In: Finance
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?
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.