Question

Problem 2 Comparing Options Using Present Value Concepts

After hearing a knock at your front door, you are surprised to see the Prize Patrol from a large, well-known magazine subscription company. It has arrived with the good news that you are the big winner, having won $12.5 million.

You discover that you have three options:

(1) you can receive $1.25 million per year for the next 10 years,

(2) you can have $10 million today, or

(3) you can have $4 million today and receive $1 million for each of the next eight years.

Your lawyer tells you that it is reasonable to expect to earn 10 percent on investments.

a) What is the present value of the above options?

b) Which option do you prefer?

Answer 1

a) Calculation showing present value of each option:

(i) to receive $1.25 million per year for the next 10 years

Present Value = 1250000* Present Value of Annuity Factor 10% for 10 years

=1250000*6.14457

=7,680,713

(ii) to have $10 million today:

Present Value = 10,000,000

(iii) to have $4 million today and receive $1 million for each of the next eight years:

Present Value = 4000000+ (1000000* Present Value of Annuity Factor 10% for 8 years)

= 4000000+(1000000*5.33493)

= 9,334,930

b) Present Value of each Option

(i) 7,680,713

(ii) 10,000,000

(iii) 9,334,930

Since Option (ii) has higher present value prefer option (ii) to have $10 million today