Question

Redo the previous problem using the same data, but now assume that the bondmakes its coupon payments annually. Why are the yields you compute lower in thiscase?

A 20-year maturity bond with par value \(1,000 makes semiannual coupon payments ata coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity ofthe bond if the bond price is:

a. \)950

b. \(1,000

c. \)1,050

Short answer

a. 8.53% and 8.53%

b. 8% and 8 %

c. 7.51% and 7.51%

Step-by-step solution

Calculation of bond equivalent and effective annual yield to maturity of the bond if the bond price is $950

Since the bond payments are now made annually instead of semi-annually, the bond equivalent yield to maturity is the same as the effective annual yield to maturity.

Available inputs: n = 20, FV = 1000, PV = – 950, PMT = 80.

The yield to maturity on a semi-annual basis = Yield To Maturity=(Face Value/Current BondPrice)^(1/Years To Maturity)−1

= (1000 / -950))^(1/20)−1

= 8.53%.

Since a bond equivalent yield to maturity = Effective annual yield to maturity

= 8.53%

Calculation of bond equivalent and effective annual yield to maturity of the bond if the bond price is $1000

b. Since the bond is selling at par, the yield to maturity on annual basis is the same as the annual coupon, 4%.

The bond equivalent yield to maturity is 8%.

Since a bond equivalent yield to maturity = Effective annual yield to maturity

= 8%

Calculation of bond equivalent and effective annual yield to maturity of the bond if the bond price is $1050

Available inputs: n = 20, FV = 1000, PV = –1050, PMT = 80.

The yield to maturity on a semi-annual basis = Yield To Maturity=(Face Value/Current Bond Price)^(1/Years To Maturity)−1

= (1000 / -1050))^(1/20)−1

= 7.51 %.

Since a bond equivalent yield to maturity = Effective annual yield to maturity

= 7.51%

Explanation on yields being lower with annual coupon payments

The yields of annual coupon rates are lower when compared with semi-annual coupon payments. It is, therefore, less attractive to investors who receive less payment after more time.