In Exhibit 2, ... "fixed expenses ... are $88 x 3.8% / 17.8%" which in fact
equals $18.78 and that rounds to $19, not $20 ($20 is shown in the Exhibit).
According to the footnote, the trending is supposed to start in the subsequent
year (Year 3), but note that if the trending begins in Year 2, then $18.78 x
1.05 = $19.73, and that gives us our desired $20.
In Exhibits 3, 7, and 8, fixed expenses in the first renewal year (Year 2) DO
have the 1.05 trend factor figured in. In Exhibits 1, 4, 5, and 6, the fixed
expense trend does NOT begin until Year 3, as the footnotes attest.
Now, for your question, $142 = 17.8% of $880 premium, and this is shown in
Exhibit 1. But 17.78% of $550 average Pleasure Use premium reduced 10% for for
adult drivers (adults have better experience than average) is $88 ($550 x 17.8%
x .9 = $88.11) as shown in Exhibit 2. In Exhibit 7, the Column 7 clearly
spells out that the renewal year fixed expenses are computed off of $800
premium. So why calculate the renewal fixed expenses off of $550 x .90
premium, you ask?
Well, if you look on page 260, bottom paragraph, (follow along closely) "... we
begin with the standard asset share analysis shown in Exhibit I," and then on
page 263, second paragraph, "...Exhibit 8 shows as asset share exhibit with the
same starting premium and assumptions for losses, expenses, persistency rates,
and cost of capital, except now we get into excel and try to save some time by
cutting and pasting values from the wrong exhibits until it's all screwed up.
Note in the third paragraph that "...the actuary does not try to change the
course of the exam writing cycle; the solitary student cannot do this. Rather,
the pricing actuary sees the exam cycle as a constraint on her actions, and she
sets stress levels, rage relativities, and various neuroses and disappointments
in that context."