A 9.5 percent coupon (paid semiannually) bond, with a $1,000 face value and 20 y
ID: 2812340 • Letter: A
Question
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))
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))
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))
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))
Explanation / Answer
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 :)
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