After consistently failing to win the lottery for several years, you notice the

following article in the Wall Street Journal. Here's your chance to buy a lottery

ticket that is a guaranteed winner. But since it will apparently cost a bit over the

original $$1$ ticket price, the winning ticket is considerably out of your price range.

The investment company you work for is$,$ however, interested in such

opportunities. You decide to research a bit further and gather the interest rate

data $($on the next page$)$ for the day before the ticket is auctioned. In your "first

cut" at the analysis, you decide to ignore taxes. The winner will receive the first

of the $16$ payments almost immediately, with the rest stretched out over $15$ years.

If you can purchase the ticket for $$2\mathrm{.}0$ million, what annual rate of return will you get on your

investment? What about if you win the bid at $$1\mathrm{.}5$ million?

Given the current $($July $1,1992)$ prices and yields in the capital markets, what do you think is the

approximate "fair market value" of the ticket?

If you factored taxes into this situation, how would it change your valuation of the ticket?

Tables for Problem #$3$ are extracted from

The Wall Street Journal, July $2,1992$

TREASURY BONDS, NOTES & BILLS

MORTGAGE$-$BACKED SECURITIES

Representative Issues, quoted by Salomon Brothers Inc.

'Based on projections from Salomon's prepayment model, assuming interest

rates remain unchanged from current levels

$\frac{?}{\text{b}\text{a}\text{r}}($ Pricey, but Perhaps the Only Way $)$

To Buy a Certain Lottery Winner

By ANDREA GERLIN

Staff Reporter of The Wall Street Journal

NEW YORK $-$ After the late Solomon

Keith bought a lottery ticket at the Chirag

Newsstand on Wall Street in $1987,$ his

number came up not once but twice.

Mr$.$ Keith won a $$5$ million share of

a larger jackpot but didn't live to enjoy

much of it$.$ Unfortunately, the $55-$year$-$old

bank janitor died in an auto accident $15$

months later, not long after collecting the

second of $21$ annual installments of $$240,245$

each.

As a result, surrogate's court in lower

Manhattan will be the scene of some

unusual bidding tomorrow morning when

Mr$.$ Keith's $$3\mathrm{.}8$ million taxable lottery

proceeds $-$ the remainder after he and his

heirs collected five payments$-$are offered

in an estate auction.

This time, the award will cost more

than the "dollar and a dream" advertised

by New York state's lottery. A minimum

bid of $$1\mathrm{.}3$ million has already been set in

this latest of gambles on interest rates.

Although the $$240,245$ annual payments

may look attractive, would$-$be investors

should bear in mind that the end payment

in $2007$ would have a net present value of

$$68,281,$ discounted at $8\mathrm{.}18\%$ annually.

Charles Milo, an attorney involved

in the auction, declines to speculate about

whether the minimum bid is a bargain or

how much the prize may fetch. "That's for

each individual to calculate, depending on

what they think the future of interest rates

is going to be$,"$ he says.

Using the $15-$year Treasury bond at

recent yields as a benchmark, a Wall

Street financial analyst predicts that the

successful bid is likely to hover around $$2\mathrm{.}1$

million. But if a bidder were to walk away

with rights to the payments in exchange

for the minimum $$1\mathrm{.}3$ million, the financial

analyst figures that the investor will have

parked the money in the equivalent of a

$17\%$ investment. And while that yield

would be high, the risk is low, because the

state isn't likely to default.

In the past, living prize winners have

sold their lottery futures in private auc$-$

tions, but many states prohibit such trans$-$

actions. New York state allows them only

with a judge's approval. A public estate

auction is even less common.

The lucky bidder will buy into an

exclusive club of $800$ grand prize winners.

Merely playing this game may require

membership in an exclusive club, though:

Bidders must present a certified or bank

check payable to the public administrator

of New York for $$130,000.$