Question

The concept that timing of the receipt of cash affects it is demonstrated by present and future value. These values are based on several variables: the amount of cash, whether it is a one-time payment, a series of equal payments, or unequal payments, and when the cash is received. The interest rate is another variable that has a very large effect on the present and future values. Use these concepts to answer why a lottery winner would choose to take their winnings as a lump sum today instead of receiving more cash if they took their winnings as a series of payments over a number of years. Provide numerical examples based on winning the lottery. You will have to design the examples yourself. Use a discount rate of 4% and payoff period of 30 years

Answer 1

Discount rate is 4%

Let the lottery value be 30 million

If one takes series of payments, he will get 30/30=1 million every year with first payment 1 year from now

Present value=Amount/rate*(1-1/(1+rate)^t)=1/4%*(1-1/1.04^30)=17.292033 million

However, if he is given 18 million as lumpsum today he will accept lumpsum even though the total cahs payment in series is 30 million

This happens because of time value of money and if he invests the lumpsum at 4% the value he will receive in total at 30 years will be more than the value from series of payments of 1 million every year