Remember that risk & return are directly correlated.) The insurer may, for example, only be permitted to invest in an instrument with y=8%. This presents a problem if a direct investment by the investor can yield a return of say 12%.

Note that this effect is in addition to the double-taxation discussed above, but it still falls on the policyholders to make up the difference through higher margins on their premiums.(With these challenges, Ian-the-Intern wonders whether outside investment in an insurer ever actually occurs. It does!)

Now, to understand the example on this from Feldblum's paper, you must understand that he uses the terms cost of double-taxation and cost of capital differently as explained below: (I have no idea why he does this. It's very confusing.)

When considering double-taxation only:

• cost of double-taxation

=    y ⋅ T_C(1 - T_P)    ← this is on an after-personal-tax basis

• cost of capital

=    cost of double-taxation

When considering double-taxation and the penalty regarding restrictions on investments:

• cost of double-taxation

=    y ⋅ T_C    ← this is on a before-personal-tax basis

• cost of capital

=    ( cost of double-taxation )    +    ( penalty regarding restrictions on investments )

Numerical Example: if an investor can get 10% on a direct investment, but the insurer can invest only at 8%, and TC = 35%, TP = 30%, calculate the cost of double-taxation and the cost of capital

• cost of double-taxation

= 35% x 8%

= 2.8%

• cost of capital

= 2.8% + 2%

= 4.8%

If we want now to calculate the margin required on policyholder premium to offset both double-taxation and the penalty regarding restrictions on investments, we must now back out corporate tax and account for the time value of money (as before) to find:

• margin

= 4.8% / (1 - 35%) * (1 + 8%)^-1/2

= 7.11%

Pop Quiz!    :-o

• See if you can follow the example in Feldblum. The only difference is that the investor gets 12% on a direct investment (rather than 10%.)

Final comment: I found the notion of double-taxation and how to resolve it quite interesting but very confusing. I didn't create a practice template for the Atkinson-Dallas modification because the calculations and concepts aren't that difficult – the difficulty is in the Feldblum's presentation. I wouldn't dare critique it, but Alice thinks that section from the source reading could have used a little extra editing. :-)

Problem Type: Liquidate or Continue Operations

Alice-the-Actuary and Ian-the-Intern invested in an insurance company 5 years ago. They had been receiving regular dividend checks, but while they were on vacation last week in Key West, a psychic told them to beware of impending financial calamity. Based on this reliable advice, they decided to look more closely at this investment by calculating the invested capital and the present value of the future income.

Formula:    invested capital    =    S    +    ( % acq x UEP )    +    ( 1 - % disc ) x R    -    DTA

Formula:    PV(future income)    =    (pre-tax income)    x    ( 1 - % tax )    /    ( % CoC )

Based on the results, they will either want the company to liquidate or to continue operations. The notation and solution are given in the pdf below. [I will give a permanent shout-out to the first person to to email the correct answer to the BONUS QUESTION contained in the pdf. I will also give an honourable mention to all correct solutions. (email: info@battleacts.ca) ← This challenge has ended.]

Solution to 2018.Spring #12

Of course, this is just the exam problem:

E (2018.Spring #12)

Note that this problem was modeled on an example from p14 of Feldblum's paper in the section Valuation: Cost of Holding Capital.

A couple of miscellaneous things to finish up this section:

• ( % acq x UEP ) is also called → equity in the UEP
• ( 1 - % disc ) x R is also called → equity in undiscounted reserves

Recall that

• (% acq) = pre-paid acquisition cost
• (% disc) = discount factor for loss reserves
• R = undiscounted loss reserve.

mini BattleQuiz 2 You must be logged in or this will not work.

Review: Balance Sheet and Income Statement

The exam problems in quiz #3 below are a good review of Odomirok material that you've already covered. Make sure to pay attention to the footnote under the BattleTable. I've copied it below:

• Recall from chapter 6 of Odomirok that another way to calculate surplus is to calculate assets MINUS liabilities. But this means you have to be good at recognizing which line items are assets, which are liabilities and which are neither. (You can learn this by practicing the location quiz from quiz #2 available here).

mini BattleQuiz 3 You must be logged in or this will not work.

Full BattleQuiz You must be logged in or this will not work.

  Forum