How can they be overcome?
17. The bidders in a Dutch auction are as follows:
The number of shares being auctioned is 210,000. What is the price paid by investors? How many shares does each investor receive?
18. An investment bank has been asked to underwrite an issue of 10 million shares by a company. It is trying to decide between a firm commitment where it buys the shares for $10 per share and a best efforts where it charges a fee of 20 cents for each share sold. Explain the pros and cons of the two alternatives.
CHAPTER 3
Insurance Companies and Pension Plans
The role of insurance companies is to provide protection against adverse events. The company or individual seeking protection is referred to as the policyholder. The policyholder makes regular payments, known as premiums, and receives payments from the insurance company if certain specified events occur. Insurance is usually classified as life insurance and nonlife insurance, with health insurance often being considered to be a separate category. Nonlife insurance is also referred to as property-casualty insurance and this is the terminology we will use here.
A life insurance contract typically lasts a long time and provides payments to the policyholder's beneficiaries that depend on when the policyholder dies. A property-casualty insurance contract typically lasts one year (although it may be renewed) and provides compensation for losses from accidents, fire, theft, and so on.
Insurance has existed for many years. As long ago as 200 B.C., there was an arrangement in ancient Greece where an individual could make a lump sum payment (the amount dependent on his or her age) and obtain a monthly income for life. The Romans had a form of life insurance where an individual could purchase a contract that would provide a payment to relatives on his or her death. In ancient China, a form of property-casualty insurance existed between merchants where, if the ship of one merchant sank, the rest of the merchants would provide compensation.
A pension plan is a form of insurance arranged by a company for its employees. It is designed to provide the employees with income for the rest of their lives once they have retired. Typically both the company and its employees make regular monthly contributions to the plan and the funds in the plan are invested to provide income for retirees.
This chapter describes how the contracts offered by insurance companies work. It explains the risks that insurance companies face and the way they are regulated. It also discusses key issues associated with pension plans.
3.1 LIFE INSURANCE
In life insurance contracts, the payments to the policyholder depend – at least to some extent – on when the policyholder dies. Outside the United States, the term life assurance is often used to describe a contract where the event being insured against is certain to happen at some future time (e.g., a contract that will pay $100,000 on the policyholder's death). Life insurance is used to describe a contract where the event being insured against may never happen (for example, a contract that provides a payoff in the event of the accidental death of the policyholder.)4 In the United States, all types of life policies are referred to as life insurance and this is the terminology that will be adopted here.
There are many different types of life insurance products. The products available vary from country to country. We will now describe some of the more common ones.
Term Life Insurance
Term life insurance (sometimes referred to as temporary life insurance) lasts a predetermined number of years. If the policyholder dies during the life of the policy, the insurance company makes a payment to the specified beneficiaries equal to the face amount of the policy. If the policyholder does not die during the term of the policy, no payments are made by the insurance company. The policyholder is required to make regular monthly or annual premium payments to the insurance company for the life of the policy or until the policyholder's death (whichever is earlier). The face amount of the policy typically stays the same or declines with the passage of time. One type of policy is an annual renewable term policy. In this, the insurance company guarantees to renew the policy from one year to the next at a rate reflecting the policyholder's age without regard to the policyholder's health.
A common reason for term life insurance is a mortgage. For example, a person aged 35 with a 25-year mortgage might choose to buy 25-year term insurance (with a declining face amount) to provide dependents with the funds to pay off the mortgage in the event of his or her death.
Whole Life Insurance
Whole life insurance (sometimes referred to as permanent life insurance) provides protection for the life of the policyholder. The policyholder is required to make regular monthly or annual payments until his or her death. The face value of the policy is then paid to the designated beneficiary. In the case of term life insurance, there is no certainty that there will be a payout, but in the case of whole life insurance, a payout is certain to happen providing the policyholder continues to make the agreed premium payments. The only uncertainty is when the payout will occur. Not surprisingly, whole life insurance requires considerably higher premiums than term life insurance policies. Usually, the payments and the face value of the policy both remain constant through time.
Policyholders can often redeem (surrender) whole life policies early or use the policies as collateral for loans. When a policyholder wants to redeem a whole life policy early, it is sometimes the case that an investor will buy the policy from the policyholder for more than the surrender value offered by the insurance company. The investor will then make the premium payments and collect the face value from the insurance company when the policyholder dies.
The annual premium for a year can be compared with the cost of providing term life insurance for that year. Consider a man who buys a $1 million whole life policy at the age of 40. Suppose that the premium is $20,000 per year. As we will see later, the probability of a male aged 40 dying within one year is about 0.0022, suggesting that a fair premium for one-year insurance is about $2,200. This means that there is a surplus premium of $17,800 available for investment from the first year's premium. The probability of a man aged 41 dying in one year is about 0.0024, suggesting that a fair premium for insurance during the second year is $2,400. This means that there is a $17,600 surplus premium available for investment from the second year's premium. The cost of a one-year policy continues to rise as the individual gets older so that at some stage it is greater than the annual premium. In our example, this would have happened by the 30th year because the probability of a man aged 70 dying in one year is 0.0245. (A fair premium for the 30th year is $24,500, which is more than the $20,000 received.) The situation is illustrated in Figure 3.1. The surplus during the early years is used to fund the deficit during later years. There is a savings element to whole life insurance. In the early years, the part of the premium not needed to cover the risk of a payout is invested on behalf of the policyholder by the insurance company.
FIGURE 3.1 Cost of Life Insurance per Year Compared with the Annual Premium in a Whole Life Contract
There are tax advantages associated with life insurance policies in many countries. If the policyholder invested the surplus premiums, tax would normally be payable on the income as it was earned. But, when the surplus premiums are invested within the insurance policy, the tax treatment is often better. Tax is deferred, and sometimes the payout to the beneficiaries of life insurance policies is free of income tax altogether.
Variable Life Insurance
Given
In theory, for a contract to be referred to as life assurance, it is the event being insured against that must be certain to occur. It does not need to be the case that a payout is certain. Thus a policy that pays out if the policyholder dies in the next 10 years is life assurance. In practice, this distinction is sometimes blurred.
