Chapter 3 Cash Flow Analysis of Commercial endowment insurance

Document directory

• 3.2.1 Product Structure Analysis
• 3.2.2 product Cash Flow Model
• 3.2.3 product cash flow Scenario Analysis
• 3.3.1insureoutflowpv Function
• 3.3.1insureinflowpv Function

Chapter 3 Cash Flow Analysis of Commercial endowment insurance

I am writing one of the chapters in my book recently. I hope readers can provide different opinions for discussion.

Currently, China's pension insurance consists of three parts:

1. Basic Endowment Insurance: a social insurance system established and implemented by the State forcibly according to laws and regulations. In this system, employers and workers must pay endowment insurance premiums in accordance with the law. After a worker retires at the retirement age specified by the State or withdraws from the job for other reasons, social insurance agencies should pay their pensions and other benefits in accordance with the law to ensure their basic life. Basic endowment insurance and unemployment insurance, basic medical insurance, work injury insurance, maternity insurance and so on constitute a modern social insurance system, and is one of the most important types of insurance in the social insurance system.

2. Supplementary Pension Insurance for enterprises (enterprise annuities): the enterprise annuities come from countries with relatively developed free-market economies and are a voluntary employee welfare plan established by employers. Enterprise annuities are pensions provided by the enterprise pension plan. The essence is the part of the employee's labor remuneration that exists in the deferred payment method or the part of the employee's share of the enterprise's profit.

3. Commercial endowment insurance: personal endowment insurance is a form of endowment insurance that employees voluntarily participate in based on their income. Personal savings pension insurance is voluntarily selected by individual employees and owned by individuals and savings pension insurance funds. The implementation of personal savings pension insurance for Commercial endowment insurance is based on the insurance products provided by insurance companies or self-saving.

The payment ability of basic endowment insurance is protected by national financial support. The income of supplementary endowment insurance is affected by the investment income of enterprises. The cash flow of commercial endowment insurance is basically determined according to the insurance product specification, you can use quantitative analysis to analyze it. Therefore, this chapter uses commercial pension insurance as the main object for quantitative analysis.

3.1 cases of commercial endowment insurance

This chapter uses case studies to analyze the cash flow of commercial pension insurance. The following is an example of a company's pension insurance (product ):

For a 30-year-old male, the insurance product A is paid for within 10 years. The basic insurance amount is RMB 0.1 million. The 60-Year-Old warranty will be received on the anniversary day, and will be collected on a yearly basis. As long as the insured survive, you can continue to receive the 100-Year-Old warranty.

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Premium:

The annual premium is 15940 RMB.

 

Basic insurance benefits:

1. Pension Insurance: from the age of 60, you can receive the pension insurance on the annual warranty anniversary until the warranty Anniversary of the age of 100.

For the survival of the insured, you can receive the Pension Insurance Fund as follows:

 

 

Number of recipients	1-3 times	4-6 times	......	40-41 times
Amount received	10000 RMB/Time	10600 RMB/Time	For each 3 times of receipt, the increase is based on 0.6% of the insurance amount, and so on.	17800 RMB/Time

Table: 3.1

2. During the 20-year warranty period, if the insured dies, the amount to be received is 234200 yuan minus the amount already received;

3. Zhu shoujin: The 0.1 million Yuan Zhu shoujin will be received on the anniversary day of the policyholder's survival to the Age of 88;

4. death Insurance: the death of the insured before the anniversary of the 60-Year-Old insurance policy, based on the sum of the premium and 0.1 million yuan, and the cash value of the current primary insurance contract (excluding the relevant benefits arising from dividend distribution) larger users receive death insurance.

 

Product dividend:

In accordance with the relevant provisions of the Insurance Regulatory Authority, each year, we will determine the dividend distribution based on the actual operating conditions of the dividend insurance business. The dividend is uncertain. If we determine a dividend distribution, the dividend will be distributed to you on the warranty anniversary day.

3.2 case analysis 3.2.1 Product Structure Analysis

Cash flow is a summary of the cash expenditure and income of an individual or an enterprise. Commercial endowment insurance is essentially a financial product that determines cash flow under certain conditions according to the product manual.

