until 10 years from today. rgratulations: You just won a $1 M lottery. BUT, it w

Question

until 10 years from today. rgratulations: You just won a $1 M lottery. BUT, it will not pay the $1.000,000 Coincidentally, you were watching late nig ht TV and heard an ad for one of those y your lottery prize today with an immediate single cash payment: a. What is the least you would sell the claim for comparable risk? if you can earn 6% on an investment of (4 points) e Imillion in 10 years or $ 80,000 a year for the next 10 years, with the first $80,000 in one year. Which would you choose and why? (5 points) b. I the $1 million in 10 years arcent lis the appropriate interest rate and the lottery company gave you the choice of

Explanation / Answer

XI.. a. Since the payment of $1,000,000 would be received after 10 years, so the least amount at which the claim should be sold, considering return on 6% on an investment of same risk, should be determined by discountig $1,000,000 by 6% per annum. Hence,

$1,000,000 / (1 + 6%)^10 = $1,000,000/ 1.06^10 = $558,395

b. If the lottery company offers $80,000 a year for next 10 years, with the first $80,000 in one year, we should determine hte present value of such offer by discounting it with 6% interst rate as,

NPV = CF1/(1.06^1) + CF2/(1.06^2)... + CF10/(1.06^10)

NPV = $80,000/(1.06^1) + $80,000/(1.06^2) ... + $80,000/(1.06^10)

NPV = $588,807

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