You have just won a $3,900,000 lottery which pays out $130,000 at the beginning of every...

You have just won a $3,900,000 lottery which pays out $130,000 at the beginning of every year for 30 years. If the required rate of return on lottery winnings is 7.5%, then how much did you win (i.e. at what price are you willing to sell your winnings for)?

Expert Solution

The cash flow stream constitutes an annuity due

Present value of annuity due= P*((1-(1+r)^-n)/r)*(1+r)

Where P= Periodical cash flow ($130,000), r= rate of return (7.5%) and n= number of payments (30)

Plugging the values,

Amount actually woe (Present Value of payments) PVA_Due= 13000*((1-(1+0.075)^-30)/0.075)*(1+0.075)

= 130000* 11.81038627* 1.075

= $1,650,501.48

jeff jeffy answered 2 years ago

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