The Jackpot Company

Questions: 1. Three friends (Abel, Barbie and Cain) paid for a lottery ticket in equal shares. Their ticket won the jackpot prize of $10 million. The jackpot company gave the friends three choices to withdraw the $10 million: Option 1 - an immediate lump sum payment of $ X (lesser than $10 million); Option 2 - a yearly equal payment of $1 million over ten years; or Option 3 - a lump sum payment of $10 million in ten years. The opportunity cost of funds is 5 percent per annum.Required:(a) Advise the friends if they should choose option 2 or option 3. Support your answer with appropriate calculations.(b) Under what circumstances would option 1 be the most preferable choice to withdraw the winnings?(c) The friends decided to choose option 1 and negotiated with the jackpot company for $X to be the present value of option 2. They donated $221,735 to a charitable organization and divided the remainder balance amongst them. Abel used his share of the proceeds to invest in a stock fund which promises t o pay him $3,673,320 in five years. Compute the effective annual interest rate on Abels investment.(d) Using the option in part (c), Barbie entrusted her share of the winnings to Cain and Cain placed their winnings in a deferred annuity. The monies earned interest for five years. Thereafter, the annuity paid a fixed yearly amount for ten years. Assuming a rate of interest of 8 percent, what is this annual sum?2. ASR Fashions issued a $1,000 par value bond that pays an 8 percent interest annually. The bond matures in 15 years and is currently selling at $1,125. Your required rate of return is 7 percent.Required:(a) Compute the bonds expected rate of return.(b) Determine the value of the bond to you, given your required rate of return.(c) Should you purchase the bond? Answers: (a) Advise the friends if they should choose option 2 or option 3. Support your answer with appropriate calculations. Option 2 Year Cash Flow PVF @5% Disc PVF 1 $10,00,000.00 0.952 $9,52,380.95 2 $10,00,000.00 0.907 $9,07,029.48 3 $10,00,000.00 0.864 $8,63,837.60 4 $10,00,000.00 0.823 $8,22,702.47 5 $10,00,000.00 0.784 $7,83,526.17 6 $10,00,000.00 0.746 $7,46,215.40 7 $10,00,000.00 0.711 $7,10,681.33 8 $10,00,000.00 0.677 $6,76,839.36 9 $10,00,000.00 0.645 $6,44,608.92 10 $10,00,000.00 0.614 $6,13,913.25 $77,21,734.93 Option 2 Year Cash Flow PVF @5% Disc PVF 1 $100,00,000.00 0.952 $95,23,809.52 2 $100,00,000.00 0.907 $90,70,294.78 3 $100,00,000.00 0.864 $86,38,375.99 4 $100,00,000.00 0.823 $82,27,024.75 5 $100,00,000.00 0.784 $78,35,261.66 6 $100,00,000.00 0.746 $74,62,153.97 7 $100,00,000.00 0.711 $71,06,813.30 8 $100,00,000.00 0.677 $67,68,393.62 9 $100,00,000.00 0.645 $64,46,089.16 10 $100,00,000.00 0.614 $61,39,132.54 Conclusion Under option 2 the total present value is $77,21,734.93 Under option 3 the lump sum money should be asked in 5th year or before as after 5th year the present value of all the cash flows falls below $77,21,734.93 b) Under what circumstances would option 1 be the most preferable choice to withdraw the winnings? Under option 1 the immediate payment would be less than $10 million. This amount we dont know. But we have done the analysis of option 2 and option 3 from which we can conclude that if the amount is more than $95,23,809.52, we should go with option 1 else in the other case we should go with option 2 or option 3 as applicable c) The friends decided to choose option 1 and negotiated with the jackpot company for $X to be the present value of option 2. They donated $221,735 to a charitable organization and divided the remainder balance amongst them. Abel used his share of the proceeds to invest in a stock fund which promises to pay him $3,673,320 in five years. Compute the effective annual interest rate on Abels investment. Here we need to assume an amount below $10 million which is the present value as per option 1. The lump sum amount is $98,21,735.00. The amount left after making a contribution to a charitable organization is $9600000. Share for each person amounts to $ 3200000. Able invested in stock funds that yielded him $3673320 in five years. The effective annual rate of interest is [(1+i/n)n -1] I=annual rate of interest N=number of compounding periods Therefore, $3673320=$3200000[(1+i/5)5-1] Hence, i=8.23% Using the option in part (c), Barbie entrusted her share of the winnings to Cain and Cain placed their winnings in a deferred annuity. The monies earned interest for five years. Thereafter, the annuity paid a fixed yearly amount for ten years. Assuming a rate of interest of 8 percent, what is this annual sum? The formula for calculating the compound interest is A =P(1 + r)t Here A=Amount P=Principal Invested R=Rate of Interest N=Number of years A=$6400000(1+0.08)5 Hence A=$ 9403699.692 The amount is than repaid in 10 yearly instalments. So the annual sum paid for 10 years is $9403699.692/10=$940369.9692 2. ASR Fashions issued a $1,000 par value bond that pays an 8 percent interest annually. The bond matures in 15 years and is currently selling at $1,125. Your required rate of return is 7 percent. a) Compute the bonds expected rate of return. The formula for calculating the return on the bond calculated as follows [Interest (1-Tax rate)-(Redemption Value- Fair Value)/Term of Bond]/ (Redemption Value+ Fair Value)/2 This is calculated as follows Return of Bond=[$80-($1125-$1000)/15]/ ($1125+$1000)/2 =6.75% The required rate of return is 7%. Hence the bond is overvalued. The investor should sell the bond if it is there in his basket as the actual return is less than the required return. In such case the price of bond is going to fell in future b) Determine the value of the bond to you, given your required rate of return. The value of bond is the present value of future expected cash flows discounted at Kd after tax. There is no tax in our case. The present value annuity factor for 15 years at 7% is 9.1079 So the present value of interest is $80*9.1079=$728.633 When we deduct the current selling price from above we will get the value of bond. Hence, the value of the bond is $728.633-$1125.00=-$396.367 c) Should you purchase the bond? The value of bond is negative. Hence the investor should not purchase the bond.