74 Bond Yields Yield to cal 1000 par value The bonds had a 9

7-4: Bond Yields Yield to cal 1,000 par value. The bonds had a 99 call premia with 5 years of call years ago the Singleton Company issued 20-year bonds with a 14% annual coupon rate at ther protection. Today Singleton called the bonds a.Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Round your answer to two decimal places 15.33

Solution

The realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called is bond’s yield-to-call .The formula to calculate the bond\'s yield-to-call is

P = C * {(1 – 1/ (1 + YTC) ^ t) / (YTC)} + (CP / (1 + YTC) ^t)

Where,

P = the current market price of bond = $1,000 (par value)

C = coupon payment = 14% of $1000 = $140

CP = the call price (with 9% call premium) =$1,000 * (1+9%) = $1,090 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call = 6 years

YTC = the yield to call =?

Therefore,

$1,000 = $140 *{(1- 1/ (1+ YTC) ^6)/ (YTC)} + ($1,090/ (1+YTC) ^6)

With the help of above equation and by trial and error method we can calculate the value of YTC = 15.03% per year

[Or you can use excel function for YTC calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(6,-140,1000,-1090)” = 15.03%]

Therefore the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called is 15.03%.