Assorted Exam-Style Questions for Actuarial Exam 6 -- Part 10

Some of the questions here ask for short written answers. This is meant to give the student practice in answering questions of the format that will appear on Exam 6. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Some of the problems in this section were designed to be similar to problems from past versions of Exam 6, offered by the Casualty Actuarial Society. They use original exam questions as their inspiration - and the specific inspiration is cited to give students an opportunity to see the original. All of the original problems are publicly available, and students are encouraged to refer to them. But all of the values, names, conditions, and calculations in the problems here are the original work of Mr. Stolyarov.

Sources:
Financial Accounting Standards Board, "Interpretation No. 14," Paragraphs 1-6.

Past Casualty Actuarial Society exams: 2007 Exam 6.

Original Problems and Solutions from The Actuary's Free Study Guide

The following conditions apply to Problems S6-20-1 and S6-20-2.

On January 1, 2054, Insurer X had total assets in cash of $3 million.
In calendar year 2054, the insurer collected $30 million in premiums and had $9 million in losses and expenses.
If there were no reinsurance, the insurer's balance sheet as of December 31, 2054, would appear as follows:

Assets
Cash: $24 million

Liabilities
Unearned premium reserve: $15 million
Loss reserves: $15 million
Total liabilities: $30 million

Surplus
-$6 million

Insurer X, however, participated in a pro rata reinsurance treaty, where it ceded 60% of its premiums and losses to the reinsurer. The reinsurer pays the insurer a ceding commission of 40%.

Problem S6-20-1. Similar to Problem 13(a) from the 2007 CAS Exam 6. Construct a balance sheet for Insurer X as of December 31, 2054 that takes the reinsurance transaction into account.

Solution S6-20-1. Without reinsurance, the insurer would have had cash of $24 million. With reinsurance, the reinsurer collects 60% of the premium revenue, but pays the insurer 40% of that as a ceding commission, so the reinsurer really only collects 60% of 60% of premium, or 36% of premium, or 0.36*30 million = $10.8 million. At the same time, Insurer X does not have to pay 60% of its losses, meaning that its loss payment during 2054 is reduced by 0.6*9 million = $5.4 million.

So, on the assets side, cash becomes 24 million - 10.8 million + 5.4 million = $18.6 million.

On the liabilities side, both the unearned premium reserve and the loss reserves are reduced by 60% to 0.4*15 million = $6 million each.

We therefore have the following balance sheet:

Assets
Cash: $18.6 million

Liabilities
Unearned premium reserve: $6 million
Loss reserves: $6 million
Total liabilities: $12 million

Surplus
$6.6 million

Problem S6-20-2. Similar to Problem 13(b) from the 2007 CAS Exam 6. Did the reinsurance transaction described provide surplus relief? Explain why or why not.

Solution S6-20-2. Yes, surplus relief did occur. Because of the reinsurance transaction, the surplus was increased from -$6 million to +$6.6 million, which implies that Insurer X prevented itself from having an accounting loss. Surplus relief due to reinsurance partially remedies the accounting convention that recognizes losses as incurred immediately, while premiums must be earned over time and are considered a liability while unearned.

Problem S6-20-3. Similar to Problem 19 from the 2007 CAS Exam 6. Comment on what, according to FASB Interpretation No. 14, a company would have to present on its financial statements with regard to the following situations:

(a) A contingency which is "reasonably possible" and, if it occurs, would cost the company anywhere from $6 million to $9 million, with each outcome in the range being equally likely.

(b) A contingency which is "probable" and, if it occurs, would cost the company anywhere from $6 million to $9 million, with each outcome in the range being equally likely.

(c) A contingency which is "probable" and, if it occurs, would cost the company anywhere from $6 million to $9 million, with $8 million being the most likely amount.

Solution S6-20-3. (a) Contingencies which are not yet "probable" do not require accrual of any loss. However, a disclosure should occurof the contingency's nature and the estimated losses' range from $6 million to $9 million.

(b) Contingencies which are "probable" and for which no possible loss amount is more likely than any other require accrual of the minimum possible loss amount - in this case, $6 million - along with a disclosure of the contingency's nature and the range of possible additional losses up to $3 million.

(c) Contingencies which are "probable" and for which there is one most likely loss amount require accrual of the most likely loss amount - in this case, $8 million - along with a disclosure of the contingency's nature and the range of possible additional losses up to $1 million.

The following conditions apply to Problems S6-20-4 and S6-20-5.

You are aware of the following information regarding Insurer Z:

Written premium in 2034: 2100
Unearned premium reserve as of December 31, 2033: 1200
Unearned premium reserve as of December 31, 2034: 1150
Loss reserves as of December 31, 2034: 400
LAE reserves as of December 31, 2034: 200
Deferred policy acquisition costs as of December 31, 2034: 100
Office furniture as of December 31, 2034: 400
Electronic data processing equipment and software as of December 31, 2034: 100
Cash as of December 31, 2034: 3000

Problem S6-20-4. Similar to Problem 20(a) from the 2007 CAS Exam 6. What is the equity as of December 31, 2034, according to Generally Accepted Accounting Principles (GAAP)?

Solution S6-20-4. We are only considering assets and liabilities at the end of 2034, so figures as of the end of 2033 or items accruing during 2034 (such as written premium) are irrelevant.

Assets
Under GAAP, the following are permissible assets:
Cash as of December 31, 2034: 3000
Deferred policy acquisition costs as of December 31, 2034: 100
Office furniture as of December 31, 2034: 400
Electronic data processing equipment and software as of December 31, 2034: 100
Total assets: 3600

Liabilities
Under GAAP, the following are liabilities:
Unearned premium reserve as of December 31, 2034: 1150
Loss reserves as of December 31, 2034: 400
LAE reserves as of December 31, 2034: 200
Total liabilities: 1750

GAAP Equity
Assets - Liabilities: 1850

Problem S6-20-5. Similar to Problem 20(b) from the 2007 CAS Exam 6. What is the statutory policyholders' surplus as of December 31, 2034?

Solution S6-20-5. Under Statutory Accounting Principles (SAP), the liabilities in this case are the same as under GAAP, so their total is 1750 (see Solution S6-20-4). However, with respect to the assets, office furniture and deferred policy acquisition costs are excluded.

The treatment of electronic data processing (EDP) equipment and software is not as intuitive. Under SAP, this can be recognized as an asset, but only up to 3% of surplus.

Let x be the permitted EDP asset. The rest of the surplus calculation is (Cash - Liabilities) = 3000 - 1750 = 1250, so the total surplus is 1250 + x.

The restriction is that x/(1250 + x) = 0.03, so 33.33333333x = 1250 + x →
32.33333333x = 1250 → x = 38.65979381, and the statutory surplus is 1250 + 38.65979381 = 1288.65979381.

See other sections of The Actuary's Free Study Guide for Exam 6.