- Calc in 3 steps
- pre-tax solvency earnings
- deduct taxes to detmine after-tax solvency earnings
- adjuste after-tax solvency earnings for incr req captial and add after-tax inv income on assets backing req'd capital

- Pre-Tax Solvency Earnings
- product cash flow - ProdCashFlow(t) = Prem(t) - Ben(t) - Exp(t)
- adjust for reins if necessary
- increase in solvency reserves - SolvResIncr(t) = SolvRes(t) - SolvRes(t-1)
- investment income - InvIncome(t) = PolLoanInt(t) + InvInc(t) + CashFlowInt(t)
- PreTaxSolvEarn(t) = ProdCashFlow(t) + IncIncome(t) - SolvResIncr(t)

- After-Tax Solvency Earnings
- AfterTaxSolvEarn(t) = PreTaxSolvEarn(t) - Tax(t)

- Adjustment for Req'd Capital
- ReqCapIncr(t) = ReqCap(t) - ReqCap(t-1) -> increase in req'd capital
- ATInvIncRC(t) = InvIncRC(t) - TaxInvIncRC(t) -> after tax inv income on assets backing req'd cap
- DistEarn(t) = AfterTaxSolvEarn(t) - ReqCapIncr(t) + ATInvIncRC(t)
- often not practical to price over lifetime of product, instead use 10/20/30 years
- if n is pricing horizon, need to account for all profits beyond n
- release req'd capidal @ end of n (ReqCap(n) = 0)
- either explicitly or set lapse for n to 100%

- present value of all future events need to flow through year n calc

- release req'd capidal @ end of n (ReqCap(n) = 0)

- solvency reserves distort profit w/ significant NB strain, earnings reserves have smoother pattern, often no loss in first year
- Pre-Tax Stockholder Earnings
- similar to pre-tax solvency earnings
- product cf are identical
- main diff: change in earning reserves (net of DAC) vs change in solvency reserves
- assume invested assets = solvency reserves + req'd capital

- PreTaxStockEarn(t) = ProdCashFlow(t) - BenResIncr(t) - DACAmort(t) + InvIncome(t) + InvIncRC(t)
- DACAmort(t) = DAC(t-1) - DAC(t) where DAC(0) = 0
- From Solvency Reserves
- PreTaxStockEarn(t) = PreTaxSolvEarn(t) + SolvResIncr(t) - BenResIncr(t) - DACAmort(t) + InvIncRC(t)

- similar to pre-tax solvency earnings

- need to deduct 3 components of tax
- Tax(t) - PreTaxSolveEarn tax
- TaxInvIncRC(t) - Tax on Inv Inc earned on assets backing req cap
- DefTaxProv(t) - Tax on diff between shareholder and solvency earnings excluding II on req'd capital (aka Provision for Def Taxes)

- AfterTaxStockEarn = PreTaxStockEarn(t) - Tax(t) - TaxInvIncRC(t) - DefTaxProv(t)
- Positive Distributable earnings - max amount that can be paid to stockholders
- Negative Distributable earnings - capital contributions stockholders must pay into co
- After-Tax stockholder earnings - earnings reported to stockholders
- often exeeds distributable earnings for a growing co

- After-Tax stockholder earnings / stockholder equity base
- stockholder equity base
- stockholder equity @ BOY OR
- avg of BOY and EOY stockholder equity

- stockholder equity = Assets - Liab
- Assets = DAC + inv assets backing solvency reserve + req'd capital
- Liab = benefit reserves + def'd tax liab
- StockAssets(t) = SolvRes(t) + ReqCap(t) + DAC(t)
- StockLiab(t) = BenRes(t) + DefTaxLiab(t)
- StockEquity(t) = StockAssets(t) - StockLiab(t)
- EquityBase(t) = StockEquity(t-1) or 0.5*(StockEquity(t-1) + StockEquity(t))
- ROE(t) = AfterTaxStockEarn(t) / EquityBase(t)
- ROE varys by year therefore tough to determine if co's ROE goal is met over product lifetime

- basic questions
- which acctg basis to calc profits
- how to reflect products degree of risk
- what rate to discount future values or as targeted rate of return
- should impact of req'd capital be reflected (authors assume yes)

- Choice of Acctg Basis
- solvency earnings
- important to regulators and rating agencys
- solvency reserve and cap req drive shareholders investments

- stockholder earnings
- if co places heavy emphasis on stockholder earnings
- added difficulty so not as popular

- solvency earnings
- Reflecing Risk in Profit Goals
- profit goals related to risk (more risky, higher profit margin)
- possible ways to reflect risk
- formula that might reflect lapse/mort/exp/inv risks
- profit margin set to estimated degree of risk
- sensitivity analysis to estimate degree of risk and set profit margins

- examine product design adn origin of assumptinos used to id risks that req special treatment and possibley make design chagnes to minimize risk

- Choice of Discount Rates adn Rates of Return
- factors to consider when choosing discount rate
- company's cost of capital - weighted avg and marginal
- "opportunity cost" of capital - what could they earn if that money was elsewhere
- current capital position adn expected capital position over next few years - might be receptive to lower yield s/t opportunities
- how will discounting be used
- generally based on cost of capital or opportunity cost
- if discounting to give more weight to early years, pretax or after-tax yields on inv assets may be appropriate

- rate-of-return rate that discounts the stream of profits to zero
- it taxes are level % of pre-tax profits, pre-tax and after-tax rates of return are same

- factors to consider when choosing discount rate

- PVPrem = sum(Prem(t)*DiscFactor(t-1)) => t-1 b/c prems paid at BOY
- PV(var,n) = sum(var(t)*DiscFactor(t)) over n years
- if some PVFP < 0 [ i(t) - normal disc rate j(t) - discount rate when profits are neg - typically after-tax int rate earned on invested assets]
- PVFP(n) = Profit(n)
- for t = n to 1 step -1
- If PVFP(t) > 0 then
- PVFP(t-1) = PVFP(t)/(1+i(t)) + Profit(t-1)

