Question

Lottery problem. You win a lottery of $10 million. You have the following two options to receive it. First, to receive $1million each year at the end of each year for 10 years (annuity option). Second, to receive $5 million right now (cash option). Make sure that you draw the timelines for the two options in order to understand the alternatives. Show your work in answering the questions.

a) What is the present value of the annuity option? Assume the discount rate is 10%.

b) What is the present value of the cash option? Assume the discount rate is 10%.

c) Given your answers in (a) and (b), which option should you take and why?

d) At what discount rate would you be indifferent between the annuity and cash options, that is, at what discount rate the annuity and cash options would be equally valuable.

Answer 1

a)Present Value of Annuity option = 1 million*PVAF(10%, 10 years)

= 1 million*6.145

= $6.145 million

b)Present Value of Cash option = $5 million

c)The annuity option should be taken since is has higher worth in present value terms

d)Let the discount rate be x%

1 million*PVAF(x%, 10 years) = 5

PVAF(x%, 10 years) = 5

From present value annuity factor table,

PVAF(15%, 10 years) = 5.0188

and PVAF(16%, 10 years) = 4.8332

Using interpolation, x = 15% + (5.0188-5)/(5.0188-4.8332)

= 15.10%