Question

 (Bond valuation relationships)  You own a bond that pays $100 in annual interest, with a $1000 par value. It matures in 15 years. The market's required yield to maturity on a comparable-risk bond is 12 percent. a.  Calculate the value of the bond. b.  How does the value change if the yield to maturity on a comparable-risk bond (i) increases to 15 percent or (ii) decreases to 8 percent? c.  Explain the implications of your answers in part b as they relate to interest-rate risk, premium bonds, and discount bonds. d.  Assume that the bond matures in 5 years instead of 15 years and recalculate your answers in parts a and b. e.  Explain the implications of your answers in part d as they relate to interest-rate risk, premium bonds, and discount bonds.

Round to nearest cent

Answer 1

We can calculate the value of bonds using the present value (PV) function of Excel or financial calculators as shown below:

Part c

Discount bonds are more sensitive to rates going down than they are to rates going up. If rates go down, the prices of discount bonds shoot up. For premium bonds, it is reverse, if rates go down the fall in their value will be more than the rise if rates go up.

Part d

Part e

The implication of this is that short term bonds are less sensitive to interest rate changes as compared to long term bonds as we can see that for the same changes in YTM rates, the prices of 5-year bond fluctuated less than the 15-year bond.

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