Question

9-22 Co m m 30ulu he choose? 0.22 Consider the decision you might have to make if you won a state lottery worth $105 million. Which would you choose: a lump-sum payment of $54 million today or a payment of $3.5 million each year for the next 30 years? Which should you choose? a. If your opportunity cost is 6 percent, which alternative should you select? b. At what opportunity cost would you be indifferent between the two en alternatives?

Answer 1

C D E F G H I J A B 1 Given 2 Lump sum payment 3 Payment per year 4 Number of years 5 Opportunity cost 54 3.5 30 years 6.0% 7 Solution 8 Part a) At opportunity cost of 6%, which alternative to be selected 10 We know that, 11 12 PVAF (Present value annuity factor) = 13 14 PVF (Present Value Factor) = 15 where r is opportunity and n is Number of year (1+r)^n-1 rX(1+r)^n (1/(1+r)^n 16 17 Hence using above formula we get, 18 19 PVAF (6%,30) = 13.765 20 21 Hence, Value of yearly payment of $3.5 million for 30 years is 23 Value = Yearly payment X PVAF 3.5 X 13.765 48.18 Hence, option to receive lumpsum payment of $54 million must be selected as it's value is greater than 27 Present value of yearly payment. 28 29 Part b) At what opportunity cost you will be indifferent between both alternative Here we need to calculate opportunity cost interest rate) at which NPV of yearly payment shall be 31 lequal lumpsum payment. 32 33 Hence, 34 Opportunity cost = 4.97% 35 Excel Formula =RATE(E4, E3,-E2) 36 37 Here, opportunity cost is calculated using excel formula. 38 39 Hence, at opportunity cost of 4.97%, we shall be indifferent to select either of the alternative 40 41 *Note: We are allowed to answer only one question