Your company gives you an option of taking your pension as either a lump sum payment or a monthly check paid over life, which will you choose?
Usually a lump sum pension payment is the amount that company (pension actuary) thinks is equal to what you would recieve if you choose the monthly check for life option.
How do they make the calculation?
With the help of 2 concepts.
a) Present/future value of money
where
PV = present valueFVn = future value in year n
i = discount rate (expressed in decimal form)
n = number of years until future value occurs
is commonly called the discount multiplierb) Probability that they are going to have to make the pension payment.
Here are the steps to find out the lump sum:
Step 1
The pension actuary determines the present value of each year's pension payments.
For example, assume you, the retiree, your current age is 62, with a lifetime pension of $12000 per year. We take 20-year government bond interest rate as 3.5% (this may not be the standard practice but this is the longest risk-free long term interest rate I can find).
Please note that the present value is the amount you need today, so if it was compounded, it would grow to each future $12000 payment.
Take the payment when you reach age 75 ( that is 13 years from now) , $7672.85 is needed today before it will grow to that $12000 in 13 years at 3.5%.
The pension actuary will make this calculations for every year from age 62 to 110.
Step 2
Next, the pension actuary will take each present value and multiply it by the probability that the company is going to have to make that payment.
These probability values are obtained by predicting the probability of a person at any age living to any future age. Take for example, there is about a 65% chance that a 62 year old will be alive at age 75. Hence, multiply the present value for age 75, that being $7672.85, by 0.65 . The result is $4987.35. This is called the probability weighted present value of a $12000 payment at age 75.
They will make this same calculation for each present value all the way to age 110.
Interesting to note the probability of being alive at age 110 is less than 1%, so the probability weighted present value is less than $23.
Then they will accumulatively add up these probability weighted present values. This sum is the lump sum equivalent of the month pension checks for life.
Effect of Interest Rate on the Lump Sum
In the event that the risk free long term interest rate has rose above 3.5%, you will notice the calculated lump sum payment has shrunk. And vice versa, in case interest rate drop below 3.5%.
Take note the lump sum is always being evaluated and calculated in the interest rate of that moment. When the interest rate rise, the lump sum gets smaller. When they do down, the lump sum gets bigger.
Therefore you may try to time your retirement for when you think interest rates will be at their lowest.
How to determine the Bond prices
The price of bond is calculated following the same accumulating of present values procedure used for calculating the lump pension payment.
In the case of our government issued bonds, the probability that payments might not be made is not an issue. This removes the probability factor from the equation.
Bond prices rise and fall with interest rate directly as its coupon is fixed after it is issued.
Stock Market Model
Price = STFL + ITFL + LTFL + FVT
STFL = short term feedback loop;
ITFL = intermediate term feedback loop;
LTFP = long term feedback loop;
FVT = Fair Value term.
Fair Value is represented symbolically by the term D/I (Dividends divided by Interest rate).
This tells us that stock prices equal a fair value modified and stretched by action of 3 feedback loops of 3 time domains.
You can think over it and see if it makes sense.
Note: Ideas extracted from book "Predict Market Swings with Technical Anlaysis" by Michael McDonald.
