Replacement Cost, Actual Cash Value, Depreciation, Agreed Amounts, Stated Amounts, and Policyholder Duties in the Event of Insured Losses: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Insurance Operations, Regulation, and Statutory Accounting, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. 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.

Source:

Myhr, A.E.; and Markham, J.J. Insurance Operations, Regulation, and Statutory Accounting (Second Edition). American Institute for Chartered Property Casualty Underwriters. 2004. Chapter 9, pp. 9.17-9.24.

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

Problem S5-65-1. Insurers typically do not want to pay the replacement cost of property until the property has been repaired or replaced. What are two ways which insurers typically pursue to provide reimbursement for replacement cost to an insured?

Solution S5-65-1. This question is based on the discussion in Myhr and Markham, p. 9.17. The following are two ways in which insurers typically reimbursement for replacement cost:

1. Pay the insured the actual cash value once it is determined, and then pay the remaining amount of full replacement cost when repair or replacement is complete.

2. Gradually pay out amounts of money as repairs/replacements are completed, until the full replacement cost amount is paid.

Problem S5-65-2.

(a) What are the two main causes of depreciation?

(b) Name two situations in which the formula (Actual Cash Value) = (Replacement Cost) - (Depreciation) might not be appropriate.

(c) Briefly describe two alternative approaches some courts have used to define actual cash value.

Solution S5-65-2. This question is based on the discussion of depreciation in Myhr and Markham, pp. 9.17-9.19.

(a) The two main causes of depreciation are physical wear and tear and obsolescence.

(b) The following three examples for situations in which the formula (Actual Cash Value) = (Replacement Cost) - (Depreciation) might not be appropriate are mentioned by Myhr and Markham, p. 9.18:

1. Antiques which cannot be reproduced;

2. Buildings that feature construction methods which are no longer used;

3. Property that has appreciated in value, instead of depreciating.

Any two of the above suffice as an answer. Other valid answers may be possible.

(c) The following two alternative approaches some courts have used to define actual cash value are mentioned by Myhr and Markham, pp. 9.18-9.19:

1. Fair market value: What an item would sell for on the secondary market.

2. The broad evidence rule: A rule that requires "adjusters to consider all pertinent factors, including physical wear and tear, obsolescence, market value, and any other relevant factors" (Myhr and Markham, p. 9.19).

Problem S5-65-3. A property insurance policy has a coinsurance requirement, whereby the full value of the loss is only paid if the property is insured to 75% of its full value at the time of loss. The amount of insurance purchased by the insured is $125,000. The property has suffered a loss of $48,000. The full value of the property at the time of loss is $300,000. There is a $10,000 deductible applied to any losses that occur.

(a) How much will the insurer pay if the deductible is applied before the coinsurance penalty?

(b) How much will the insurer pay if the coinsurance penalty is applied before the deductible?

(c) Which approach - the approach of part (a) or the approach of part (b) - is the default approach that adjusters should use unless the insurance policy explicitly states otherwise?

Solution S5-65-3. This question is based on the discussion of the application of deductibles and coinsurance penalties in Myhr and Markham, p. 9.19:

(a) We apply the deductible to the loss first: $48,000 - $10,000 = $38,000. This is the amount to which the coinsurance penalty will be applied. The amount of insurance needed to avoid the penalty is 0.75*300000 = $225,000. Thus, the insurer will pay only 125000/225000 = 5/9 of any covered loss amount. In this case, the insurer will pay (5/9)*380000 = $21,111.11.

(b) We apply the coinsurance penalty - a multiplicative factor of 5/9 - to the loss amount of $48,000: 48000*(5/9) = 26666.67. Now we subtract the deductible: 26666.67 - 10000 = $16,666.67, which is what the insurer will pay if the coinsurance is applied first.

(c) Applying the deductible before the coinsurance penalty is the default approach. It should be used unless the insurance policy states otherwise. This approach is also always more favorable to the insured.

Problem S5-65-4.

(a) If property is insured for a stated amount, how much is the insured entitled to at the time of loss?

(b) If property is insured for an agreed amount, how much is the insured entitled to at the time of loss?

(c) What kinds of property are typically more likely to be insured for an agreed amount, as opposed to a stated amount?

Solution S5-65-4. This question is based on the discussion of stated amounts and agreed amounts in Myhr and Markham, pp. 9.19-9.20:

(a) If property is insured for a stated amount, the insured, in the event of loss, is entitled to the least amount of the following three values: "(1) the property's actual cash value, (2) the cost to repair or replace the property, (3) the applicable amount of insurance" (Myhr and Markham, p. 9.20).

(b) If property is insured for a agreed amount, the insured, in the event of loss, is entitled to either of the following:
1. The insurer's restoration of the property to its pre-loss condition.
2. The insurer's payment of the agreed amount.

(c) Property that is extremely difficult or impossible to replace is more likely to be insured for an agreed amount. This includes valuable papers and fine arts (Myhr and Markham, p. 9.20).

Problem S5-65-5. Name four typical duties of the policyholder in the event of loss, as specified in insurance policies.

Solution S5-65-5. The following policyholder duties in the event of loss are discussed by Myhr and Markham, pp. 9.21-9.24:

1. Providing prompt notice;
2. Protecting property;
3. Assisting with the loss adjustment process;
4. Providing proof of loss;
5. Submitting to examination under oath.

Any four of the above suffice as an answer. Other valid answers may be possible.

See other sections of The Actuary's Free Study Guide for Exam 5.