C5 - Ratemaking Book - Excercise 3.3 & 3.4

[yeppers-wsmn]

The answers to these two for calculating the Gross Premium rate seem inconsistent.

3.3 subtracts the flat $ amount of commision before multiplying by the ratio.

ie. (NewGrossPrem - 50)*(1 - 0.21) = NetPrem

3.4 subtracts the flat $ amount of expenses and profits after multiplying by the ratio.

ie. (NewGrossPrem)*(1 - 0.85) - 80 - 50 = NetPrem


Anyone know why?

[WWSituation]

I don't have the book on me, but I remember a question asking what happened if they made the commission a flat $ amount as opposed to a % of premium. This could be the source of the perceived inconsistency.

[Not Mike]

Indeed, WWS is correct...

It has to do with that GP(1-V) = Loss Cost + F formula that I thought I didn't need to know....

You have to treat the Variable and Fixed portions differently...

[yeppers-wsmn]

In both of those problems, the book says that the amount is changing from a % of premium to a fixed amount. But it puts them in different places in the equation.

Not Mike, could you plug the actual #'s from these 2 problems into that formula you are referring to?

Thanks.

<font size=-1>[ This Message was edited by: yeppers on 2001-10-26 14:03 ]</font>

[Not Mike]

3.3

GP(1-V) = Expected Loss Cost + F

Expected loss cost = 500*(1-.33) = 335

GP(1-.15-.03-.03) = 335 + 50

Yes, it appears as though this doesn't work for this example... instead the 50 is added AFTER the division, i.e.

GP = 335/(1-V) + 50

3.4

GP(1-V) = Loss Cost + F

GP(1-.12-.03) = 640 + 80 + 50

implies GP = 905.88, which ties to the book answer, but should it really be:

GP = 640/(.85) + 80 + 50 = 882.94

That's interesting.... I do recall running into this situation when doing these problems and thinking that I understood the difference.... one thing that I do know is that in 3.4, I "checked" the solution by leaving comm at 20% (i.e. 1-V = .77), and seeing that GP = 1000 doing it with the formula, and doesn't = 1000 using the 3.3 method.... now I'm confused....

[yeppers-wsmn]

Is it something to do with treating fixed commisions differently than other fixed expenses?

[Not Mike]

I could be wrong, BUT after further review, I'd have to say that 3.3 is wrong....

OK, they develop the final rate as 474.05...

50 of that is for commissions
335 is for claims
21% is for Gen, Taxes, P&C
(.21)*(474.05) = 99.55

50 + 335 + 99.55 = 484.55

That doesn't tie back to the total rate, so the solution has to be wrong....

[yeppers-wsmn]

On 2001-10-26 14:42, Not Mike wrote:

I could be wrong, BUT after further review, I'd have to say that 3.3 is wrong....

OK, they develop the final rate as 474.05...

50 of that is for commissions
335 is for claims
21% is for Gen, Taxes, P&C
(.21)*(474.05) = 99.55

50 + 335 + 99.55 = 484.55

That doesn't tie back to the total rate, so the solution has to be wrong....


But, if you exlude the $50 in commisions from Gen, Taxes and P&C, you get

50 of that is for commissions
335 is for claims
21% is for Gen, Taxes, P&C
(.21)*(474.05 - 50) = 89.05

which is 50 + 335 + 89.05 = 474.05


Now I'm more confused. 3.4 does the opposite

[Not Mike]

One thing that I just noticed in re-reading....

"Assume all other expenses do *not* apply to the new commission."

I guess it boils down to the fact that $50 will be collected for commission no matter what and this amount should be excluded from the pricing analysis. To me then, the new "developed" gross rate is 424. And, oh by the way, we need 50 for commission...

This boils down to the most important part of the exam, actually reading the question, which I have definite problems with...