Elements of Commercial endowment insurance products:

1. determine the initial premium expenditure of the policyholder;

2. Determine the late pension income and income of the insured;

3. The insured receives product dividends, and his or her income is uncertain;

4. The additional income of the insured is uncertain, for example, zhushoujin.

3.2.2 product Cash Flow Model

Assume that the ROI of an insurance company is equal to that of the investment cash. In order to make it easier to discount the cash flow of the product to the age of 30, the income is uncertain due to the dividend of the person who receives the product, and the product dividend is assumed to be zero.

Model Creation:

1. Set the discount interest rate (the ROI of insurance companies) to R;

2. the warranty period is from X: 30 ~ 100 years old;

3. The current INPV (x, R) and INPV (x, R) of the policyholder are functions of R and X;

4. Functions of outpv (x, R) and INPV (x, R) as R and X in the current income value of the insured.

3.2.3 product cash flow Scenario Analysis

Situation analysis based on X in the death period of the insured

1. If X is greater than 30 and less than or equal to 40:

Cash expenditure is the premium expenditure outcf of the X-30;

Cash income is the sum of the premium and 0.1 million yuan and the cash value of the Active Risk contract at the time of death (excluding the relevant benefits arising from dividend distribution, max (sum (outcf) + 10, PV (outcf )).

 

2. If X is greater than 40 and less than 60:

The cash expenditure is 10 times of premium expenditure outcf;

Cash income is the sum of the premium and 0.1 million yuan and the cash value of the Active Risk contract at the time of death (excluding the relevant benefits arising from dividend distribution, max (sum (outcf) + 10, PV (outcf )).

3. If X is greater than or equal to 60 and less than 80:

The cash expenditure is 10 times of premium expenditure outcf;

Cash income is the product annuities of X-60, plus 234200-sum (incf ).

 

4. If X is greater than or equal to 80 and less than 88:

The cash expenditure is 10 times of premium expenditure outcf;

Cash income is the product annuities of X-60.

 

5. If X is greater than or equal to 88 and less than 100:

The cash expenditure is 10 times of premium expenditure outcf;

Cash income for X-60 product annuities incf, plus 88 years of age to receive 0.1 million yuan

 

Eye-catching: in the above cases, the time value varies depending on the time of cash inflow or outflow. For example, the price of RMB 15940 at the end of the last 30 years (at the beginning of the 31 years) is different from that at the end of the 35 years (at the beginning of the 36 years) the value of 15940 yuan is different. The current cash flow calculation must consider the time value of the currency.

3.3 case programming computing 3.3.1insureoutflowpv Function

Compile the insureoutflowpv file based on the analysis of the current value of the policyholder's premium expenditure in function compute.

Pv = insureoutflowpv (startpayage, endpayage, deadage, outpayment, rate)

Input parameters:

Startpayage: the start age of the premium fee. In this case, the value is 30.

Endpayage: the end age of the premium expenditure. In this case, the value is 40.

Deadage: age of the insured

Outpayment: premium expenditure amount

Rate: Premium discount rate

Output function:

PV: current value of the policyholder's premium expenditure

 

Function source code:

Function Pv = insureoutflowpv (startpayage, endpayage, deadage, outpayment, rate)

% Code by ariszheng@gmail.com

% 2009-6-16

If deadage <startpayage

Error ('destage must bigger than startpayage ')

Elseif deadage <endpayage

Pv = pvfix (rate, deadage-startpayage, outpayment );

Else

Pv = pvfix (rate, endpayage-startpayage, outpayment );

End

Procedure Note: based on the terms of the product, the premium fee is divided into two types. When the death age of the insured is greater than 30 and less than or equal to 40, the death age of the insured is greater than 40.

 

3.3.1insureinflowpv Function

Compile the insureinflowpv file based on the analysis of the current value of the insured's premium income using function compute.

Pv = insureinflowpv (startpayage, deadage, outpayment, rate)

Input parameters:

Startpayage: the start age of the premium fee. In this case, the value is 30.

Deadage: age of the insured

Outpayment: premium expenditure amount

Rate: Premium discount rate

Output function:

PV: current value of the insured's premium income

 

Function source code:

Function Pv = insureinflowpv (startpayage, deadage, outpayment, rate)

% Code by ariszheng@gmail.com

% 2009-6-15

% Inpayment Vector

Temppay = 1:0. 06. 78;

Temppay = repmat (temppay, 3, 1 );

Tempay = reshape (temppay, 1, 42 );

Inpayment = zeros (1,100 );

Inpayment (60: 100) = 1e4 * tempay );

%

If deadage <startpayage

Error ('destage must bigger than startpayage ')

Elseif startpayage <deadage & deadage <= 40

Pv = max (deadage-startpayage) * outpayment + 1e5)/(1 + rate) ^ (deadage-startpayage ),...

