Life Insurance Products and Financing (Atkinson/Dallas) - Chapter 11

Life Insurance Products and Financing (Atkinson/Dallas) - Chapter 11 - PROFIT MEASUREMENT AND ANALYSIS

Distributable Earnings

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

Stockholder Earnings

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)

After-Tax Stockholder 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

Return on Equity (ROE)

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

Selection of Profit Goals

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
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

Present Value

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
next
PVFP(n) = PVFP(0)
if n = 1, Profit(0) = 0

Profit Measures

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)
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
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)

Sample Problems - text p

Copyright © 2004 Steve Welander.
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