To determine whether the line of insurance is profitable before dividends, we need to calculate the combined ratio, which is the sum of the loss ratio and the ratio of commissions and other expenses.
Combined Ratio = Loss Ratio + Commissions and Other Expenses Ratio
In this case, the loss ratio is given as 70 percent, so:
Loss Ratio = 70%
Now, let's evaluate the options:
A. Commissions and other expenses are 15 percent.
B. Commissions and other expenses are 5 percent.
C. Commissions and other expenses are 16 percent.
D. Commissions and other expenses are 15 percent.
E. Commissions and other expenses are 6 percent.
We'll calculate the combined ratio for each option using the loss ratio and the provided commissions and other expenses ratio:
A. Combined Ratio = 70% (Loss Ratio) + 15% (Commissions and Other Expenses) = 85%
B. Combined Ratio = 70% (Loss Ratio) + 5% (Commissions and Other Expenses) = 75%
C. Combined Ratio = 70% (Loss Ratio) + 16% (Commissions and Other Expenses) = 86%
D. Combined Ratio = 70% (Loss Ratio) + 15% (Commissions and Other Expenses) = 85%
E. Combined Ratio = 70% (Loss Ratio) + 6% (Commissions and Other Expenses) = 76%
To determine profitability, we also need to consider investment yields. The line is profitable if the combined ratio plus the investment yield is less than 100 percent. Let's calculate the total combined ratio plus investment yield for each option:
A. Total = 85% (Combined Ratio) + 10% (Investment Yield) = 95%
B. Total = 75% (Combined Ratio) + 6% (Investment Yield) = 81%
C. Total = 86% (Combined Ratio) + 20% (Investment Yield) = 106%
D. Total = 85% (Combined Ratio) + 12% (Investment Yield) = 97%
E. Total = 76% (Combined Ratio) + 4% (Investment Yield) = 80%
Based on the calculations, option B (commissions and other expenses at 5 percent and investment yields at 6 percent) is the only option where the combined ratio plus the investment yield is less than 100 percent, indicating that the line of insurance is profitable before dividends. So, the correct answer is option B.