Question

(Bond valuation ) You own a bond that pays $120 in annual interest, with a $1,000 par value. It matures in 10 years. Your required rate of return is 11 percent. a. Calculate the value of the bond. b. How does the value change if your required rate of return (1) increases to 14 percent or (2) decreases to 7 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 4 years instead of 10 years. Recompute your answers in part (b ). e. Explain the implications of your answers in part (d ) as they relate to interest rate risk, premium bonds, and discount bonds.

Show work in excel if possible

Answer 1

a) Coupon = 120
Par Value = 1000
Maturity = 10
YTM = 11%
a) Price of bond = PV of Coupons + PV of Par Value = 120*(1-(1+11%)^-10)/11% + 1000/(1+11%)¹⁰ = 1058.80

YTM = 14%
Price of bond = PV of Coupons + PV of Par Value = 120*(1-(1+14%)^-10)/14% + 1000/(1+14%)¹⁰ = 895.68

YTM = 7%
Price of bond = PV of Coupons + PV of Par Value = 120*(1-(1+7%)^-10)/7% + 1000/(1+7%)¹⁰ = 1351.18

b) If YTM = 11% risk premium is less and it is a premium bond.
If YTM =14% risk premium is more and it is a discount bond
If YTM = 7% risk premium is less and it is a premium bond.

c) Maturity = 4
YTM = 11%
Price of bond = PV of Coupons + PV of Par Value = 120*(1-(1+11%)^-4)/11% + 1000/(1+11%)⁴ = 1031.02

YTM = 14%
Price of bond = PV of Coupons + PV of Par Value = 120*(1-(1+14%)^-4)/14% + 1000/(1+14%)⁴ = 941.73

YTM = 7%
Price of bond = PV of Coupons + PV of Par Value = 120*(1-(1+7%)^-4)/7% + 1000/(1+7%)⁴ = 1169.36

e) If YTM = 11% risk premium is less and it is a premium bond . Risk is less than higher maturity bond
If YTM =14% risk premium is more and it is a discount bond Risk is less than higher maturity bond
If YTM = 7% risk premium is less and it is a premium bond. Risk is less than higher maturity bond

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