A life insurance company issues a 10-year unit-linked endowment assurance policy to a person currently aged exactly 55, that offers the following benefits: • on death, the higher of the unit fund value and 10,000 • on maturity, the unit fund value, plus a bonus of 0%, 3%, or 5% of the unit fund value, chosen by the policyholder at outset. The death benefits are payable at the end of the policy year of death, based on unit fund values at the end of the year of death, after deduction of all charges. Surrenders are not permitted. Premiums of 1,000 are payable annually in advance throughout the term of the policy or until earlier death. The basic policy information and charging structure (ie allocation rates, bid-offer spread and fund management charge) are given in the 'Q2 Policy info & basis' sheet, along with the basis used by the company to calculate any non-unit reserves required and to profit test the policy. The company sets up non-unit reserves at the start of each year in order to zeroise any negative expected cashflows, apart from at the start of the first year where the non-unit reserve is assumed to be zero. Negative non-unit reserves are not permitted. The company's profit criterion is that the net present value of the policy's cashflows, calculated at the risk discount rate, should be equal to 20% of the annual premium. Consider a policy with a 3% maturity bonus and an allocation rate of 50% in the first policy year. (i) (ii) Calculate the non-unit cashflows on this policy.

To calculate the non-unit cashflows for this policy, we need to break down the information given and apply the relevant principles. The non-unit cashflows represent the profits or losses the insurance company experiences, excluding the investment fund's value (which is the unit fund). These cashflows typically involve premium income, expenses, charges, and benefit payments.

### 1. **Understanding the Policy Structure:**
- **Policy Term**: 10 years
- **Age of Policyholder at Start**: 55 years
- **Annual Premium**: £1,000, payable in advance
- **Death Benefit**: Higher of the unit fund value and £10,000
- **Maturity Benefit**: Unit fund value plus a 3% bonus (as selected)
- **Allocation Rate in the First Year**: 50% (meaning 50% of the first premium is used to purchase units)
- **No Surrenders Permitted**: This means the policyholder cannot terminate the policy early to receive the fund value.
- **Non-Unit Reserves**: Set up at the start of each year to zeroize any negative expected cashflows, except for the first year.

### 2. **Steps to Calculate Non-Unit Cashflows:**
   - **Premium Income**: The insurance company receives £1,000 at the start of each policy year.
   - **Expenses and Charges**: These would typically include initial and renewal expenses, fund management charges, and any mortality charges deducted from the premium or fund.
   - **Death Benefits**: Payable at the end of the policy year in which the death occurs.
   - **Non-Unit Reserve**: Set up to cover any expected negative cashflows in the following year.
   - **Maturity Benefit**: At the end of the 10 years, the maturity benefit is paid.

### 3. **Non-Unit Cashflows Calculation:**
   - **First Year**:
     - **Premium Received**: £1,000
     - **Allocated to Units**: 50% of £1,000 = £500 (This is not part of non-unit cashflows)
     - **Expenses and Charges**: (Assume any given values or percentages from the policy info)
     - **Death Benefit**: Not applicable if no death occurs.
     - **Non-Unit Reserve**: Start of year 2 reserve to zeroize any expected negative cashflows.
   - **Subsequent Years**: For years 2 to 10, the calculation involves a similar process but with a different allocation rate (assumed 100% unless otherwise stated), consideration of charges, and any non-unit reserve adjustments.
   - **Maturity Year**: Consider the payout of the unit fund value plus a 3% bonus.

Given that we need more specific details (e.g., expenses, charges, mortality rates, allocation rates for subsequent years), the precise calculation would require those inputs.

However, in principle, the non-unit cashflows for each year would be computed as:

\[
\text{Non-unit cashflow} = \text{Premium income} - \text{Expenses and charges} - \text{Death benefits} + \text{Non-unit reserve released (if any)}
\]

This calculation would be repeated for each year, with the appropriate values plugged in, and the non-unit reserves adjusted to ensure no negative cashflows for the subsequent year.

Would you like to proceed with a specific part of this process or need further details? 

Here are five related questions to explore further:
1. How do non-unit reserves impact the insurer's profit over time?
2. What factors would influence the calculation of the expected negative cashflows?
3. How does the allocation rate in the first year affect the policy’s profitability?
4. How is the risk discount rate applied in profit testing?
5. How do different maturity bonuses (0%, 3%, 5%) influence the non-unit cashflows?

**Tip:** When calculating non-unit cashflows, it's crucial to understand the timing of cashflows and how reserves are set up to cover potential shortfalls, especially in insurance policies with varying benefits and charges.

Learn how to calculate non-unit cashflows for a 10-year unit-linked endowment assurance policy with a detailed breakdown. This problem involves actuarial science principles, insurance policy analysis, and cash flow modeling. Suitable for professionals and students studying insurance and financial analysis.

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