CAS Exam 9 Spring 2015, Question 19
Study guide: Exam 9
The actuarial department of a property and casualty insurer is reviewing two potential growth opportunities, referred to as Option A and Option B. Given the following information about these options:
- Policies are in-force for one year.
- Premium is collected at the beginning of the policy period.
- Variable expenses equal to 25% of the premium are paid at policy inception.
- Both options are expected to achieve an 85% loss ratio.
- Equal loss amounts are expected to be paid out at the end of each year over a two-year period for both options.
- The company allocates capital in a way that results in a reserve-to-surplus ratio of 2:1 for Option A and 3:1 for Option B.
- Initial required surplus is set to the loss portion of the unearned premium reserve.
- Supporting capital can be invested at a 10% rate of return.
- The cost of capital is 8% per year.
- Investment income is earned at the end of a given policy year.
- There are no taxes.
Calculate the internal rate of return (IRR) and net present value (NPV) for each growth opportunity.
Part a (2.25 points)
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