Question

Sandy wins $2 million in the lottery and she has to choose between the following options:

Option 1) $2,000,000 today

Option 2) 10 annual payments of $245,000 per year starting today.

Option 3) $80,000 per year every year forever starting one year from today.

Option 4) 10 payments of $255,000 per year starting 2 years from today.

Regardless of the option she chooses, she would invest the funds in an investment earning 4% compounded quarterly.

Which option would she choose?  Show your work.  

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+4/(4*100))^4-1)*100

Effective Annual Rate% = 4.06

2

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 245000*((1-(1+ 4.06/100)^-10)/(4.06/100))*(1+4.06/100)

PV = 2061685.92

3

PV of perpetual CF = Perpetual CF/interest rate

PV of perpetual CF = 80000/0.0406

PV of perpetual CF = 1970443.35

4

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 255000*((1-(1+ 4.06/100)^-10)/(4.06/100))

PV = 2062114.52

Future value = present value*(1+ rate)^time

2062114.52 = Present value*(1+0.0406)^1

Present value = 1981659.16

Choose option 2