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)?

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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 1 year ago

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