Life Insurance and Annuities

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Chapter 15

• Life Insurance and Annuities

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Product Overview

• Term
• Pure life insurance
• Cash value policies
• Pure life insurance Savings accumulation
• Examples
• whole life
• universal life
• variable life

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Product Overview

• Can obtain savings accumulation by surrendering
  the policy
• Why bundle death protection savings
  accumulation?
• Tax advantaged method of saving

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Terminology

• Death benefit amount beneficiaries receive
• Cash value amount of savings accumulation
• Death protection amount of pure death
  protection
• death benefit - cash value
• Face amount stated amount of coverage
• death benefit (for term, whole life, some
  universal life)
• death benefit - cash value (for some universal
  life)

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Term Insurance

• Data
• 1/4 of policies
• almost half of death protection purchased
• Guaranteed renewable
• Premium increases over time

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Endowment Insurance

• Pays face amount
• if the insured dies
• or
• if the insured survives the policy period

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Whole Life Insurance

• Policy period ends when insured reaches 100
• Equivalent to endowment policy to 100
• Premiums
• single premium
• limited pay
• continuous premium

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Whole Life Insurance

• Premiums generally do not increase over time
• But probability of dying increases over time
• higher upfront premiums than with term
• Policyholder prepays part of the cost of future
  death protection
• entitled to prepayments if policy is surrendered
• this is the cash value (savings accumulation)

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Whole Life Insurance

• If insured dies,
• beneficiaries receive face amount
• death protection cash value
• Structured so
• cash value ? over time
• death protection ? over time

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Whole Life Insurance
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Participating Policies

• Can (and usually does) pay annual dividends
• always with mutual companies
• often with stock companies
• Why? - premiums based on conservative assumptions
• Key assumptions interest rate levels and
  mortality rates
• These variables are correlated across
  policyholders
• Insurers methods of dealing with correlated
  risk
• Bear the correlated risk and hold a lot of
  capital
• Share correlated risk with policyholders
• Illustrated versus actual dividends

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Other Whole Life Policy Provisions

• Surrender Options
• Take cash value
• Use cash value as a single premium for
• paid up whole life
• term policy
• Policy loans
• borrow against cash value
• interest now varies with market rates
• in 1970s 80s, fixed rate disintermediation

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Expense Loadings

• Front-end expense charges
• Cash value grows slowly at first
• Implicit return on savings accumulation
• initially low

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Universal Life

• Similar to whole life
• Main differences
• Greater flexibility in premium payments
• Cash value does not follow a fixed schedule it
  varies with
• policyholders premium payments
• insurers expense and mortality charges
• rate insurer uses to credit interest to cash
  value
• minimum rate usually guaranteed
• rate often linked to short term interest rates

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Factors Affecting UL Cash Value
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Death Benefit Options with UL

• Level death benefit (as with WL)
• Death benefit varies with cash value

Death benefit
Death benefit
Cash value
Cash value
age
age
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Variable Life

• Similar to whole life
• Main differences
• Cash value does not follow a fixed schedule it
  varies with
• return earned on portfolio of mutual funds chosen
  by policyholder
• Death benefit
• minimum is guaranteed,
• varies with cash value

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Tax Treatment of Life Insurance

• Death benefits are not taxed
• Income tax is not paid on increases in cash value
  while the policy is in force
• Upon surrender, income tax is paid on
• Cash surrender value - sum of all premiums
• sum of all policyholder dividends

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Implications of Tax Treatment

• Implicit returns on savings accumulation
• Escape taxation if insured dies
• Tax deferred if the policy is surrendered
• Partially taxed if policy is surrendered
• Amount which is taxed is less than implicit
  return b/c part of premiums is cost of death
  protection

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Annuity Contracts

• Large and growing part of life insurance business
• Divide contract period in two
• Accumulation period
• Policyholder pays premiums
• Payout period
• Insurer makes payments

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Use of Annuities

• Risk management perspective
• Protection against outliving resources
• Savings perspective
• Tax advantaged method of saving
• Implicit returns are tax deferred

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Savings Features

• Fixed annuities
• Return credited varies with interest rates
• Variable annuities
• Return credited varies with return on mutual
  funds chosen by contract holder

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Overview of Annuity Contracts
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Life Insurance Pricing

• Ignore expenses and risk load
• focus on net premiums
• Use mortality table
• Probability of dying at age x conditional on
  living through age x-1
• Example Probability of male dying at age 40
  0.00302
• Assume
• Premiums paid at beginning of year
• Claims paid at end of year

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Pricing 1-Year Term

• Find fair premium for 100,000 1-year term for 40
  year-old
• Interest rate 10
• Insurers cash flows
• Beg. of Year End of Year
• -100,000 with
  prob 0.00302
• Premium
• 0
  with prob. 0.99698
• Premium Present value of expected claim cost
• 302 / 1.1 275