Pvfix (rate, deadage-startpayage, outpayment ));

Elseif 40 <deadage & deadage <60

Pv = max (10 * outpayment + 1e5)/(1 + rate) ^ (deadage-startpayage ),...

Pvfix (rate, 10, outpayment ));

Elseif 60 <= deadage & deadage <80

Pv = pvvar (inpayment (60: deadage), rate)/(1 + rate) ^ 30 +...

Max (0, (234200-sum (inpayment (60: deadage)/(1 + rate) ^ (DeadAge-30 );

Elseif 80 <= deadage & deadage <88

Pv = pvvar (inpayment (60: deadage), rate)/(1 + rate) ^ 30;

Else

Pv = pvvar (inpayment (60: deadage), rate)/(1 + rate) ^ 30 + 1e5/(1 + rate) ^ 58;

End

Program Note: For repmat and reshape functions in the program, please refer to help + function name and divide the premium expenditure into five situations according to product terms. If the age of the insured is greater than 30 or equal to 40, when the person's death age is greater than 40 and less than 60, when the person's death age is greater than or equal to 60 and 80, when the person's death age is greater than or equal to 80 and 88, the person's death age is greater than or equal to 88.

 

3.4 Case Numerical Analysis

Because the term of commercial pension insurance products is several decades and the compound interest discount method used in the case analysis, the current cash flow value of the products is extremely sensitive to the discount rate.

Assuming that the discount rate is 3%, the analysis program r3test. m

Startpayage = 30;

Endpayage = 40;

Outpayment = 15940;

Rate = 0.03;

Deadage = 41;

% Pv = insureoutflowpv (startpayage, endpayage, deadage, outpayment, rate)

%

% Deadage = [35,45, 61,75, 89,95];

Deadage = 31: 100;

PVI = zeros (1, length (deadage ));

PVO = zeros (1, length (deadage ));

For I = 1: length (deadage)

PVI (I) = insureinflowpv (startpayage, deadage (I), outpayment, rate );

PVO (I) = insureoutflowpv (startpayage, endpayage, deadage (I), outpayment, rate)

End

Plot (31: 100, PVI, '-*', 31: 100, PVO, '-O ')

Legend ('insuinflowpv', 'insureoutflowpv ')

 

Result image:

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Fig 3.2

Assume that the discount rate is 2%:

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Fig 3.3

3.5 case analysis results

If the discount rate is 3%, the relationship between the current value of the policyholder's premium expenditure and the current value of the insured's premium income is shown in Figure 3.2, and the discount rate is 2%, figure 3.3 shows the relationship between the current value of the policyholder's premium expenditure and the current value of the insured's premium income.

From Figure 3.2, we can see that if the insured died between the age of 60 and the age of 88, then, the present value of the net income of the policyholder and the insured (current value of net income = current value of the insured's premium income-current value of the policyholder's premium expenditure) is negative, as shown in Figure 3.3, if the same insurer died between the ages of 60 and 88, the present value of net income between the policyholder and the insured is negative.

The essence of insurance is to spread risks without extra excess profits. As a management and sales organization for Commercial endowment insurance, insurance companies are risk-neutral and management fee income requirements. The risks of insurance products must be distributed among policyholders. With a certain discount rate, the current net income of investors who buy pension insurance is zero. Therefore, some investors who buy pension insurance must have a negative net income value.

The cash flow chart 3.1 provided by insurance companies did not take into account the time value of cash. From a simple computing analysis, during the 10-year period, the company paid 15940 yuan a year, totaling 159400 yuan, assume that you get 10000 yuan a year from the age of 60, you can get 75 years old. If we consider the periodic table of human life, we expect a high mortality rate around 75 years old.

When selecting an insurance product, you can compare the net cash flow of similar products of the same product with different insurance ages or different companies, and select the product with the maximum net income value.

Note: contract agreements for major illness insurance and medical insurance of insurance companies are more complex, resulting in complicated cash flow of insurance products.