Mark Grace Inc. has $572,000 to invest. The company is trying to decide between two alternative uses of the funds. One alternative provides $80,000 at the end of each year for 12 years, and the other is to receive a single lump sum payment of $1,900,000 at the end of the 12 years. Which alternative should Grace select? Assume the interest rate is constant over the entire investment.
Here we have a simple annuity vs lump sum payment question. First, some background info:
What is an Annuity?
An annuity is a series of payments made at regular intervals over a period of time. Annuities are issued by insurance companies. Typically, you pay in an amount of money and receive regular payments in return.
State lotteries are typically paid as annuities. A 10 million dollar winner does not receive 10 million dollars upon winning. The winner receives a payout of $500,000 per year for 20 years. The state has purchased an annuity at a cost considerably less than 10 million dollars to do so.
Many company retirement plans are annuities that will pay a regular income to the retiree for his or her lifetime.
Income for Life
The original driving force behind annuities was an income for life. Insurance companies could statistically predict the life expectancy of a large group of people with a fair degree of accuracy. Their annuity product could then be priced accordingly. With life insurance, you collect if you die. With a life annuity, you collect if you live. It's the life insurance "bet" in reverse.
The annuities became popular as a means of growing invested dollars tax deferred. The deferral opportunities coupled with changes in regulations have lead to a huge growth in the sale of annuities.
If you choose the lump sum payment, the present value for this option would be $1,057,991.
If you choose the annual payments, the present value for this option would be ...