Actuarial Control Cycle 2
Assignment 1
Due 9am Monday 18th October 2021
Abstract
The total number of marks for this assessment is 100 and this assess-
ment contributes 10% towards your total mark in this subject. Please
submit your answers as a single pdf document, including either screen-
shots or output of your spreadsheet calculations which are clearly la-
belled and explained.
Aim
The aim of this assignment is to test your understanding on how the
liability assumptions will impact on the emergence of the annual profits.
The different methods to set liability assumptions are covered in Chapter
12 of the textbook, mainly in section 12.4. Whilst Profit is covered later in
the textbook, Chapter 12 uses profit signatures to illustrate the impacts of
changing the liability assumptions. Profit-testing methods were covered
in the Contingencies subject.
The first stage is to set up a profit-testing projection, ignoring liabili-
ties. For the subsequent stages, liabilities need to be calculated and then
included within the profit-testing projections.
The details are as follows:
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Policy Details
Policy Type Non-Profit Endowment
Term 20 years
Benefits Death benefit, surrender value and maturity value
Sum Insured $500,000 (payable at maturity or on earlier death)
Premium Frequency Annual in advance
Premiums $47,500 pa
Surrender Value At the discretion of the insurance company. Assume
payable at the end of each year. Assume that each sur-
render value is the value of premiums paid, without in-
terest. As a result, the surrender value payable at the
end of Year 1 is $47,500
Expense Assumptions
Item Assumption
Initial Expenses $1,000
Renewal Expenses $100 pa in Year 1, increasing subsequently with CPI
Initial Commission Rate 25% of annual premium
Initial Commission Period 24 months
Renewal Commission Rate 2% of annual premium
Financial Assumptions for the Main Profit
Testing Cashflows
Item Assumption
Risk Discount Rate 5% pa
Investment Return on Assets 2.5% pa
CPI 1.5% pa
2
Demographic Assumptions for the Main Profit
Testing Cashflows
Item Assumption
Mortality (Year 1) 0.25% pa
Mortality (Year 2 onwards) 0.25% pa increased at 10% pa, so the Year 2 rate is
0.275% pa
Lapse Rate (Year 1) 10% pa
Lapse Rate (Year 2 onwards) 5% pa
Financial Assumptions to Calculate Liabil-
ities
Item Assumption
Investment Return 2.5% pa
CPI 1.5% pa
Demographic Assumptions to Calculate Li-
abilities
Item Assumption
Mortality (Year 1) 0.25% pa
Mortality (Year 2 onwards) 0.25% pa increased at 10% pa, so the Year 2 rate is
0.275% pa
Lapse Rate (Year 1) 10% pa
Lapse Rate (Year 2 onwards) 5% pa
Question 1 (20 Marks)
Produce a cashflow projection of income and outgo for the whole policy
term, including a net present value of future profits. Ignore the impact
of liabilities within these calculations. Furthermore, provide an explana-
tion of how you have performed your calculations, including any relevant
mathematical formulas.
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Question 2 (20 Marks)
Calculate the liabilities under the following liability assumptions:
(i) Best Estimate Liabilities (BEL);
(ii) Best Estimate Liabilities (BEL) + 10% expenses;
(iii) A “cautious” set of liability assumptions by reducing the Investment
Return to calculate liabilities from 2.5% pa to 2% pa, holding the
Investment Return for the main Profit Testing cashflows at 2.5%
pa.;
(iv) Margin on Services, assuming that death claims are the profit car-
rier; and
(v) Margin on Services, assuming that expenses are the profit carrier.
For each of the liability assumptions, provide an explanation of how
you have performed your calculations, including any mathematical for-
mulas.
Question 3 (20 Marks)
For each of the liability calculations as listed in Question 2:
(i) Produce the annual profits and net present value of future profits;
(ii) Provide an explanation of how you have performed your calcula-
tions in Part (i).
Question 4 (40 Marks)
For each of the liability calculations as listed in Question 2:
(i) Test whether you can achieve a similar pattern of liabilities by re-
ducing only the Investment Return to calculate liabilities, keeping
that assumed Investment Return at a positive rate;
(ii) Explain how the liability calculation method works (i.e. explain for
each of BEL, BEL + 10%, “cautious” and Margin on Services);
(iii) Explain the consequent impacts on the timing of future profits and
the net present value of future profits.
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