Question

Henry Long has just learned he has won a $500,600 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Henry takes all the money today, the state and federal governments will deduct taxes at a rate of 46% immediately. (2) Alternatively, the lottery offers Henry a payout of 20 equal payments of $39,200 with the first payment occurring when Henry turns in the winning ticket. Henry will be taxed on each of these payments at a rate of 26%. Click here to view factor tables Compute the present value of the cash flows for lump sum payout. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to O decimal places, e.g. 458,581.) Lump sum payout $ 270324 Assuming Henry can earn an 10% rate of return (compounded annually) on any money invested during this period, compute the present value of the cash flows for annuity payout. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) Present value of annuity payout $ Which pay-out option should he choose? Annuity Payout

Answer 1

solution: Part a: Lump sum payout 500600*(1-0.46) 270,324 Part b: after tax Annuity due=39200*(1-0.26) 129,008 | x PVAD(10%,20) 9.36492 Present value 271,658 **factor working: PVAD(R%,n) PVAD(10%,20) 1+(1-((1+r)^-(n-1)))/r 1+(1-((1+0.1)^-(20-1)))/0.1 9.36492 Part c: Annuity payout (as it has higher PV)