Question

Suppose the semiannual 10% coupon bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return at 10%, or at 13%, or at 7%?

Answer 1

Assuming Par Value of Bond = $100

When, Required rate of Return = 10%

Number of periods to maturity = n = 10 years

Yield to Maturity = r = 0.1

Face Value FV = $100

Annual Coupon Payment P = 0.10*100 = $10

Hence, Value of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 10[1-(1+0.1)-10]/0.1 + 100/(1+0.1)10 = $100

When Required rate of Return = 13%

Number of periods to maturity = n = 10 years

Yield to Maturity = r = 0.13

Face Value FV = $100

Annual Coupon Payment P = 0.10*100 = $10

Hence, Value of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 10[1-(1+0.13)-10]/0.13 + 100/(1+0.13)10 = $83.72

When Required Rate of return = 7%

Number of periods to maturity = n = 10 years

Yield to Maturity = r = 0.07

Face Value FV = $100

Annual Coupon Payment P = 0.10*100 = $10

Hence, Value of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 10[1-(1+0.07)-10]/0.07 + 100/(1+0.07)10 = $121.07