A straight bond has a coupon of 8% paid semi-annually and a maturity of 3 years.

Question

A straight bond has a coupon of 8% paid semi-annually and a maturity of 3 years. Currently the market interest rate for comparable 3-year maturity bonds in 5%.

A. What is the bond's price today?

B. What will the bond's price be in six months after the next coupon is paid, assuming the market interest rate for comparable bonds is unchanged?

C. If you buy the bond today and sell it after the next coupon is paid, what is the total rate of return on your investment?

A 20-year maturity bond has an annual coupon of 7% paid semi-annually.

A. Find the current yield and the yield to maturity if the bond is priced at 103.5.

B. Assume the coupon is paid annually. Find the current yield and yield to maturity of the bond is priced at 103.5.

C. Explain why you would expect the yields to be lower in the second case.  

Explanation / Answer

1

Par Value or Face value=1000

Coupons=C1=C2=C3=C4=C5=C6=8%*1000/2=40

r=5%

Price=C1/(1+r/2)+C2/(1+r/2)^2+C3/(1+r/2)^3+C4/(1+r/2)^4+C5/(1+r/2)^5+(C6+Face value)/(1+r/2)^6

=40/1.025+40/1.025^2+40/1.025^3+40/1.025^4+40/1.025^5+1040/1.025^6

=1082.62

Bond's Price in six months=+C2/(1+r/2)+C3/(1+r/2)^2+C4/(1+r/2)^3+C5/(1+r/2)^4+(C6+Face value)/(1+r/2)^5

=40/1.025+40/1.025^2+40/1.025^3+40/1.025^4+1040/1.025^5

=1069.687

Return=5% as yield is constant

2

a)

Coupon=7%*100/2=3.5

So, annual coupons=3.5*2=7

Current Yield=Annual Coupon/Current Price=7/103.5=6.76%

YTM Calcualtion:

0=-103.5+3.5/(1+r/2)+3.5/(1+r/2)^2............3.5/(1+r/2)^40+100/(1+r/2)^40

=>0=-103.5+3.5/(1+r/2)*(1-1/(1+r/2)^40)/(1-1/(1+r/2))+100/(1+r/2)^40

=>0=-103.5+7/r*(1-1/(1+r/2)^40)+100/(1+r/2)^40

Hence, YTM=r=6.68%

b)

Coupon=7%*100=7

So, annual coupons=7*1=7

Current Yield=Annual Coupon/Current Price=7/103.5=6.76%

YTM Calcualtion:

0=-103.5+7/(1+r)+7/(1+r)............7/(1+r)^20+100/(1+r)^20

=>0=-103.5+7/r*(1-1/(1+r)^20)+100/(1+r)^20

Hence, YTM=r=6.67%

The yield are lower in second case because in semiannual money is received earlier than annual and which can be reinvested

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