Question

The first two questions below rely on the following assumptions: Exactly one year ago, you purchased $10,000 of U.S Treasury Bonds. These bonds have a maturity date 30 years from the time of purchase. The annual coupon rate on these bonds at the time of purchase was 4%. The U.S Treasury today has issued 30 year bonds with an initial coupon rate of 5%. There are no transactions fees to buy or sell these bonds. 1. Calculate the current price of these bonds if you were to sell them today. (Hint: use formula from table 18.5). Also, provide a written explanation of why the price you receive for selling these bonds is different than face value. 2. Calcualte the amount of interest income you received to date from this investment.

Answer 1

Solution 1:

Current price of bond = Present value of maturity and interest amount discounted at 5%

= ($10,000*4%) * Cumulative PV factor at 5% for 29 periods + $10,000 * PV Factor at 5% for 29th period

= $400 * 15.14107 + $10,000 * 0.242946 = $8,486

The price received fro selling these bonds is different then face value because interst rate has been increased to 5% and these bond will pay only 4% interest for next 29 years, therefore in order provide return equivalent to market, bond will be sold at discount.

Soution 2:

Amount of interest income received to date from this investment = $10,000 * 4% = $400