Suppose that an insurance company's loss ratio is 79.8 percent, its expense ratio is 27.9 percent and the company pays 2 percent of its premiums earned to policyholders as dividends. a. What is…

Solution to Management of Financial Institutions (TU Board 2080)

Given:

• Loss ratio = 79.8%
• Expense ratio = 27.9%
• Dividend payout ratio = 2%

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a. Combined Ratio After Dividend

The combined ratio is calculated as: $$\text{Combined Ratio}=\text{Loss Ratio}+\text{Expense Ratio}+\text{Dividend Ratio}$$

Substituting the given values: $$\text{Combined Ratio}=79.8\%+27.9\%+2\%=109.7\%$$

Answer: 109.7%

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b. Operating Ratio

The operating ratio is derived from the combined ratio and investment income. First, we calculate the net operating ratio (combined ratio minus investment income):

$$\text{Net Operating Ratio}=\text{Combined Ratio}-\text{Investment Income Ratio}$$

Given that the investment portfolio yielded 12%, we adjust the combined ratio:

$$\text{Operating Ratio}=109.7\%-12\%=97.7\%$$

Answer: 97.7%

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c. Overall Profitability

The overall profitability is determined by comparing the operating ratio to 100%:

• If the operating ratio is below 100%, the company is profitable.
• If it is above 100%, the company is operating at a loss.

Since the operating ratio is 97.7%, the company is profitable by: $$100\%-97.7\%=2.3\%$$

Answer: The company is profitable with a net gain of 2.3%.