Tutorial 4
Review Questions Question 1
(a) What are the three major sections of a balance sheet?
(b) What is the balance sheet equation?
Question 2
Briefly discuss the two principal types of financial reserves needed to be maintained by property and casualty insurers. Question 3
(a) What are the two major sources of revenue for a property and casualty insurance company?
(b) What are the major expenses of a property and casualty insurance company?
Question 4
Identify the various ways of measuring profit or loss for an insurance company.
Question 5
Name three ways in which the assets of a life insurance company differ from the assets of a property and casualty insurance company.
Question 6
What do the reserves on a life insurance company’s balance sheet represent?
Question 7
What are the major categories of expenses for a life insurance company?
Question 8
(a) What are the major regulatory objectives that must be satisfied in insurance rate making?
(b) What are the major business objectives?
Question 9
In the context of rate making, explain the meaning of:
(a) rate
(b) exposure unit
(c) pure premium
(d) gross premium
Question 10
Briefly describe the following methods for determining a class rate:
(a) pure premium method
(b) loss ratio method
Question 11
Explain the following methods of merit rating:
(a) schedule rating
(b) experience rating
(c) retrospective rating
Case Application
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
premium 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?
Application Question
1. Based on the following information, determine the policyholders’ surplus for XYZ Insurance Company:
Total invested assets
$50,000,000 $40,000,000
Loss reserves
Total liabilities
Bonds
Unearned premium reserve $25,000,000 Total assets $90,000,000
2. Based on the following information, determine Mutual Life Insurance Company’s gain from operations before income taxes and dividends to policyholders:
Total premium income Licenses, taxes, and fees
Death benefits paid
Net investment income Commission paid General insurance expenses
$70,000,000 $35,000,000
$25,000,000 $5,000,000
$20,000,000 $580,000
$6,000,000 $3,000,000
$5,900,000
$2,500,000 $800,000 $1,600,000
Surrender benefit paid
Annuity benefit paid
3. A large casualty insurer writes a substantial amount of private passenger auto insurance. An actuary analyzed claims data for a specific class of drivers for a recent one-year policy period. The claims data showed that the insurer paid out $30 million for incurred losses and loss adjustment expenses for each 100,000 cars insured for one year. Based on the pure premium method, calculate the pure premium.
4. For the past calendar year, a property insurer reported the following financial information for a specific line of insurance:
Premium written
Expenses incurred
Incurred losses and loss
Adjustment expenses
Earned premium
a. What was the insurer’s loss ratio for this line of coverage? b. Calculate the expense ratio for this line of coverage.
c. What was the combined ratio for this line of coverage?
5. a. Why are property and casualty insurance company required to maintain loss reserves?
b. Briefly explain the following methods for determining loss reserves:
(i) judgement method
(ii) average value method
(iii) tabular method
c. What is the incurred but not reported (IBNR) loss reserve?
$14,000,000 $20,000,000