Re: Expense Provisions

He, Qing ( Chris_Coleianne@USFG.COM )
Thu, 12 Feb 1998 12:34:46 -0500

Thanks for the reply. I am still not very clear. If the $75 is
everything,
then based on the first part, the loss and variable expenses together is
$70.20 (93.6%), and fixed expenses is $4.80 (6.4%). But the new Variable
Base
Rate is $68.2299 (~91%), and Expense Fee will be $6.7701 (~9%). I think
the loss
is still expected at $48.375 (64.5%). Then why we move some variable
expenses into
fixed expenses bucket through this procedure? By charging everyone $7
Expense Fee,
who get more benefit? low-rate insured or high-rate one? Does insurer
reduce its
total premium income by following this procedure? I am just worry my
salary raise :-)

===========================================================
OK... I think your calculation for the expense fee is flawed.

We need to determine an average base rate for the territory (let's assume
this is $75 also). Then we need an average increased limits factor. Let's
say this is 1.50 (I know this is PD, but if I used a typical PD AILF, the
example wouldn't be as clear!). Then the average total limits rate for the
coverage becomes $112.50 = $75*1.50.

Then, to calculate the expense fee, we multiply the $112.50 by the FER
(0.064) to get the average fixed expense per policy. This is 7.20. Then we
have to gross this up for the variable expenses associated with the total
premium, so divide by 0.709. The resulting expense fee is 10.16.

Let's see how this affects the premiums for the three insureds in this
territory. The old base rate is $75.

Insured A has a class factor of 0.75 and an ILF of 1.5. The old premium is
($75 * 0.75 * 1.5) = $84. The new premium would be ($68 * 0.75 * 1.5) + $10
= $87.

Insured B has a class factor of 1.00 and an ILF of 1.5. The old premium is
$113. The new premium is $112.

Insured C has a class factor of 1.25 and an ILF of 1.5. The old premium is
$141. The new premium is $138.

The old total premium for territory 1 is 84+113+141 = 338. The new total
premium is 87+112+138 = 337. There is a negligible premium effect to the
company.
HOWEVER, we have redistributed the fixed expenses in a more equitable
manner. Insured A was paying $84 * .064 = $5 in fixed expenses, Insured B -
$7 and Insured C - $9. Now, each pays $7.20 (plus a variable expense load).

This example also tracks with the comments on page 9 - "This system would
directly reduce premiums for high-rated insureds. However, low-rated
insureds may experience a significant percentage increase in their premiums
(although a small dollar increase)."