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Pricing 1-Year Term

• Find fair premium for 100,000 1-year term for 41
  year-old
• Interest rate 10
• Insurers cash flows
• Beg. of Year End of Year
• -100,000 with
  prob 0.00329
• Premium
• 0
  with prob. 0.99671
• Premium Present value of expected claim cost
• 329 / 1.1 299

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Pricing 1-Year Term

• Premium increases as probability of dying
  increases

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Pricing 2-Year Term

• Find fair premium for 100,000 2-year term for 40
  year-old
• Insurers claim costs
• Beg. of Year 1 End of Year 1 End of Year 2
• -100,000 -100,000
• with prob 0.00302 with prob x
• 0 0
• with prob. 0.99698 with prob 1-x

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Pricing 2-Year Term

• What is x? it is the probability of a 40
  year-old dying in his 42nd year?
• Mortality table
• Number Number
• Age of People of Deaths
• 40 937723 2832
• 41 934891 3076
• Probability of 40 year-old dying in 41st year
  0.00302
• Probability of 40 year-old dying in 42nd year
  0.00328

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Pricing 2-Year Term

• Single premium
• Insurers expected cash flows
• Beg. of Year End of Year 1 End of Year 2
• Premium -302 -328
• Premium PV of expected claim costs
• 302 / 1.1 328 / 1.12
• 275 271 546

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Pricing 2-Year Term

• Level Premium
• same premium paid at beginning of each year (if
  insured survives)
• Insurers expected cash flows
• Beg. of Year End of Year 1 End of Year 2
• Premium Premium x 0.99698
• -302 -328
• Find Premium so that PV of expected premiums
  PV of expected claims

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Pricing 2-Year Term

• Premium (1 0.99698/1.1) 546
• Premium 286.41
• Note
• 286.41 1/2 of single premium (546)
• Why?
• Chance second premium payment will not be made
• Second premium is discounted b/c of time value of
  money

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A Comparison

• Expected costs of three alternative methods of
  obtaining coverage

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Implications

• Annual premiums for successive term policies
  reflect the annual cost of insuring
• Annual cost 275 and 298
• With 2-year policy,
• premium in year 1 275
• premium in year 2
• With this example, size of difference is small
• With whole life policies (UL, VL)
• difference can be large
• gives rise to cash value

Essentially, pre-funding costs
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Pricing Immediate Annuities

• Example Find single premium for a 5,000 life
  annuity for a 95-year-old
• Assume person dies by age 100
• Interest rate 10
• Premium PV of expected payments to annuitant
  4,530
• Probability Expected PV of
• of 96-year- Payment Expected
• Age old surviving 5,000 x prob Payment
• 97 6050/9831 3077 3,077 / 1.1 2,797
• 98 3145/9831 1,600 1,322 / 1.12 1,322
• 99 1076/9831 547 547/ 1.13 411
• 100 0 0 0

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Pricing Single Premium Whole Life

• Apply same principles used with term
• Forecast expected cash flows to age 100
• Find single premium
• PV of expected cost
• Assume
• no expenses or profits
• 5 interest rate
• policy will not lapse

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Pricing Single Premium Whole Life
Single Premium
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Continuous Level Premium Whole Life

• Continuous level premium
• Same premium is paid until insured dies or
  reaches 100
• Equivalent to a life annuity
• Present value of a life annuity that pays P
  starting at age 40 16.30 x P
• Find P so that PV of premium payments PV of
  costs
• 16.30 x P 22,373 P 1,372.58

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Limited Payment Whole Life

• Limited payment level premium
• Same premium is paid for fixed number of years
• Example 20 years
• Equivalent to a 20 year annuity
• Present value of a 20-year annuity that pays P
  starting at age 40 12.58 x P
• Find P so that PV of premium payments PV of
  costs
• 12.58 x P 22,373 P 1,778.45

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Comparison of Cash Values in Whole Life
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How Much Life Insurance Should be Purchased?

• Rules of thumb
• Death benefit 8 times income
• Forecast beneficiaries sources uses of funds
• Uses
• Living expenses
• Education expenses
• Sources
• Social security
• Earnings

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Term Insurance Cost Comparisons

• Adjusted cost index
• Idea calculate accumulated future value of all
  costs
• Procedure
• accumulate premiums (P) per 1,000 of coverage
• less policyholder dividends (D)
• for 20 years
• at a 5 interest rate

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Whole Life Cost Comparisons

• One approach use adjusted cost index again
• but subtract cash value (CV) at end of 20 years
• AC20 AC20 - CV20
• In practice adjust cost indices are scaled to get
  interest adjusted cost (IAC)
• Another approach calculate implicit rate of
  return

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Universal Life Cost Comparisons

• More complex
• One approach
• Use interest adjusted cost index subtracting an
  estimate of cash value
• under common assumptions(across policies being
  compared) about premiums and interest rates
• No consensus exists