Question

Turquoise Company purchased a life insurance policy on the company's chief executive officer, Joe. After the company had paid $400,000 in premiums, Joe died and the company collected the $1.5 million face amount of the policy. The company also purchased group term life insurance on all its employees. Joe had included $16,000 in gross income for the group term life insurance premiums. Joe's widow, Rebecca, received the $100,000 proceeds from the group term life insurance policy. Rebecca can exclude the life insurance proceeds of $100,000, but Turquoise Company must include $1,100,000 ($1,500,000 - $400,000) in gross income. Turquoise Company and Rebecca can exclude the life insurance proceeds of $1,500,000 and $100,000, respectively, from gross income. Turquoise Company can exclude $1,100,000 ($1,500,000 - $400,000) from gross income, but Rebecca must include $84,000 in gross income. Turquoise Company must include $1,100,000 ($1,500,000 - $400,000) in gross income and Rebecca must include $100,000 in gross income. None of these.

Answer 1

The actuarially fair premium for each group can be calculated based on the probability of death and the benefit amount. If the insurance company charges the actuarially fair premium to the group as a whole, it may face adverse selection.

Step-by-step explanation:

If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group can be calculated based on the probability of death and the benefit amount. For the group of men with a family history of cancer, 20% have a chance of dying in the next year (1 in 50 chance) and the benefit amount is $100,000. So, the actuarially fair premium for this group would be $100,000 divided by 0.2 (the probability of death), which is $500,000.

For the group without a family history of cancer, 80% have a chance of dying in the next year (1 in 200 chance) and the benefit amount is also $100,000. The actuarially fair premium for this group would be $100,000 divided by 0.8 (the probability of death), which is $125,000.

If the insurance company is offering life insurance to the entire group without knowing the family cancer histories, the actuarially fair premium for the group as a whole can be calculated by taking the weighted average of the premiums for each group. Since 20% of the group has a family history of cancer, the weighted average premium would be 20% of $500,000 plus 80% of $125,000, which equals $145,000.

If the insurance company tries to charge the actuarially fair premium to the group as a whole rather than each group separately, it may face adverse selection. This means that people with a higher risk of death (those with a family history of cancer) may be more likely to purchase the insurance, while those with a lower risk may choose not to. This imbalance of risk could lead to higher claims for the insurance company, resulting in financial losses.