# Two dimensions of pure risk

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2 How much life insurance does one need? There are two approaches to determine the amount life insurance needed The income approach (also called the replacement income approach ): This approach calculates the life insurance face value amount as the investment funds necessary to replace the insured s future income that is not replaced by other sources income such as Social Security Survivor s benefits. The expense approach (also called the need approach ): This approach computes the life insurance face value needed to pay for the expected expenses the beneficiaries that won t be covered by other sources income. The Approach to Life Insurance Needs An example is used to illustrate this approach. John Doe, age 43, earns \$70,000 annually and expects to receive pay raises 2% per year after inflation. John has three financial dependents: his wife Jan and two children, 12 and 10. From his annual Social Security statement, John finds out that Social Security will pay \$3000 a month to his wife and children when both children are under the age 18, \$2500 a month when one child is under 18, and 0 when both children are 18. The Doe family has \$10,000 in savings which will be applied to replace some John s future income. John wants a life insurance face value amount which will replace 80% his future real income until the youngest child reaches the age Step 1. Decide on the number years income replacement is needed. A common possibility is to insure until the youngest child is out school, either 18 or 22. This number is called life insurance term. In this example, the younger child is 10, so the life insurance term should be 8 years (18-10). Step 2. For each year the life insurance term, write down the insured s real income. Multiply the real income by the percentage income to be replaced. In this example, John s income is expected to increase by 2% per year in real terms (about 5% per year in nominal terms, minus a 3% expected inflation rate). The table income is illustrated on the right. 80% income = 80% * 80% Step 3. Social Security Benefits: For each year the life insurance term, write down the Social Security survivorship benefit. SS adjusts for inflation. The first 6 years benefits are higher because both children are under 18. Step 4. real income: Subtract the SS survivorship benefit from the replacement income for each year. Also subtract any other income (such as pension). In this example we assume no income from other sources. real income = 80% income SS benefit 80% SS Benefit % SS Benefit Step 5. Use a real discount rate, such as 3%, to calculate the present value the net real income. PV net real income = net real income /(1+r)^n E.g., for year 8, PV 34336=34326/[(1+3%)^8]= Step 6. Add up all the PVs, and then subtract family savings. The end result is the life insurance face value amount. In this example, the sum all PV net real income is 177,361. The family already has \$10,000 savings. So the PV income needs is \$167,361. PV 80% SS Benefit PV 80% SS Benefit sum Minus savings Life Insurance Needed = The Expense Approach to Life Insurance Needs This approach uses a 6-step process to compute life insurance needs based on the future net expenses the beneficiaries. We will use the same example John Doe s family. 12 2

3 Step 1. Decide on the number years for which family expenses will be covered by life insurance. In this example the life insurance term is still 8 years. Assume after the children are 18, Jane will go to work again and support herself. The children will be financially independent. Step 2. For each year the term, list the annual expenses, include expenses for children, housing, etc. In this case, assume it will be \$50,000 for the first year, and will increase at 5% per year in real terms. Typically expenses increase in real terms as kids get older, and as society gets more affluent in general Step 3. Write down the Social Security Survivors benefits for each year. This column is the same as in the income approach. Step 4. expenses: For each year the life insurance term, subtract Social Security Survivors benefit. E.g. For year #8, expenses = = SS Benefit SS Benefit Step 5. Use a real discount rate, such as 3%, to calculate the present value the net annual expenses. PV net annual = net expenses /(1+r)^n E.g., for year 8, PV 40355=40355/[(1+3%)^8]= Step 6. Add up all the PVs annual expenses, and then subtract family savings. The end result is the life insurance face value amount. In this example, the sum all PV net annual expenses is 172,699. The family already has \$10,000 savings. So the PV income needs is \$162,699. SS Benefit PV SS Benefit PV Sum Minus savings Life Insurance Needed = A Note on Estimating Life Insurance Needs The expense approach I give here is slightly different from the example given in the textbook. I assume no debt and mortgage does not need to be paid f, while the textbook example assumes mortgage and all debts will be paid f using life insurance proceeds. If college education needs are taken into consideration, the expense approach will typically generate a larger face value amount. tax is not taken into consideration here. These two examples are more conceptual than practical. In real planning, more factors will need to be considered. In real world the life insurance term is likely to be much longer as one need to have life insurance when the children are born. 16 Inflation Effect and Term Effect In both the income and expense approaches all money numbers and discount rates are in real terms, in that they have been adjusted for inflation. There is another complication caused by inflation. As the insured lives an additional year, inflation has occurred during that year. This increase all future projected expenses. The face value would have kept up with the inflation if it had been invested. But it was not since the insured lived. The face value is now inadequate to cover the higher future expenses. This is called the inflation effect. Counterbalancing the inflation effect is the term effect, in that as the insured lives a year longer, there is one less year coverage needed. When the inflation rate is low, the term effect is larger than the inflation effect so overall the face value provides adequate coverage. If the inflation rate if very high, the inflation effect is larger than the term effect so face value is no longer adequate. There are policy options one can choose to deal with this issue, such as buy a cost--living rider so the face value is adjusted for inflation. Types Life Insurance Policies There are several ways to group life insurance policies. One way is to group policies into Temporary (protection for a specified period time) Permanent (protection for one s entire life) Another way is to group policies by Protection only Protection + From the point view economic comparison, the second method grouping makes more sense

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