CAS Exam 7 Spring 2014, Question 24
Study guide: Exam 9
The following information ($000,000) is available for an insurer:
| Item | Amount |
|---|---|
| Earned premium | 1,000 |
| Expected losses | 200 |
| Acquisition expenses | 150 |
| Beginning surplus | 2,000 |
| Risk-free rate | 3% |
| Investment rate of return | 5% |
The insurer is considering a reinsurance program for accident year 2015:
| No Reinsurance | Reinsurance | |
|---|---|---|
| Reinsurance premium | 0 | 450.0 |
| Reinsurance commission | 0 | 67.5 |
| Expected recovery | 0 | 110.0 |
| Probability of distress | 3.00% | 0.40% |
Assume the following:
- All premiums are collected at the beginning of the year.
- Losses are paid in full at the end of the year.
- All expenses are paid at the beginning of the year.
- There is no growth or change in the insured portfolio.
- The insurer cannot operate in a financially distressed state.
- Regulatory considerations are negligible.
- The firm value is the risk-adjusted present value of all future earnings.
Part a (1.5 points)
Calculate the insurer's expected underwriting profit both with and without reinsurance.
Part b (2.5 points)
Calculate the change in firm value of the insurer at the beginning of 2015 if the insurer purchases the reinsurance program.
Answer this question and see the worked solution