CHAPTER 9: TIME VALUE ANALYSIS Homework 4.4, Chapter 9 a. Assume that you just S
ID: 2820073 • Letter: C
Question
CHAPTER 9: TIME VALUE ANALYSIS Homework 4.4, Chapter 9 a. Assume that you just S30 million in the Texas lottery, and hence the state will pay you 20 annual payments of S1.5 million at the end of each year. If the rate of return on securities of similar risk to the lottery earning (e.g., the rate on 20-year U.S. Treasury bonds) is 5%, what is the present value of your winnings? Option 1: a lump sum payment of S30 million up front -Option 2: 20 annual payments of $1.5 million b. Considering this, which option should you take? Explain your answer.Explanation / Answer
Answer a:
Option 1:
A lump sum payment of $30,000,000 up front.
As payment is up front, Present value of winnings under option 1 = $30,000,000
Option 2:
Annual payments at the end of each year = $1,500,000
Number of annual payments = 20
Rate of return = 5%
Present value = Annual payments * [1 - 1/ (1 + Rate of return) Number of annual payments ] / Rate of return
= $1,500,000 * [1 - 1/ (1 + 5%) 20 ] / 5%
= $18,693,315.51
Present value of winnings under option 2 = $18,693,315.51
Answer b:
I shall take option 1 (Upfront lump sum payment of $30,000,000) since Present value of option 1 is higher than present value of option 2 by ($30,000,000 - $18,693,315.51 =) $11,306,684.49