Solving the Financial Challenge - Financial Management

Recall from the “Financial Challenge” at the beginning of this chapter that a lottery winner needs to decide which alternative payoff from the Powerball Lottery is the best option. The ticket holder has two choices:

  1. A lump-sum payment today of $41.4 million; or
  2. Twenty -five beginning -of-the-year payments of $2.948 million each

Based upon a careful study of the material in this chapter, you have decided to compute the rate of return that will make the ticket holder indifferent between the two options.You set up the following problem using the present value of an annuity due formula:

$41,400,000 = $2,948,000(PVIFAi, 25)(1 + i)

This problem can be solved best with the help of a financial calculator, yielding an indifference rate of return of 5.59 percent.

This indifference rate of return can now be compared with the investment opportunity rate of return for investments of similar risk. Because the payment stream from the multistate Lottery Board is virtually risk-free, you believe it is appropriate to compare the 5.59 percent indifference rate of return with the return on 25-year U.S. government Treasury bonds, which are also considered to be free of default risk. If the ticket holder can earn a return greater than 5.59 percent on the Treasury bonds, he or she should take the lumpsum payment and invest it in Treasury bonds, because its present value will exceed the present value of the 25-year annuity payments. On the other hand, if the rate of return on the Treasury bonds is less 5.59 percent, the ticket holder would be better off taking the stream of annuity payments.

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Financial Management Topics