A 15-year maturity bond with par value of $1,000 makes annual coupon payments at a coupon rate of 10%. Find the bond equivalent and effective annual yield to maturity of the bond for the following bond prices. List Bond Equivalent Annual Effective annual
bond prices Yield to maturity Yield to maturity
a $940 % %
b $1,000 % %
c $1,040 % %

A. Bond equivalent 10.82%

Effective annual yield to maturity of the bond 11.11%

B. Bond equivalent 10%

Effective annual yield to maturity of the bond 10.25%

C. Bond equivalent 9.49%

Effective annual yield to maturity of the bond 9.73%

Explanation:

A. Calculation to Find the bond equivalent

We would determine the yield to maturity on a semi-annual basis using Financial Calculator which is:

N = 10*2 = 30

PV = -940

PMT = [10%/2]*1000 = 50

FV = 1000

Press CPT, then I/Y, which gives us 5.41%

Bond equivalent yield to maturity=5.41% × 2

Bond equivalent yield to maturity= 10.82%

Calculation to determine the Effective Annual Yield To Maturity of the bond

Effective annual yield to maturity = (1+.0541)^2– 1

Effective annual yield to maturity = (1.0541)^2– 1

Effective annual yield to maturity =1.1111 – 1

Effective annual yield to maturity = 0.1111 *100

Effective annual yield to maturity = 11.11%

Therefore the bond equivalent and effective annual yield to maturity of the bond will be:

Bond equivalent 10.82%

Effective annual yield to maturity of the bond 11.11%

b. Calculation to determine the bond equivalent

Based on the information given the bond is selling at par which therefore means that the yield to maturity on a semi annual basis will be the same as the semi annual coupon 5%.

Bond equivalent yield to maturity =5%*2

Bond equivalent yield to maturity= 10%.

Calculation to determine Effective annual yield to maturity

Effective annual yield to maturity = (1+.05)^2– 1

Effective annual yield to maturity = (1.05)^2– 1

Effective annual yield to maturity=1.1025-1

Effective annual yield to maturity=.1025*100

Effective annual yield to maturity =10.25%

Therefore the bond equivalent and effective annual yield to maturity of the bond will be:

Bond equivalent 10%

Effective annual yield to maturity of the bond 10.25%

c.Calculation to determine the bond equivalent

N = 10*2 = 30

PV = -1,040

PMT = [10%/2]*1000 = 50

FV = 1000

Bond equivalent yield to maturity=9.49%, or 4.75% on a semi-annual basis.

Calculation to determine the Effective Annual Yield To Maturity of the bond

Effective annual yield to maturity = (1+.0475)^2– 1

Effective annual yield to maturity = (1.0475)^2– 1

Effective annual yield to maturity =1.0973– 1

Effective annual yield to maturity = 0.0973*100

Effective annual yield to maturity = 9.73%

Therefore the bond equivalent and effective annual yield to maturity of the bond will be:

Bond equivalent 9.49%

Effective annual yield to maturity of the bond 9.73%

answer(d) all of the choices are correct;