Cfa portfolio management

Life Insurance Pricing Example

by

The net payment cost index assumes that the insured person will die at the end of a specified period, such as 20 years. Calculation of the net payment cost index includes the following steps:

  1. Calculate the future value of an annuity due of an amount equal to the premium, compounded at a 5% discount rate for 20 years. An annuity due—an annuity for which the premium payment is received at the beginning of the period (versus an ordinary annuity, for which the premium payment is received at the end of the period)—is used because premiums are paid at the beginning of the period.
  2. Calculate the future value of an ordinary annuity of an amount equal to the projected annual dividend (if any), compounded at 5% for 20 years. An ordinary annuity is used because dividend payments are made at the end of the period.
  3. Subtract B from A to get the 20-year insurance cost.
  4. Calculate the payments for a 20-year annuity due with a future value equal to C and a discount rate of 5%. This amount is the interest-adjusted cost per year. Again, an annuity due is used because premium payments occur at the beginning of the year.
  5. Divide by the number of thousand dollars of face value.

The surrender cost index assumes that the policy will be surrendered at the end of the period and that the policy owner will receive the projected cash value. Calculation of the surrender cost index includes the following steps:

  1. Calculate the future value of an annuity due of an amount equal to the premium, compounded at 5% for 20 years. We use an annuity due here for the same reason indicated for the net payment cost index.
  2. Calculate the future value of an ordinary annuity of an amount equal to the projected annual dividend (if any), compounded at 5% for 20 years. We use an ordinary annuity here for the same reason indicated for the net payment cost index.
  3. Subtract B and the Year 20 projected cash value from A to get the 20-year insurance cost.
  4. Calculate the payments for a 20-year annuity due with a future value equal to C and a discount rate of 5%. This amount is the interest-adjusted cost per year.
  5. Divide by the number of thousand dollars of face value.

To illustrate the issues, assume a 25-year time horizon till death and a 5% discount rate on a $100,000 insurance policy.

  • Policy XX has annual beginning of year premiums of $2,000 and an assumed annual end of year dividend (return of premium) of $500. Terminal 25 year cash value projected (by the insurance company) to be $25,000.
  • Policy YY has annual beginning of year premiums of $2,200 and an assumed annual end of year dividend (increase in cash value) of $550. Terminal 25 year cash value projected (by the insurance company) to be $27,500.

Net payment cost index assumes the individual dies at the end of the horizon and cash value is not considered. It is often used if the insurance is projected to be paid up at that point:

Step 1:Compute the FV of the premiums paid, an annuity due (premiums paid at start of year).XX: 2,000 PMT, 5 iP , 25 n, FV = 100,227YY: 2,200 PMT, 5 iP , 25 n, FV = 110,250
Step 2:Compute the FV of the dividends, an ordinary annuity (dividends at end of year).XX: 500 PMT, 5 iP  , 25 n, FV = 23,864YY: 550 PMT, 5 iP  , 25 n, FV = 26,250
Step 3:The 25-year FV cost of insurance is Step 1 − Step 2.XX: 100,227 − 23,864 = 76,363YY: 110,250 − 26,250 = 84,000
Step 4:Annuitize this FV difference for the annual cost. Use an annuity due to match the requirement to pay premiums at the start of the year.XX: 76,363 FV, 5 iP  , 25 n, PMT = 1,524YY: 84,000 FV, 5 iP  , 25 n, PMT = 1,676
Step 5:Divide by $1,000 of insurance policy amount to index the annual cost ($100,000 / $1,000 = 100 units of insurance).XX: $1,524 / 100 = $15.24 per $1,000 of insurance per year.YY: $1,676 / 100 = $16.76 per $1,000 of insurance per year.

Net surrender cost index assumes the individual terminates the policy (insurance ceases) at the end of the horizon and the cash value is received. Step 1 and Step 2 are the same. Step 3 will be different and have consequences for Step 4 and Step 5.

Step 1:Compute the FV of the premiums paid, an annuity due (premiums paid at start of year).XX: 2,000 PMT, 5 iP  , 25 n, FV = 100,227YY: 2,200 PMT, 5 iP  , 25 n, FV = 110,250
Step 2:Compute the FV of the dividends, an ordinary annuity (dividends at end of year).XX: 500 PMT, 5 iP  , 25 n, FV = 23,864YY: 550 PMT, 5 iP  , 25 n, FV = 26,250
Step 3:The 25-year FV cost of insurance is Step 1 − Step 2 less the projected cash value.XX: 100,227 − 23,864 − 25,000 = 51,363YY: 110,250 − 26,250 − 27,500 = 56,500
Step 4:Annuitize this FV difference for the annual cost. Use an annuity due to match the requirement to pay premiums at start of year.XX: 51,363 FV, 5 iP , 25 n, PMT = 1,025YY: 56,500 FV, 5 iP  , 25 n, PMT = 1,127
Step 5:Divide by $1,000 of insurance policy amount to index the annual cost ($100,000 / $1,000 = 100 units of insurance).XX: $1,025 / 100 = $10.25 per $1,000 of insurance per year.YY: $1,127 / 100 = $11.27 per $1,000 of insurance per year.

Table of Contents

Leave a Comment