Question

You just purchased a 30-year bond with 6% annual coupon, par value of $1000, and 15 years to maturity. The bond makes payments semi-annually and the interest rate in the market is 7.0%. Calculate bond price as of today

• $936.74 • $1015.76 • $918.04 • $908.04

You just purchased a 30-year bond with 6% annual coupon, par value of $1000, and 15 years to maturity. The bond makes payments semi-annually and the interest rate in the market is 7.0%. The bond can be called in 6 years, starting June 1, 2026 at 117% of par. Calculate its yield to call

• 10.36% semiannually • 6.5% semiannually • 5.11% semiannually • 3.5% semiannually

Answer 1

Solution

a. Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Face value =1000

n=number of periods to maturity=15*2=30

r-intrest rate per period=Semiannual YTM=7/2=3.5%

Semi annual Coupon payment=coupon rate *face value/2=6%*1000/2=30

Putting values in formuLA

Price of bond=30*((1-(1/(1+.035)^30))/.035)+1000/(1+.035)^30

Solving we get

Price of bond=$908.04

b

Now the current bond price is alraedy calulated=908.04

Price of bond=Present value of coupon payments+Present value of value at the time of call

Price of bond=Coupon payment*((1-(1/(1+i)^m))/i)+Call price/(1+i)^m

Here

Call price=117%*face value=117%*1000=1170

m=number of periods to call=6*2=12

ri-intrest rate per period=Semiannual yield to call

Semi annual Coupon payment=coupon rate *face value/2=6%*1000/2=30

Putting values in formula

908.04=30*((1-(1/(1+i)^12))/i)+1000/(1+i)^12

Solving we get

i=5.105%

Thus

Yield to call=5.11% semiannual

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