Suppose the opportunity cost of capital is 10 percent and you have just won a $1

Question

Suppose the opportunity cost of capital is 10 percent and you have just won a $1 million lottery that entitles you to $100,000 at the end of each of the next ten years. a. What is the minimum lump sum cash payment you would be willing to take now in lieu of the ten-year annuity? b. What is the minimum lump sum you would be willing to accept at the end of the ten years in lieu of the annuity? c. Suppose three years have passed and you have just received the third payment and you have seven left when the lottery promoters approach you with an offer to settle-up for cash. What is the minimum you would accept (the end of year three)? D) how would your answer to part a change if the first payment came immediately at t=0 and the remaining payments were at the beginning instead of at the end of each year?

Explanation / Answer

present value =100000/1.1 +100000/1.1^2 +.......100000/1.1^10 =614456.7$ a)hence the min lumpsum cash payment willing to take at start =614456.7$ b)min lumpsum payment at the end=100000*1.1^10 +100000*1.1^9+....100000*1.1 =1593724$ c)minimum money to be accepted at the end of 3 is =100000/1.1 +100000/1.1^2 +....+10000/1.1^7 =435526.1$ d)the power of rate decreases by 1 if money is given at the starting of the year

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