Last Updated on 3, April 2014
Someone asked me how to calculate bonuses for participating life policies. I asked the individual to provide me with the latest benefit illustration. The policy was already in-force for some time already. I will use this policy as an example on how to calculate bonuses. Unfortunately, there was insufficient information to calculate bonuses for surrender values. So the illustration below is only for bonuses due to death claims.
The relevant information provided by the benefit illustration is shown below:
First, the benefit illustration clearly shows that the guaranteed death benefit at the end of year X is $87,420.17. This consists of two components, the sum assured of $50,000 and the accumulated attaching bonuses that were already previously declared amounting to $37,420.17. Sanctity check: 50000+37420.17 = $87,420.17.
To calculate the non-guaranteed death benefit at the end of year X, the following steps are required to be taken:
New revisionary bonuses
= $22 per $1000 sum assured x $50000 sum assured + (100% + 2.5%) of attaching bonuses
= (22/1000) x 50000 + 1.025 x 37420.17
= $39,455.67 … (1)
Upon death, there is also a terminal bonus which is 25% of attaching bonuses
= 25% x (1)
= 25% x $39,455.67
= $9863.92 …(2)
Therefore, the projected death benefit at the end of year X is 50000 + (1) + (2) = 50000+39455.67+9863.92 = $99,319.60. This is exactly the same as that shown by the benefit illustration for end of year X.
Let’s say we are in X+1 and assumed the insurer honors the stated revisionary bonus in the previous year. This means the new attaching bonus is (1) which is equal to $39,455.67.
New revisionary bonuses
= $22 per $1000 sum assured x $50000 sum assured + (100% + 2.5%) of attaching bonuses
= (22/1000) x 50000 + 1.025 x (1)
= (22/1000) x 50000 + 1.025 x to $39,455.67
= $41,542.07 … (3)
Upon death, there is also a terminal bonus which is 25% of attaching bonuses
= 25% x (3)
= 25% x 41542.07
= $10,385.52 … (4)
Therefore, the projected death benefit at the end of year X+1 is 50000 + (3) + (4) = 50000+41542.07+10385.52 = $101,927.60. This is exactly the same as that shown by the benefit illustration for end of year X.
There is insufficient information to calculate the bonuses for surrendering of the policy. So I cannot give an example. However, the basic idea of surrender value is that it is a present value (PV) of the future payout. The death benefit of a life policy is a future (unknown) event. Hence, the death benefit’s bonuses are expected to be paid out in the future. If the policyholder terminates a policy, he will be getting a payout using some discount rate. In practice, the insurer could also impose a further penalty to recoup other expenses. The discounted approach explains why the surrender value and death benefit converge to the same value when the life assured gets older.
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