Life Insurance and Annuities
 Terminology
 Types of life insurance products
 Tax treatment of life insurance
 Term insurance
 Endowment insurance
 Whole life insurance
 Universal insurance
 Variable insurance
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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)

Cash surrender value = the amount of money that the
policyholder can withdraw (=cash value - surrender
penalty)
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Life Insurance Products: General
Introduction

Term insurance


pure life insurance
Cash value life insurance





pure life insurance + Savings accumulation
whole life
universal life
variable life
Variable universal life
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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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Term Insurance


Typically provides pure death protection over a
fixed term, usually one year or five years. There is
no savings feature and therefore no cash surrender
value.
Data




1/4 of policies
almost half of death protection purchased
Guaranteed renewable
Premium increases over time. Why?
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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%
 Insurer’s cash flows:
Beg. of Year
End of Year
$100,000 with prob 0.00302
Loss
$0
with prob. 0.99698
Expected claim cost = ________
Premium = Present value of expected claim cost
= __________
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Pricing 1-Year Term

Find fair premium for $100,000 1-year term for 41
year-old
 Interest rate = 10%
 Insurer’s cash flows:
Beg. of Year
End of Year
-$100,000 with prob ____________
Premium
$0
with prob. ____________
Expected claim cost = ___________
Premium = Present value of expected claim cost
= ____________
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Pricing 1-Year Term
Premium increases as probability of dying increases
Expected Claim Costs

$1,000
$800
$600
$400
$200
$0
35 40 45 50 55 60 65 70 75 80 85 90 95
Age
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Pricing 2-Year Term


Find fair premium for $100,000 2-year term for 40
year-old
Insurer’s claim costs:
Beg. of Year 1
End of Year 1
-$100,000
with prob 0.00302
End of Year 2
-$100,000
with prob x
$0
with prob. 0.99698
$0
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
of People
937723
934891
Age
40
41
Number
of Deaths
2832
3076

Probability of 40 year-old dying in 41st year =_____ = ______
Probability of 40 year-old dying in 42nd year =_____ = ______
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Pricing 2-Year Term
 Single
 Level
premium
Premium
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Endowment Insurance



Pays face amount if the insured dies, or if the
insured survives the policy period
It is similar to a saving account
The US no longer grants tax advantage to
endowment policies unless they have a very long
duration, such as whole life insurance.
Ins301 Chp15 –Part1
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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 – a level premium paid for a 10-year or
20-year period
continuous premium – level premium continue until
the policyholder dies, surrenders the policy, or reaches
the age of 100 (whichever comes first)
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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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Pricing Single Premium Whole Life



Apply same principles used with term insurance
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
Probability of 40
year old dying in
Expected
Present value of
year at left
claim cost
expected claim cost
40
0.003020
$302.00
$302.00/1.05 =
$288
41
0.003280
$328.00
$328.00/1.05 2 =
$298
42
0.003538
$353.80
$353.80/1.05 3 =
$306
43
0.003832
$383.20
$383.20/1.05 4 =
$315
44
0.004133
$413.30
$413.30/1.05 5 =
$324
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
96
0.004032
$403.20
$403.20/1.05 57 =
$25
97
0.003098
$309.80
$309.80/1.05 58 =
$18
98
0.002207
$220.70
$220.70/1.05 59 =
$12
99
0.001147
$114.70
$114.7/1.05 60 =
$6
Age
45
Total
22,373
Ins301 Chp15 –Part1
Single
Premium
20
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 * P
Find P so that PV of premium payments = PV of costs

16.30 * 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
Ins301 Chp15 –Part1
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Comparison of Cash Values in Whole
Life
$100,000
$90,000
C
A
S
h
$80,000
$70,000
$60,000
V
A
L
U
E
S
payments for life
20 Year Payments
Single Premium
$50,000
$40,000
$30,000
$20,000
$10,000
$0
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
Age
Ins301 Chp15 –Part1
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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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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
 Insurer’s 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
Ins301 Chp15 –Part1
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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

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
 policyholder’s premium payments
 insurer’s 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
Cash value
at beginning of period
+
Premium payments
at beginning of period
Mortality charge
at beginning of period
Expense charge
at beginning of period
+
Interest credited
at end of period
=
Cash value
at end of period
Ins301 Chp15 –Part1
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Death Benefit Options with Universal
Life

Level death benefit (as with Whole Life)

Death benefit varies with cash value
Death
benefit
Death
benefit
Cash
value
age
Ins301 Chp15 –Part1
Cash
value
age
29
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, but varies with cash value
Ins301 Chp15 –Part1
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Life Insurance and Annuities (part3)




What is annuities
The purpose of annuity
Classification of annuity
Overview of annuity contracts
Ins301 Chp15 –Part1
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What is Annuity



An annuity is simply a series of periodic payments.
An annuity contract is an insurance policy that
promises to make a series of payments for a fixed
period or over someone’s lifetime
It is typically used as long-term retirement funding
vehicles.
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Two Periods of Annuity

Accumulation period
-- the period when the policyholder pays premiums to
the insurer

Payout period
-- the insurer makes payments to the policyholder
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Purpose of Annuity
 Risk management purpose

Reduce the risk that savings are exhausted before
the annuitant dies
 tax-deferred saving vehicle

Returns earned from these contracts are not taxed
until the insurer distribute them
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Classification of Annuity
 Immediate annuity and deferred annuity


Immediate
Deferred


Flexible premium deferred annuities (FPDAs)
Single premium deferred annuities (SPDAs)
 Fixed annuity and variable annuity


Fixed annuity
Variable annuity
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Overview of Annuity Contracts
Characteristic
Variations
Premium payments
(a) Single premium
(b) Fixed period, level premium up to an advanced age
(c) Flexible premium over time
Annuity benefits begin
(a) Immediately
(b) Deferred
Annuity benefits end
(a) Fixed number of years
(b) Death of one or more individuals
(c) Combination of (a) and (b)
Insurer payments
(a) Fixed
(b) Vary with interest rates, with guaranteed minimum
(c) Vary with returns on stock and bond funds chosen by policyholder
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