Question

1. (10 Points) You purchase a 15-year U.S. Treasury bond (maturity amount of $1,000) which has an 8-percent coupon payment. You pay a price of $1,090.80 for the bond; at the time you purchase the bond you are told that the bond has a yield-to-maturity (implied interest rate) of 7 percent. (a) Using the interest-rate tables, verify that the bond has a 7-percent yield-to-maturity using the present-value tables. Show your calculations and carefully explain your reasoning. Also, explain why the bond does not have a yield-to-maturity equal to its coupon rate of 8 percent. (b) If you discover that the yield-to-maturity or interest rate on the bond rises to 10 percent immediately after you purchase the bond, at what price could you now sell the bond? Do you have a gain or loss on your initial investment in the bond? Explain.

Answer 1

80 Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate. (a) verifying of YTM of 7% discounting discounted year cashflow factor at7% cash flow 1 80 0.9346 74.7663551 2 0.8734 69.8750983 3 80 0.8163 65.3038302 4 80 0.7629 61.031617 5 80 0.7130 57.0388944 6 80 0.6663 53.3073779 7 80 0.6227 49.8199794 8 80 0.5820 46.5607284 9 80 0.5439 43.5146994 10 1080 0.5083 549.017236 total cashflow 1070.23582

80 actual YTM computng irr using excel IRR= 6.72% which is rounded to 7% discounting discounted year cashflow year cashflow factor at 6.72% cash flow 0 -1090.8 1 80 0.9370 74.96252 1 80 2 0.8780 70.24224 2 80 3 0.8227 65.81919 3 4 0.7709 61.67465 4 80 5 80 0.7224 57.79109 5 80 6 80 0.6769 54.15207 6 80 7 80 0.6343 50.7422 7 80 8 80 0.5943 47.54704 8 80 9 0.5569 44.55307 9 80 10 1080 0.5218 563.593 1080 total cash flow 1091.077 which is approximatly equal to price of the bond ($1090.90) 80 80 80 80 10

5 80 proof of why the bond does not have a YTM of 8% discounting discounted year cashflow factor at 8% cash flow 1 80 0.9259 74.0740741 2 80 0.8573 68.5871056 3 80 0.7938 63.5065793 4 80 0.7350 58.8023882 5 0.6806 54.4466558 6 80 0.6302 50.4135702 7 80 0.5835 46.6792316 8 80 0.5403 43.2215108 9 80 0.5002 40.0199174 10 1080 0.4632 500.248967 total cash flow 1000 which is not equal to the price of the bond. So the YTM is not 8%. Also, when YTM is equal to the coupon rate price of the bond will be the same as the maturity amount.

(b) If YTM becomes 10% the price of the bond will be as follows 1 2 3 4 discounting discounted year cashflow factor at 10% cash flow 80 0.9091 72.7272727 so the price I will be able to sell the bond will be $877.11 80 0.8264 66.1157025 so I will incurr a loss of (1090.80-877.11) 213.69 80 0.7513 60.1051841 As bond prices increase, bond yields fall. For example, assume an investor 80 0.6830 54.6410764 purchases a bond that matures in five years with a 10% annual coupon rate 5 80 0.6209 49.6737058 and a face value of $1,000. Each year, the bond pays 10%, or $100, in 6 80 0.5645 45.1579144 interest. Its coupon rate is the interest divided by its par value. 7 80 0.5132 41.0526495 If interest rates rise above 10%, the bond's price will fall if the investor decides 8 80 0.4665 37.3205904 to sell it. For example, imagine interest rates for similar investments rise to 80 0.4241 33.9278095 12.5%. The original bond still only makes a coupon payment of $100, which 10 1080 0.3855 416.386753 would be unattractive to investors who can buy bonds that pay $125 now that total cash flow 877.108658 interest rates are higher. If the original bond owner wants to sell her bond, the price can be lowered so that the coupon payments and maturity value equal yield of 12%. In this case, that means the investor would drop the price of the bond to $927.90. 9