Solution Chapter 3 What Do Interest Rates Mean and What Is Their Role in Valuation?

a. The Yield to Maturity (YTM) is the nominal rate of return which investors would realize if they held the bond to maturity and the bond did not default.

A bond with an annual coupon of $70 and originally sold at par for $1,000. The current market interest rate (yield to maturity) is 8%. This bond will sell at _______. Assuming no change in market interest rates, the bond will present the holder with capital ________ as it matures.

 10. The interest rate used to compute the present value of a future cash flow is called the:

The yield to maturity on a 15-year bond is a true estimate of the cost of 30-year bond

3. Which of the following statements about the yield-to-maturity is true? a) Discounting all cash flows of a bond with the bond’s yield-to-maturity only gives us the correct price if we have a flat term structure of interest rates. b) The yield-to-maturity is upwards sloping. c) The yield-to-maturity is always a spot rate. d) Several of the above statements are true. e) None of the above statements are true. E is correct. The yield-to-maturity, y is the constant hypothetical interest rate that solves P = 1 FV c 1− + T y (1 + y) (1 + y)T

13. What is the formula for the Present Value (PV) for a finite stream of cash flows (1 per year) that lasts for 10 years?

∆P/P = –D*(∆y) D* = D/(1 + y) = 7/1.073 = 6.52 ∆P/P = –D*(∆y) = –6.52(–0.09%) = .59% New price = $1,073(1.0059) = $1,079.33 Learning Objective: 11-02 Compute the duration of bonds; and use duration to measure interest rate sensitivity.

The Yield to Maturity (YTM) of a bond is:   Interest rate that makes the present value of the bond’s

2. An 8 percent semiannual coupon bond is priced at $1,204.60. The bond has a

Correct Answer:    Question: Compute the duration of a par value bond with a coupon rate of 8% and a remaining time to maturity of 3  years. Assume coupon interest is paid annually and the bond has a face value $100.  Correct Answer:    Question: The duration of a bond that pays coupon interest annually is 8.05 years. The yield to maturity of the bond  is 10%. If the yield falls by 25 basis points, what is the percentage change in the price of the bond?  Correct Answer:    Question: Which of the following are true about the interest‐rate sensitivity of coupon bonds?   I     Bond prices and yields are inversely related.  II    Prices of long‐term bonds tend to be more sensitive to interest rate changes than prices of short‐term bonds.  III   Interest‐rate risk is directly related to the bond's coupon rate.  IV    The sensitivity of a bond's price to a change in its yield to maturity is inversely related to the yield to maturity at  which the bond is currently selling.    Correct Answer:    Question:  You have an obligation to pay $148 in four years and 2 months. In which bond would you invest your  $100 to accumulate this amount, with relative certainty, even if the yield on the bond declines to 9.5% immediately  after you purchase the bond? All bonds pay interest annually and have a face value of $100.     Selected Answer:

The bonds have 20 years to maturity, pay interest at 9.3%, have a par value of $1,000 and are currently selling for $890.

b. Generate a graph or table showing how the bond’s present value changes for semi-annually compounded interest rates between 1% and 15%.

2. The discount rate for this bond would be 0.70%. I started with an appropriate discount rate to derive my bond purchase price, since I would not purchase a bond without finding out ahead of time what a good price should be.

Through this method, we obtained theoretical yields of the 4.25% coupon bond and 10.625% coupon bond to be 2.899% and 2.639% respectively. The corresponding theoretical prices of the bonds are $108.27 for the 4.25% coupon bond and $149.31 for the 10.625% coupon bond (see Table 1 above).

Coupon bond is one that is below its nominal value. 99.05 It is less than 100 percent of the cash value of the price, which will be traded. Above the face value of the bond premium bond. 101,15 more than 100 percent of the cash value of your price quote. Market interest rates rise above the coupon rate of the bond discount bond when the bond is. Market interest rates, the bond 's coupon rate is below the bonds when the bond underwriters.