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In: Finance

Please write out formula and steps A bond is currently sold at $980, it has 20...

Please write out formula and steps

A bond is currently sold at $980, it has 20 years to maturity and 9% coupon rate. The bond will be called in 5 years, the bond will be called at a premium of $1,050 of $1,050, what is the yield to call?

Solutions

Expert Solution

Face value $1,000
Coupen annually 9%
Coupen amount $90
RemainingMaturity years 15
Bond Price $1,050.00
YTM :
Price of bond = Coupen * PVAF( YTM, Maturity) + Redemption value * PVF( YTM,Maturity)
Here bond price is greater than face value hence YTM be less than Coupen rate
         Therefore lets assume YTM be 8%
Price of bond = 90*PVAF(8%,15) + 1000*PVF(8%,15)
90*8.5595+1000*.3152
1085.555

at coupen rate price of bond will be same as face value that is $1000

There fore YTm is between 8% and 9%

YTM = 8% +{ (1085.555-1050/(1085.555-1050)+ (1050-1000) } *(9-8)
8% + 35.555/85.555
8.42%

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