This section of sample problems and solutions is a part of The Actuary’s Free Study Guide for Exam 6, authored by Mr. Stolyarov. This is Section 55 of the Study Guide. See an index of all sections by following the link in this paragraph.
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.
Blanchard, R.S., “Premium Accounting,” CAS Study Note, May 2005.
Original Problems and Solutions from The Actuary’s Free Study Guide
Problem S6-55-1. According to Blanchard in “Premium Accounting” (p. 1), what are five possibilities for determining the time at which premium is recognized as revenue? Which of these possibilities is most commonly used in the life insurance industry? Which is most commonly used in the property/casualty insurance industry?
Solution S6-55-1. Blanchard lists the following five possibilities for determining the time at which premium is recognized as revenue:
1. The signing of the insurance contract
2. The due date of the premium from the policyholder
3. The date the premium is received by the insurer
4. The date the insurance policy becomes effective.
5. As the risk covered by the policy runs off over time.
The life insurance industry most often recognizes premium as revenue at the due date of the premium from the policyholder (Item 2 above).
The property and casualty insurance industry most often recognizes premium as revenue as the risk covered by the policy runs off over time (Item 5 above).
Problem S6-55-2. Assume an insurance policy sold on June 1, 2030, effective August 1, 2030, and having a term of one year. The risk insured does not vary over time. The premium charged is $2400. The insurer collects all the premium upfront at the sale date.
(a) Construct a balance sheet entry, from the insurer’s perspective, of the assets and liabilities associated with this policy as of July 1, 2030, assuming no insured losses.
(b) Construct a balance sheet entry, from the insurer’s perspective, of the assets and liabilities associated with this policy as of May 1, 2031, assuming no insured losses.
(a) On July 1, 2030, the policy is still not in effect, so no premium has been earned. The insurer has already collected the $2400 from the insured in cash, but this cash asset needs to be balanced by an equivalent liability of $2400, called Deposit Premium. Thus, our balance sheet looks as follows:
Balance Sheet As of July 1, 2030:
Deposit Premium: $2400
(b) As of May 1, 2031, 9 of 12 months’ premium have been earned, making the unearned premium (3/12)*2400 = $600. This is the liability known as the Unearned Premium Reserve. The insurer still has the $2400 cash asset. The surplus, the difference between assets and liabilities, represents the amount of policy premium that has already been earned. (In this case, that is all the surplus represents, as there are no insured losses.)
Balance Sheet As of May 1, 2031:
Unearned Premium: $600
(a) Describe the concept of “premium receivable”, when it applies, and how it is treated on an insurer’s balance sheet. (See Blanchard, “Premium Accounting”, p. 4.)
(b) Under GAAP accounting, how would an insurer treat premium that is ultimately never collected? (See Blanchard, “Premium Accounting”, p. 5)
(a) “Premium receivable” is an asset that appears on the balance sheet when the policy to which a premium applies has already become effective, but the premium has not yet been paid by the insured. This premium is considered “premium receivable” until it is paid, at which time this asset is eliminated, and the equivalent amount becomes a cash asset.
(b) GAAP accounting treats premium that is ultimately never collected as an underwriting expense for the amount of uncollected premium. Treating it as negative premium is another option.
(a) If premium revenue were recognized under an asset/liability paradigm rather than a deferral/matching paradigm, what would be the primary difference? (See Blanchard, “Premium Accounting”, p. 7.)
(b) Identify five phenomena that may make it difficult to estimate premium upfront for an insurance policy. (See Blanchard, “Premium Accounting”, pp. 7-8.)
(a) If premium revenue were recognized under an asset/liability paradigm rather than a deferral/matching paradigm, then there would be no Unearned Premium Reserve liability. Instead of considering unearned premium, all premium would be recorded as revenue at the policy effective date or the policy sale date. However, the asset/liability paradigm also requires an estimate of expected losses and expenses for the portion of the policy than has not expired. These would be liabilities on the insurer’s balance sheet.
(b) The following six phenomena are described by Blanchard, pp. 7-8. Any five would constitute a satisfactory answer.
1. Deposits: The “binder” premium, or initial deposit, may differ from the premium ultimately agreed upon once the details of an insurance policy are finalized.
2. Estimates: Premium may need to be estimated in cases where actual exposure to loss is not known. The estimates would need to be adjusted later as more information arises.
3. Audits: An insurer’s audit of the insured’s risk may revise the premium for a particular policy period.
4. Endorsements/cancellations: Endorsements selected by the insured or insurer may change the amount of premium, while cancellations of the policy imply the need for the insurer to issue a premium refund in most cases.
5. Reinstatements: For certain catastrophe excess-of-loss reinsurance treaties, a reinstatement premium is required to maintain coverage after a catastrophic event has occurred. This reinstatement premium is contingent on the catastrophe actually happening.
6. Retrospective premium adjustments: Premium for a retrospectively rated insurance policy depends on the insured’s actual loss experience, which cannot be known in advance.
Problem S6-55-5. You have the following information about an insurer’s book of business:
Written premium: $400
Earned premium: $360
Incurred losses: $320
Underwriting Expenses: $30
Policyholder Dividends: $15
(a) What is the loss ratio if the dividends are treated as expenses?
(b) What is the loss ratio if the dividends are treated as premium?
(c) What is the expense ratio if the dividends are treated as premium?
(d) What is the expense ratio if the dividends are treated as premium?
(a) If dividends are treated as expenses, then the loss ratio is simply
(Incurred Losses)/(Earned Premium) = 320/360 = 0.8888888889 .
(b) If dividends are treated as (negative) premium, then the loss ratio is
(Incurred Losses)/(Earned Premium – Dividends) = 320/(360 – 15) = 0.9275362319.
(c) If dividends are treated as expenses, then the expense ratio is
(Underwriting Expenses + Dividends)/(Written Premium) = (30 + 15)/400 = 0.1125.
(d) If dividends are treated as (negative) premium, then the expense ratio is
(Underwriting Expenses)/(Written Premium – Dividends) = 30/(400-15) = 0.0779220779.
See other sections of The Actuary’s Free Study Guide for Exam 6.