Question

Question 4: There is a bond that pays $100 per year interest, with a $1,000 par value. It matures in 15 years. The market required yield to maturity on a comparable bond is 12%.

1. What is the value of the bond?
2. How does the value change if the yield to maturity on a comparable bond increase to 15%? What if it decreases to 8%.
3. Explain the above questions (part b) with the concepts of interest rate risk, premium bonds and discount bonds.
4. Recalculate the answer in b, with the assumption that the bond matures in 5 years (instead of 15 years).
5. Explain the above questions (part d) with the concepts of interest rate risk, premium bonds and discount bonds.

Answer 1

4 a) Coupon = 100
Par Value = 1000
Maturity = 15 years
YTM = 12%
Price of Bond = PV of Coupons + PV of Par Value = 100*(1-(1+12%)^-15)/12% + 1000/(1+12%)¹⁵ = 863.78

if new YTM = 15%
Price of Bond = PV of Coupons + PV of Par Value = 100*(1-(1+15%)^-15)/15% + 1000/(1+15%)¹⁵ = 707.63

if new YTM = 8%
Price of Bond = PV of Coupons + PV of Par Value = 100*(1-(1+8%)^-15)/8% + 1000/(1+8%)¹⁵ = 1171.19

b) Higher the YTM higher is the interest rate risk.
When YTM is less than coupon rate then it is called premium bond.
When YTM is more than coupon rate then it is called discount bond.

c) New Maturity = 5 Years

YTM = 12%
Price of Bond = PV of Coupons + PV of Par Value = 100*(1-(1+12%)^-5)/12% + 1000/(1+12%)⁵ = 927.90

if new YTM = 15%
Price of Bond = PV of Coupons + PV of Par Value = 100*(1-(1+15%)^-5)/15% + 1000/(1+15%)⁵ = 832.39

if new YTM = 8%
Price of Bond = PV of Coupons + PV of Par Value = 100*(1-(1+8%)^-5)/8% + 1000/(1+8%)⁵ = 1079.85

Higher the YTM higher is the interest rate risk.Lower maturity lower the risk.
When YTM is less than coupon rate then it is called premium bond.Lower maturity lower the risk.
When YTM is more than coupon rate then it is called discount bond.Lower maturity lower the risk.

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