Question

As a winner of a lottery you can choose one of the following prizes:

1) £1 million now.

2) £1.5 million at the end of six years.

3) £80,000 a year forever, starting in one year.

4) £150,000 for each of the next ten years, starting in one year.

If the discount rate is 8 per cent, which is the most valuable prize?

Answer 1

Find the present value of the different options.
1)1 million now.
The present value is 1000000.
2) 1.5 million at the end of six years.
Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is 8% and t is the time period in years that is 6.
Present value = 1500000/((1.08)^6)
Present value = 1500000/1.586874
The present value is 945254.4.
3) 80000 a year forever starting in one year.
Present value of a perpetuity = C/r
C = 80000
r = .08
Present value = 80000/.08
The present value is 1000000.
4)150,000 for each of the next ten years, starting in one year.
Present Value = Future value/ ((1+r)^t)
where r is the interest rate that is 8% and t is the time period in years.
t	1	2	3	4	5	6	7	8	9	10
future value	150000	150000	150000	150000	150000	150000	150000	150000	150000	150000
present value	138888.9	128600.8	119074.8	110254.5	102087.5	94525.44	87523.56	81040.33	75037.35	69479.02
sum of present values	1006512
The present value is 1006512.
Since option 4 (150,000 for each of the next ten years, starting in one year) has the highest present value (1006512), option 4 is the most valuable prize.