Question

You just won a lottery that promises to pay you $1 million exactly 10 years from today. Because the $1 million payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate lump-sum cash payment.

What is the least you will sell your claim for if you could earn the following rates of return on similar-risk investments during the 10-year period? Make sure to show your calculations for each the interest rates.

            1.         8 percent

            2.         9 percent

            3.         15 percent

Rework part (a) under the assumption that the $1 million payment will be received in 15 rather than 10 years.

Based on your findings in parts (a) and (b), discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

Answer 1

Present value = Future Value/(1+r)^n where r is the rate and n is the time period.

At 8%= 1,000,000/((1.08)^10)=$463,193.49
At 9%=1,000,000/((1.09)^10)=$422,410.81
At 15%=1,000,000/((1.15)^10)=$247,184.71

For 15 years:
At 8%= 1,000,000/((1.08)^15)=$315,241.70

At 9%=1,000,000/((1.09)^15)=$274,538.04
At 15%=1,000,000/((1.15)^15)=$122,894.49

As rate of return increases PV decreases. Similarily as time increases present value decreases due to more discounting.