CAS Exam 9 Spring 2017, Question 1

Study guide: Exam 9

The actuarial department of a property and casualty insurer is reviewing a potential growth opportunity. Given the following information about this opportunity:

All policies are effective on the same day and are in force for one year.
Premium is collected at the beginning of the policy period and is expected to be $4 million per year.
Premium is immediately earned, so there is no unearned premium reserve.
Loss reserves are established at the beginning of the policy period, on an undiscounted basis.
Variable expenses equal to 25% of the premium are paid at policy inception.
Losses (including Loss Adjustment Expenses (LAE)) as a percentage of Written Premium are expected to be 45% paid out at the end of the first year and 30% paid out at the end of the second year, with no other loss payments.
The expected client retention rate is 80%.
The undiscounted reserve-to-surplus ratio is 2.5:1.
The risk-free interest rate is 3%.
The expected return on the market portfolio is 7%.
The cost of capital is 8% per year.
The insurer has an expected investment yield of 10%.
Investment income is earned at the end of each year.
There are no taxes.

Part a (3 points)

Calculate the internal rate of return (IRR) and net present value (NPV) for one year of policies for the growth opportunity.

Part b (1.75 points)

Assume the risk-adjusted allocated capital is $2.5 million. Calculate the projected risk-adjusted return on capital (RAROC) of the opportunity.

Part c (1.25 points)

Calculate the projected increase in franchise value resulting from the growth opportunity.

Part d (0.5 points)

Give support for why the company should pursue this project.

Part e (1 point)

The company plans a public announcement of the project in one week and it is expected that the stock price will increase as a result of the project. Briefly describe what will happen to the stock price both before and after the announcement under both the strong-form and the semistrong-form of the efficient market hypothesis.

No current syllabus covers this question; it is kept for the record.

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