Exam formulas Flashcards

1
Q
  1. Capitalization of lost income or Capital Retention Method
    – Gross/before tax
    (Life Insurance Manual – section 11.2.1)
A

Capitalized Value = Annual income before tax / rate of return
before tax

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2
Q
  1. Capitalization of lost income or Capital Retention Method
    – Net/after tax
    (Life Insurance Manual – section 11.2.2.1)
A

Capitalized Value = Annual income after tax / rate of return
after tax
This requires the following additional equation:
a) After tax rate of return = Rate of return x (1 – Tax
Rate)

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3
Q
  1. Capitalization of lost income or Capital Retention Method
    – Gross/before tax with inflation
    (Life Insurance Manual 11.2.2.2)
A

Capitalized Value = Annual income before tax / inflationadjusted rate of return before tax
This requires the following additional equation:
a) Inflation adjusted rate of return before tax = ((1 +
return) / (1 + inflation rate)) - 1

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4
Q
  1. Capitalization of lost income or Capital Retention Method
    – Net/after tax with inflation
    (Life Insurance Manual 11.2.2.3)
A

Capitalized Value = Annual income after tax / inflation adjusted rate of return after tax
This requires the following additional equations:
a) After tax rate of return = Rate of return x (1 – Tax
Rate)
b) Inflation adjusted rate of return a

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5
Q

CAPITAL NEEDS / CAPITAL RETENTION APPROACH

A

Capital Needs = cash needs + capitalized income shortfall
Capitalized income shortfall includes the Capital Drawdown
Method if necessary.
This requires the following additional equations:
a) Cash needs = assets – final expenses – tax liabilities –
debts – estate expenses – emergency fund –
education fund – estate equalization – charitable
bequests
b) Capitalized Income shortfall = (expenses – income) /
investment return
c) Capital Drawdown method = annual income shortfall
x # of year

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6
Q

Basic life:

A

face amount of the policy + extras, as entitled – policy loan
and interest to date of death – outstanding premiums = net
death benefit

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7
Q

Accidental Death Benefit (ADB) rider:

A

face amount x 2 = ADB benefit

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8
Q

Disability

A

((earned income+ unearned income) x 60% - unearned
income )) / 12 = monthly disability income benefit

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9
Q

Residual disability:

A

(pre-disability income – income earned) / pre-disability income
= residual benefit

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10
Q

Group:

A

STD: annual salary x 60% or 66 2/3% / 12 = monthly benefit
LTD: annual salary x 60% (employee-paid premium) or 75%
(employer-paid premium) / 12 = monthly benefit

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11
Q

Single deductible:

A

claim ($) – deductible ($) = reimbursement ($)

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12
Q

Co-insurance:

A

claim ($) x co-insurance (%) = reimbursement ($) e.g. if claim =
$250; coinsurance = 90%; then: $250 x 90% = $225
reimbursement

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13
Q

Deductible + coinsurance

A

claim ($) – deductible ($) = net claim ($) x co-insurance (%) =
reimbursement ($)

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14
Q

Family deductible:

A

claim ($) – (family deductible [$] – single deductible [$] already
paid) = reimbursement ($)

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15
Q

Interest

A

interest income x investor’s marginal tax rate (MTR) = tax on
interest income

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16
Q

Capital gains/loss

A

market value of capital property – cost of capital property =
capital gain or capital loss on capital property

17
Q
  1. Capitalization of lost income
    Question:
    Derek currently earns $8,400 per month before taxes (gross). Assuming a rate of return of 5%, how much insurance does
    Derek need?
A

Solution:
Capitalized value = annual income / rate of return
Capitalized value = ($8,400 × 12 months) / 5%
Capitalized value = 100,800 / .05
Capitalized value = $2,016,000
Answer:
Derek will need $2,016,000 in insurance to provide the amount of capital that would have to be invested at 5% to
replace his income.

18
Q
  1. Capitalization of lost income or Capital Retention Method – after tax
    Question:
    Derek currently earns $6,500 per month after taxes. Assuming a gross rate of return of 5%, how much insurance does
    Derek need if the average after tax rate is 25%?
A

Solution:
Capitalized value = annual income after tax / rate of return after tax
Step 1: calculate the rate of return after tax
After-tax rate of return = rate of return × (1 – tax rate)
After-tax rate of return = 5% x (1-25%)
After-tax rate of return = .05 x (1-.25)
After-tax rate of return = .05 x .75
After-tax rate of return = .0375 or 3.75%
Step 2: apply the after tax rate of return to the equation
Capitalized value = annual income after tax / rate of return after tax
Capitalized value = ($6,500 x 12) / 3.75%
Capitalized value = $78,000 / .0375
Capitalized value = $2,080,000
Answer:
Derek will need $2,080,000 in insurance to provide the amount of capital that would have to be invested at an after tax
rate of 3.75% to replace his income.