- else
- PVFP(t-1) = PVFP(t)/(1+j(t)) + Profit(t-1)

- endif

- If PVFP(t) > 0 then
- next
- PVFP(n) = PVFP(0)
- if n = 1, Profit(0) = 0

- Overview
- Embedded Value Return on Investment (ROI) Weighted-avg return on equity (ROE)
- Profit as % of Prem/Assets/revenues/risk charges
- Accum Porift at % of reserves breakeven year new business strain
- most co use ROI or ROE along w/ profit as % of prem
- publicly traded stock cos tesnd to use embeddev value, ROI/ROE as one of their profit goals - each involves a targeted rate of return

- Embedded Value (aka value added)
- simplest measure - only one decision - hurdle rate
- hurdle rate - rate of return owners expect
- s/b in line w/ weighted avg cost of capital for stock co
- s/b consistent w/ return avail on investments of comparable risk

- normally base profits on after-tax solvency earnings or distr earnings
- distr earnings better reflect owners' expected cash flows
- EmbeddedValue(n) = PV(Profit,n)

- Return on Investmetn (ROI)
- solved for discount rate that causes PV Profits = 0
- normally base profits onafter-tax solvency earnings or dist earnings
- Dist earn preferrable - better reflects owners' expeced cash flows
- ROI can be primary or seconday profit goal
- ROI fails if all policy years are profitable
- posses in later years can olso produce meaningless ROI
- Simple ROI
- 0 = sum(Profit(t)/(1+i)^t and solving for i

- Multiple ROIs
- # positive roots of polynomial = # sign changes of Profit(t)

- Generalized ROI
- if muliple sign changes, use an int rate for borrowed money (j(t)) adn use iterative process to solve for i
- PVFP(t-1) = PVFP(t)/(1+[i(t) or j(t)]) + Profit(t-1)

- if muliple sign changes, use an int rate for borrowed money (j(t)) adn use iterative process to solve for i

- Weighted-Avg Return on Equity
- calculate a weighter avg return = (after-tax stockholder earnings) / weighted avg equity base
- can weight by discounting using ROI goal or hurdle rate
- can link to targeted growth rate
- WtdAvgROE(n) = PV(AfterTaxStockEarn,n) / PV(EquityBase,n)
- hopefully each policy year ROE approx = WtdAvgROE

- Profit as Percentage of Premium
- one of most common profit measures
- advantage: fairly concrete and easy to explain
- common to use pre-tax or after-tax int rate eaerned on assets for discounting
- using ROI or Hurdle rate, PVProfits approx = 0 therefore meaningless
- this logic applies to all measures that compare PVprofit to another measure

- Proft%Prem(n) = PVProfit(n) / PVPrem(n)

- Profits as Percentage of Revenue
- generalization of Profit%Prem
- useful mainly as way to compare relative profitablilty of similar product types
- NOT useful at comparing two diverse products
- not all products use premium as important soure of revenue (ex. UL -> inv income and charges)

- Profits as Percentage of Assets (aka Return on Assets or ROA)
- many product priced w/ targeted spread between rate earned and rate credited
- useful to know how much of spread (on avg) retained as profits
- numerator and denominator need ot be in sync
- after-tax solvency earnings <-> solvency reserves
- dist earn <-> solv reserves & req'd cap
- after tax stock earnings <-> solv resv & req'd cap & DAC

- ROA(n) = PVProfit(n) / PV(Assets,n)

- Profits as Percentage of Risk Charges
- Risk charges -attempt to quantify degree of risk inherent in product
- may consist of mortality, lapse and inv components
- simpler: risk charge as % or req'd capital (assuming req'd capital is accurate measurement of risk)

- no std approaches
- PVProfits(n) / PV(risk charges,n)
- attraction: compares profit to risk
- detraction: may be illusion since risk charges somewhat arbitrary
- difficult to explain concept to management

- Risk-Free Rates and Risk Charges
- investors want higher reterns for higher risks
- minimum rate of return for risk free investment
- goal to developing meaningful risk charges - profits net of risk charges earn risk-free rate
- w/ PV based on risk-free rate, PV(Profits) = PV(Risk Charges)
- use industry avg rates of return to establish appropriate level of risk charges
- ensures pricing roughtly in line w/ rest of mkt

- Risk charges -attempt to quantify degree of risk inherent in product
- Accumulated Profit as Percentage of Reserves
- one of earliest profit goals - primarily mutuals
- goal - one generation of PO provides capital to fund next generation
- rarely used (currently) for new products
- sometimes used for setting div scales
- usually after tax solvency earnings and usually after-tax int rates
- AccumProfit(n) = sum(Profit(t)*AccumFactor(t))
- AccumProfitPct(n) = AccumProfit(n) / Res(n) where Res(n) is appropriate reserve

- Breakeven Year
- Policy year when accum profits first turn positive adn remain positive
- more of an indicator or danger signal than profit measure
- Modified Breakeven Year - assume all policies lapse at end of given year, releasing req'd capital and excess reserves inro profit calc
- first yer w/ accum profits (including releases) is modified BE year

- late BE year may be acceptable for mutual
- req'd as part of US Illustration Reg supportability test

- New Business Strain
- Not truly a profit measure
- often evaluated as part of pricing process
- often converted to % 1st yr prem
- coupled w/ prem projections, can easily estimate capital necessary to finance NB

- NBStrain = DistEarn(1) / Prem(1)

Copyright © 2004 Steve Welander.

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