just won the lottery and has been given the choice of two payout options: Option #1:...

just won the lottery and has been given the choice of two payout options:

Option #1: He can receive $31,250 every six months for sixteen years.

Option #2: He can wait and receive $33,750 every six months for sixteen years with the first payment coming one and a half years from now.

The appropriate discount rate is 9 percent compounded semiannually.

present value of option 1? 2? and what option should be chosen and why?

Solutions

Expert Solution

Ans:- we will use the PV function of excel to find the Present value of annuities.

For:- option 1, Rate=9%/2, Nper=16*2, Pmt=-$31,250, FV=0

For:- Option 2, Rate=9%/2, Nper=16*2, Pmt=-33,750, FV=0, TYPE=1

Note:- In excel formula we put TYPE=0, when investment or withdrawal is made at the end of the period and TYPE=1, when investment or payment is made at the start of of the period. In option 2 we have assumed that withdrawal is made at the start of the period.

Present Value of Option 2 is calculated by Future Value / (1+r)^n, where r is the interest rate per period and n is the number of periods.

From the above analysis it clear that option1 should be chosen because it has a higher PV value than option 2.

jeff jeffy answered 2 years ago

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