19
Q
  1. Capitalization of lost income or Capital Retention Method – Gross/before tax with inflation
    Question:
    If Derek’s gross income of $8,400 increases at a rate of 2% per year and the investment rate of return is 5%, how much
    insurance will Derek need?
A

Solution:
Capitalized Value = Annual income before tax / inflation-adjusted rate of return before tax
Step 1: calculate the inflation adjusted rate of return
Inflation adjusted rate of return = ((1 + return) / (1 + inflation rate)) – 1
Inflation adjusted rate of return = ((1 + 5%) / (1 + 2%)) – 1
Inflation adjusted rate of return = ((1 + .05) / 1 + .02)) – 1
Inflation adjusted rate of return = (1.05 / 1.02) – 1
Inflation adjusted rate of return = 1.029411764706 – 1
Inflation adjusted rate of return = .029411764706 or 2.9411764706%
Step 2: apply the inflation adjusted rate of return to the equation
Capitalized Value = Annual income before tax / inflation-adjusted rate of return before tax
Capitalized Value = ($8,400 x 12) / 2.94%
Capitalized Value = $100,800 / .0294
Capitalized Value = $3,428,571.428571 or $3,428,571
Answer:
Derek will need $3,428,571 in insurance to provide the amount of capital that would have to be invested at an inflation adjusted rate of return before taxes of 5% if his income increases by 2% annually

20
Q
  1. Capitalization of lost income or Capital Retention Method – Net/after tax with inflation
    Question
    Derek currently earns $6,500 per month after taxes. Assuming a gross rate of return of 5%, a tax rate of 25% and
    inflation of 2%, how much insurance does Derek require?
A

Solution:
Step 1: calculate the after tax rate of return
After-tax rate of return = rate of return × (1 – tax rate)
After-tax rate of return = 5% x (1-25%)
After-tax rate of return = .05 x (1-.25)
After-tax rate of return = .05 x .75
After-tax rate of return = .0375 or 3.75%
Step 2: calculate the inflation adjusted rate of return
Inflation adjusted rate of return = ((1 + return) / (1 + inflation rate)) – 1
Inflation adjusted rate of return = ((1 + 3.75%) / (1 + 2%)) – 1
Inflation adjusted rate of return = ((1 + .0375) / 1 + .02)) – 1
Inflation adjusted rate of return = (1.0375 / 1.02) – 1
Inflation adjusted rate of return = 1.017156862745 – 1
Inflation adjusted rate of return = .0171568627451 or 1.72%
Step 3: apply the inflation adjusted after tax rate of return to the equation
Capitalized Value = Annual income after tax / inflation-adjusted rate of return after tax
Capitalized Value = $6,500 x 12 / 1.72%
Capitalized Value = $78,000 / .0172
Capitalized Value = $4,534,883.720930 or $4,534,884
Answer:
Derek will need $4,534,884in insurance to provide the amount of capital that would have to be invested at an inflation adjusted after tax rate of return of 5% if his income increases by 2% annually.

21
Q

CAPITAL NEEDS / CAPITAL RETENTION APPROACH
1. Capitalization of Income Shortfall
Question:
Derek and Becky are a married couple with three children.
Becky does not currently work, and she does not expect to return to work for at least 6 years, at which time she believes
that her take-home pay would be about $4,500 per month. However, Derek would feel better if he knew that she could
manage the household financially without working until their son turns 18. Neither of them currently earns investment
or pension income.
If Derek dies, Becky would be eligible for a Canada Pension Plan (CPP) survivor benefit of about $570 per month, and all
three of the children would be eligible for a CPP benefit of about $230 per month as children of a deceased CPP
contributor.
Derek wants to ignore any potential benefits his family could receive under his province’s Workers’ Compensation
Board, because there is no guarantee that his death will be work-related.
Derek’s non-registered investment portfolio currently produces after-tax income of $7,200 annually, but because these
assets may be needed to meet estate expenses, this income is not being included at this point.
If Derek were to die Beckey would have a monthly income of $1,260 (CPP would provide $570 for Becky and $230 for
each child) and monthly expenses of $4,150. If the after tax inflation adjusted rate of return is 1.71% what is the
capitalized income shortfall? In other words, how much insurance does Derek need to make up for this income
shortfall?

A

Solution:
Capitalization of Shortfall = (Annual Expenses – income) / investment return
Step 1: calculate the income shortfall
Income Shortfall = Annual expenses – income
Income Shortfall = ($4,150 x 12) – ($1,260 x 12)
Income Shortfall = $49,800 - $15,120
Income Shortfall = $34,600
Step 2: apply shortfall to the equation
Capitalization of Shortfall = (Annual Expenses – income) / investment return
Capitalization of Shortfall = $34,680 / 1.71%
Capitalization of Shortfall = $34,680 / .0171
Capitalization of Shortfall = $2,028,070.175439 or $2,028,070
Answer:
Derek will need $2,028,070 in insurance coverage to replace his income

22
Q
  1. Capital Drawdown Method
    Question:
    Derek and Becky’s child named Robbie has just been born. Derek would prefer that Becky not have to work until Robbie
    is 18 years old. At that time, she could find work and likely take home enough money to cover all of her expenses. Using
    the capital drawdown method and an income shortfall of $34,680, how much is the capitalized value of the family’s
    income shortfall?
A

Solution:
Capital Drawdown = annual income shortfall x # of years
Capital Drawdown = $34,680 x 18
Capital Drawdown = $624,240
Answer:
Derek will need insurance in the amount of $624,240 to cover the family’s income shortfall for 18 years.