Question

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A 11% semiannual pay NYC bond has exactly 12 years to maturity and is currently trading at 104. What is the bond's current YTM? Assuming a 50 basis point increase in yield, what's the bond new price? Assuming a 50 basis point decrease in yield, what's the bond new price?

Answer 1

1. Current YTM has to be found using RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

Please remember that payments are semi-annual

nper=2*12=24

pmt=semi-annual coupon=(11%*1000)/2=110/2=55

pv=104%*1000=1040

fv=1000

=RATE(24,55,-1040,1000,0)=5.20%

Annual yield to maturity=2*5.20%=10.41%

2. Use PV function to find the price of the bond if rate becomes 10.91% (10.41%+0.5%)

rate=10.91%/2=5.46%

nper=2*12=24

pmt=semi-annual coupon=(11%*1000)/2=110/2=55

fv=1000

=PV(5.46%,24,55,1000,0)=$1005.94

Price of the bond=$1005.94

3. If rate becomes 9.91% (10.41%-0.5%)

ate=9.91%/2=4.96%

nper=2*12=24

pmt=semi-annual coupon=(11%*1000)/2=110/2=55

fv=1000

=PV(4.96%,24,55,1000,0)=$1075.53

Price of the bond=$1075.53