 |
Determine
Initial Payment | Determine Future Payments
Discount Future Payments | Discount
for Proability of Living
Add All Discounted Future Payments | Programming
Considerations
Examples | Conclusion
4: DISCOUNT EACH PAYMENT FOR PROBABILITY
OF
LIVING TO COLLECT THE PAYMENT
Not
all persons entitled to receive payments for the remainder of his
or her life
live to be 100 years old. The present value must take this into
consideration.
This is done by discounting each payment for the probability of
living to collect the
payment. One method is to accumulate all of the payments from the
DOC to the
number of years the person is expected to live after the date of
commutation.
But this isn’t the most accurate method and may not comply
with LC 5101.
For example, in Table 2 in WORKERS’ COMPENSATION Laws of California
2007
edition page 1398 the number for a male age 50 is 907.98 for an
annuity that
begins at the DOC (zero years delay). If the payment were $490.00
per week the
present value, using Table 2 is 907.98 x 490 = $444,910.20. The
U. S. Life Table
for 1989-91 lists the life expectancy of a 50 year old male at 26.37
years. The
present value using the life expectancy method is 490 x 52.17857
x 26.37 =
$674,214.94. The life expectancy method yields a value considerably
higher than
the probability method.
The better method is to multiply the probability that the person
will live to collect the
particular payment times the payment. Present value of a particular
payment is the
probability of living to collect the payment multiplied by the payment.
PVi = piPaymenti
where: p is the probability of living to collect the payment, and
Payment is the amount calculated in the above sections. It is the
weekly rate multiplied by 2 because payments are actually made every
two weeks and not weekly.
The probability of living to collecting
a payment is based upon U.S. Life Tables
as required by Cal.Ad. Reg 10169. The latest table is for the year
2003 as reported
in the National Vital Statistics Reports, Vol. 54, April 19, 2006. 7
http://www.cdc.gov/nchs/data/nvsr/nvsr54/nvsr54_14.pdf
http://www.cdc.gov/nchs/products/pubs/pubd/lftbls/life/1966.htm
On page 2 of that report explains how the probability of survival
is determined.
“For example, to calculate the probability of surviving from
age 20 to age 85,
one would divide the number of survivors at age 85 (36,988) by the
number
of survivors at age 20 (98,693), which results in a 37.5 percent
probability
of survival.”
There are separate tables for males and females. Table 8 shows the
life table for
males. The tables in the report lists the number of persons surviving
to a particular
age based upon a starting number of 100,000 persons.
7Note that the table on the web
site differs from the tables originally published. An
explanation for this difference has not been found. The tables from
the web site were used in the program. It is assumed this is the
most valid data.
Table 8. Life Table 2003 for Males
(click to enlarge)
The probability at any age is:
Px = survivors at end / survivors at start
Example: A 53 year old male is receiving a life pension. The probability
of
collecting a payment at age 75 from table 8 is: Probability = 59,229
/ 90,161 = .6569
or 65.69%
Example: A male born 1/1/57; date of injury 1/1/06;
payments start 1/1/07; date of
commutation 1/1/07; weekly earnings 881.65. The first payment is
due 1/14/07.
The person’s age at the time of the first payment (payment
number is 1) is
1/1/07 + 14 – 1/1/57 = = 50.03833.
The probability of receiving the first payment is obtained from
Table 8. The survivors
at age 50 are 91,846. The survivors at age 51 are 91,322. The difference
is 524.
The survivors at age 50.03833 is 91,846 – (524 x .03833) =
91,846 – 20.08 =
91825.92.
The probability of living to the date the first payment is
P1 = 91825.92 / 91846 = 0.999781.
It’s almost a sure bet the person will live to collect the
first payment. But this
probability drops as the person gets older.
The life table must be interpolated between whole year ages to get
the probability
for a particular two-week payment. It is assumed that the probability
of survival is
linear between whole age numbers. The U.S. Life Table text explaining
the tables
validates this assumption. So, the probability of survival at any
age is:
P = (Lpaymentage – age fraction x (Lpaymentage – Lpaymentage
+1)) / LDOC
The age fraction is the fractional number between whole number ages.
The L is
the number of persons living from Table 8. L + 1 is the age at date
of payment plus
one year, i.e. the next bracket.
Determine Initial
Payment | Determine Future Payments
Discount Future Payments | Discount
for Proability of Living
Add All Discounted Future Payments | Programming
Considerations
Examples | Conclusion
|
