Question

a.	A 9.5 percent coupon (paid semiannually) bond, with a $1,000 face value and 20 years remaining to maturity. The bond is selling at $960. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Yield to maturity___________

% per year

b.	An 10 percent coupon (paid quarterly) bond, with a $1,000 face value and 10 years remaining to maturity. The bond is selling at $902. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Yield to maturity

_______ % per year

c.	An 9 percent coupon (paid annually) bond, with a $1,000 face value and 6 years remaining to maturity. The bond is selling at $1,052. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

Yield to maturity

______ % per year

Answer 1

a.Given:

Face value= $1,000

Market value of the bond= $960

Time period= 20 years*2= 40 semi-annual periods

Coupon rate= 9.5% (7/2=4.75%)

Coupon payments= 0.0475*1000= $47.50

Formula for calculating the bond’s YTM:

Bond price= Cash flow1/(1+YTM)^1+Cash flow 2/(1+YTM)^2+Cash flow 3/(1+YTM)^4………………+Cash flow 40/(1+YTM^40+1000/(1+YTM)^40

960=47.50/(1+YTM^1+47.50/(1+YTM)^2+47.50/(1+YTM)^3+47.50/(1+YTM)^4+47.50/(1+YTM)^5+47.50……+47.50/(1+YTM^40+1000/(1+YTM)^40

YTM is calculated using a trial and error method.

Through trial and error, it is found that the bond’s YTM is 4.983. Therefore, the YTM is 4.983*2= 9.965%

YTM can also be calculated using a financial calculator.

Calculator solution is:

N=20; PMT= 47.50; FV=1,000; PV= -960; PMT=$47.50

CPT---I/Y=4.4062

The YTM is 4.983*2= 9.965% per annum.

b.Given:

Face value= $1,000

Market value of the bond= $902

Time period= 10 years*4= 40 quarter periods.

Coupon rate= 10% (10/4=2.50%)

Coupon payments= 0.0250*1000= $25

Formula for calculating the bond’s YTM:

Bond price= Cash flow1/(1+YTM)^1+Cash flow 2/(1+YTM)^2+Cash flow 3/(1+YTM)^4………………+Cash flow 40/(1+YTM)^40+Maturity value/(1+YTM)^40

902=25/(1+YTM^1+25/(1+YTM)^2+25/(1+YTM)^3+25/(1+YTM)^4+47.50/(1+YTM)^5+..……+25/(1+YTM^40+1000/(1+YTM)^40

YTM is calculated using a trial and error method.

Through trial and error, it is found that the bond’s YTM is 2.918. Therefore, the YTM per annum is 2.918*2= 5.837%

YTM can also be calculated using a financial calculator.

Calculator solution is:

N=40; PMT= 25; FV=1,000; PV= -902; PMT=$25

CPT---I/Y=2.918*2= 5.837%

c.Given:

Face value= $1,000

Market value of the bond= $1,052

Time period= 6 years

Coupon rate= 9%

Coupon payments= 0.09*1000=$90

Formula for calculating the bond’s YTM:

Bond price= Cash flow1/(1+YTM)^1+Cash flow 2/(1+YTM)^2+Cash flow 3/(1+YTM)^4………………+Cash flow 6/(1+YTM)^6+Maturity value/(1+YTM)^6

1052=90/(1+YTM^1+90/(1+YTM)^2+90/(1+YTM)^3+90/(1+YTM)^4+90/(1+YTM)^5+..……+90/(1+YTM^6+1000/(1+YTM)^6

YTM is calculated using a trial and error method.

Through trial and error, it is found that the bond’s YTM is 7.879. Therefore, the YTM is 7.879% per annum.

YTM can also be calculated using a financial calculator.

Calculator solution is:

N=6; PMT= 90; FV=1,000; PV= -1,052;

CPT---I/Y=7.879. Therefore, the YTM is 7.879% per annum.

I hope that was helpful :)