Aurora Case Study

14.9

A 20-year maturity bond with par value of $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent annual yield to maturity of the bond if the bond price is:

a) $950

On a financial calculator, enter the following:

n = 40; FV = 1000; PV = –950; PMT = 40

You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity equal to: 4.26% × 2 = 8.52%

Effective annual yield to maturity = (1.0426)2 – 1 = 0.0870 = 8.70%

b) $1,000

Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon rate, i.e., 4%. The bond equivalent yield to maturity is 8%.

Effective annual yield to maturity = (1.04)2 – 1 = 0.0816 = 8.16%

c) $1,050

Keeping other inputs unchanged but setting PV = –1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis.

Effective annual yield to maturity = (1.0376)2 – 1 = 0.0766 = 7.66%

14.10

Repeat Problem 9 using the same data, but assuming that the bond makes its coupon payments annually. Why are the yields you computed lower in this case?

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. Using a financial calculator, enter: n = 20; FV = 1000; PV = –price, PMT = 80.

The resulting yields for the three bonds are:

|Bond Price |Bond equivalent yield = |

| |Effective annual yield |

|$950 |8.53% |

|$1,000 |8.00% |

|$1,050 |7.51% |

14.11

Fill in the table below for the following zero-coupon bonds, all of which have par values of $1,000

|Price |Maturity (yrs) |Bond-Equivalent Yield to |

| | |Maturity |...