Carolyn is senior vice president of finance and chief actuary for Rock Solid Ins
ID: 2755159 • Letter: C
Question
Carolyn is senior vice president of finance and chief actuary for Rock Solid Insurance Company (RSIC). Lonnie is double-majoring in finance and mathematics at State University. Lonnie applied for an internship with Rock Solid, and he is working for the company during the summer before the start of his senior year of college. Curious to learn what Lonnie knew about insurance company financial statements and ratemaking, Carolyn prepared a quiz for Lonnie to take on his first day on the job. See if you can help Lonnie answer these questions.
1. At year-end last year, Rock Solid had total liabilities of $640 million and total assets of $900 million. What was the company's policyholders' surplus?
2. Explain how it is possible for Rock Solid to have $500 million in written premiums last year and $505 million in earned premiums last year.
3. Rock Solid's net underwriting result last year was a $540,000 loss. Explain how it is possible that Rock Solid was required to pay income taxes.
4. Rock Solid provides collision coverage for one year on 50,000 autos located in a specific territory within the state. During the one-year period, the company expects to pay $10 million in incurred losses and loss-adjustment expenses for these 50,000 autos. Based on this information, what is the pure premium?
5. The pure premium per unit of personal liability insurance for one group of prospective purchasers is $300. If Rock Solid wants to allow for a 40 percent expense ratio for this line of coverage, what gross rate per unit of coverage should be charged?
Explanation / Answer
1) Company’s policy holder surplus = Company’s asset – Company’s liabilities
= 900 m – 640 m = 260 m
2) Written premium is on which is registered on the books of an insurer or a reinsurer at the time of a policy is issued or paid for and earned premium is the part of the written premium. It is one which is considered to be earned by the insurer. It is based on the part of the policy period that has been in effect. So it is possible for Rock Solid to have $500 million in written premiums last year and $505 million in earned premiums last year
3) Underwriting losses are different from the operating losses. Underwriting losses are calculated based on Premium earned plus fee income – net losses incurred and expenses related to the underwriting. This loss is purely based on the underwriting activities. And the operating losses which incurs are due to the operating activities which shows the actual profit and loss of the firm. So it is possible that Rock solid has to pay the income tax because income tax is calculated on the operating profits and not on underwriting profits.
4) Pure premium is the actual or the expected indemnity payment that the insurer have to pay to the insured. In our case the total expected indemnity payment is $10M which is a pure premium for the company.
5) Pure premium of personal liability insurance = 300 per unit
Expense ratio = 40%
gross rate per unit of coverage = Pure premium + expenses = 300 + 300 x 40% = 300 + 120 = 420