AbCo Insurance enters into a reinsurance contract with two reinsurance companies
ID: 464957 • Letter: A
Question
AbCo Insurance enters into a reinsurance contract with two reinsurance companies: Apple Re and Northern Re. The three companies work together to insure a cargo ship valued at $250 million. The insurance limits are as follows:
AbCo - $75 million
Apple Re - $125 million
Northern Re - $50 million
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Assume a pro-rata reinsurance policy.
Q1: If the total premium collected from the owners of the cargo ship is $5 million, how much does each insurance company stand to collect as a premium?
Q2: If a $200 million loss occurs, how much does each insurer pay? What if a $250 million loss occurs?
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Assume an excess-of-loss reinsurance policy. The pay order is the same order listed above (1-3).
Q3: If the total premium collected from the owners of the cargo ship are $5 million, how much does each insurance company stand to collect as a premium?
Q4: How much does each insurer pay for the following losses: $100m, $225m, $240m?
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AbCo Insurance holds total assets of $800 million and recognizes liabilities of $550 million.
Q5: What is AbCo’s policyholder surplus?
Q6: According to the Kenney Ratio, what is the maximum amount of insurance AbCo can safely sell? Assume some mixture (the mixture doesn’t matter) of property and liability insurance is being sold.
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Q7: AbCo writes $150 million in premiums in 2012. In 2012, AbCo pays $117 million for losses and for loss expenses. In 2012, AbCo pays $31.5 million in underwriting/administrative expenses. What is AbCo’s loss ratio, expense ratio, and combined ratio? Can you make any statements about AbCo’s profitability?
Explanation / Answer
Answer 1 – According to pro-rata reinsurance policy, the insurance collected will be shared by each company proportionate to the risk covered by each. Therefore premium collected by each company is as below
AbCo - $75 / 250 * 5 = $ 1.5 million
Apple Re - $125 / 250 * 5 = $ 2.5 million
Northern Re - $50 / 250 *5 = $ 1 million
Out of the premium thus collected, Reinsurance companies will pay to the ceding company a ceding commission to defray the expenses and acquisition costs.
Answer 2 - Liability of loss is equally shared by each company. Therefore $ 200 million and $ 250 million loss will be borne proportionate to the risk covered by each company.
Loss of $ 200 million
AbCo - $75 / 250 * 200 = $ 60 million
Apple Re - $125 / 250 * 200 = $ 100 million
Northern Re - $50 / 250 * 200 = $ 40 million
Loss of $ 250 million
AbCo - $75 / 250 * 200 = $ 60 million
Apple Re - $125 / 250 * 200 = $ 100 million
Northern Re - $50 / 250 * 200 = $ 40 million
Answer 3 – premium collected by each company from an excess of loss reinsurance policy is not distributed on pro-rata basis, but is based on various formula guidelines, underwriter’s evaluation of risk, primary rates, increase limits rates. The ceding company providing the first layer of insurance keeps the maximum share which is more than the premium calculated on pro-rata basis. Reinsurance company stands to collect less premium than pro-rata basis.
Answer 4 – Loss based on the same pay order will be distributed as under
Loss = $ 100 million
AbCo - $75 million
Apple Re - $25 million
Loss = $ 225 million
AbCo - $75 million
Apple Re - $125 million
Northern Re - $25 million
Loss = $ 240 million
AbCo - $75 million
Apple Re - $125 million
Northern Re - $40 million
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