The +1 is for surplus.
Rearrange the second line thus (1.3P +S)/S =(1.3P/S +1)
1.3P is the liabilities + Surplus = Assets
This is what you start with in the first line (IA/S)
Glen Calihan
---------------------- Forwarded by Glen R. Calihan/Westfield Companies on
02/25/98 03:28 PM ---------------------------
(Embedded image
moved to file: CREEDR@towers.com
PIC17183.PCX) 02/25/98 03:00 PM
To: studygroup6@lists.casact.org
cc: (bcc: Glen R. Calihan/Westfield Companies)
Subject:
I was working a problem from the CAS study manual concerning Total Rate
of Return according to D'Arcy. I don't understand the answer given in
the study manual. I have included the question and model answer for
reference.
Q. Suppose an insurer writes business which, over time, generates a
ratio of investable liabilities to annual earned premium of 1.3 and
produces an underwriting profit margin of -1% of earned premium. If
the insurer obtains an 8% investment return on total assets, what is
the minimum premium-to-surplus ratio required to provide at least a 20%
return on stockholder's equity?
A. TRR = (IA/S)(IRR) + (P/S)(UPM)
.20 = [(1.3P/S + 1)(.08) + (P/S)(-.01)
.20 = .08 + [P/S][(.8)(1.3) - .01]
P/S = 1.28
Specifically, I do not understand the "+ 1" in the second line of the
model solution. Can anyone explain where this comes from? Or is this
a mistake in the model answer? I got an answer of P/S = 2.12. Does
anyone agree with this?
--0__=OWQF1ij8PjMV2gwlrfFbuZ5L3DkWKkGVtlvFU6eGlD0Ye2oampAhTka5
Content-type: application/octet-stream;
name="PIC17183.PCX"
Content-transfer-encoding: base64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--0__=OWQF1ij8PjMV2gwlrfFbuZ5L3DkWKkGVtlvFU6eGlD0Ye2oampAhTka5--