Question

(Related to Checkpoint 9.3) (Bond valuation relationships) You own a bond that pays $100 in annual interest, with a $1,000 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. a. What is the value of the bond if the market's required yield to maturity on a comparable-risk bond is 12 percent? (Round to the nearest cent.) b. (i) What is the value of the bond if the yield to maturity on a comparable-risk bond increases to 15 percent? $ (Round to the nearest cent.) b. (ii) What is the value of the bond if the yield to maturity on a comparable-risk bond decreases to 8 percent? $ (Round to the nearest cent.)

Answer 1

Answer a.

Par Value = $1,000
Annual Coupon = $100
Annual YTM = 12%
Time to Maturity = 15 years

Value of Bond = $100 * PVIFA(12%, 15) + $1,000 * PVIF(12%, 15)
Value of Bond = $100 * (1 - (1/1.12)^15) / 0.12 + $1,000 / 1.12^15
Value of Bond = $863.78

Answer b.

If YTM on comparable-risk bond is 15%:

Value of Bond = $100 * PVIFA(15%, 15) + $1,000 * PVIF(15%, 15)
Value of Bond = $100 * (1 - (1/1.15)^15) / 0.15 + $1,000 / 1.15^15
Value of Bond = $707.63

If YTM on comparable-risk bond is 8%:

Value of Bond = $100 * PVIFA(8%, 15) + $1,000 * PVIF(8%, 15)
Value of Bond = $100 * (1 - (1/1.08)^15) / 0.08 + $1,000 / 1.08^15
Value of Bond = $1,171.19

Answer c.

The change in the value of a bond caused by changing interest rate is called interest-rate risk. Based on the answer in part b, a decrease in interest rates (the yield to maturity) will cause the value of a bond to increase; by contrast, an increase in interest rates will cause the value to decrease.

Also, based on the answers in part b, if the yield to maturity (current interest rate)
equals the coupon interest rate, the bond will sell at par.
exceeds the bond’s coupon rate, the bond will sell at discount.
is less than the bond’s coupon rate, the bond will sell at premium.

Answer d.

Par Value = $1,000
Annual Coupon = $100
Annual YTM = 12%
Time to Maturity = 5 years

If YTM on comparable-risk bond is 12%:

Value of Bond = $100 * PVIFA(12%, 5) + $1,000 * PVIF(12%, 5)
Value of Bond = $100 * (1 - (1/1.12)^5) / 0.12 + $1,000 / 1.12^5
Value of Bond = $927.90

If YTM on comparable-risk bond is 15%:

Value of Bond = $100 * PVIFA(15%, 5) + $1,000 * PVIF(15%, 5)
Value of Bond = $100 * (1 - (1/1.15)^5) / 0.15 + $1,000 / 1.15^5
Value of Bond = $832.39

If YTM on comparable-risk bond is 8%:

Value of Bond = $100 * PVIFA(8%, 5) + $1,000 * PVIF(8%, 5)
Value of Bond = $100 * (1 - (1/1.08)^5) / 0.08 + $1,000 / 1.08^5
Value of Bond = $1,079.85

Answer e.

From the findings in part b, we can conclude that a bondholder owing a long-term bond is exposed to higher interest-rate risk than one owing a short-term bond