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Which investment alternative should be chosen

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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.

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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 ...

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Decision Models

Pharmgen Corporation is a pharmaceutical company developing a new drug to fight cancer. It recently discovered a rival company is just one year away from finishing its development in a similar drug which will take away some market share if released. Pharmgen identifies two possible scenarios. The first one, which has a probability of 0.30, is if its development finishes ahead of its rival. In this case Pharmgen estimates that its profit will be $100 million. The second one, which has a probability of 0.70, is if its development finishes after its rival does. In this case, Pharmgen estimates that its profit will be $30 million only.

Management in Pharmgen Corporation has come up with three possible decisions. The first one, the base case, is to leave things the way it is. The second one is to embark on an aggressive advertising campaign which would change the profit number in the two scenarios to $120 million and $15 million respectively (after all the costs are subtracted). The third decision is to sell its current development to the rival company. In this case the overall profit is $40 million in both scenarios.
What would be the best option based on the following criterion?

1. Maximax
2. Maximin
3. Minimax regret
4. Expected value

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