Question

As the winner of the Friendly Lottery, you are entitled to one of the following prizes:

a) $80,000 per year forever (the first payment starting next year).

b) $144,000 per year for the next 10 years starting immediately.

c) $320,000 payable every 2 years over 20 years.

d) $20,000 starting next year growing by 5.5% forever. Which prize will provide you a higher present value if r = 7%?

Answer 1

Calculating present value of each option available.

a). for a perpetuity, present value = annual payment/r = 80000/0.07 = $1142857.14

b). PV of an annuity due is calculated using formula

PV = PMT*(1+r)*(1 - (1+r)^-t)/r = 144000*1.07*(1 - 1.07^-10)/0.07 = $1082193.44

c). $320,000 payable every 2 years over 20 years.

2 year rate = 1.07^2 - 1 = 14.49%

So, PV = PMT*(1 - (1+r)^-t)/r = 320000*(1 - (1+0.1449)^-10)/0.1449 = $1637722.01

d).  $20,000 starting next year growing by 5.5% forever.

PV is calculated using constant growth model

PV = CF1/(r-g) = 20000/(0.07-0.055) = $1333333.33

So, Present value of option c is highest.