1) Fooling Company has a 11.4 percent callable bond outstanding on the market wi
ID: 2713788 • Letter: 1
Question
1) Fooling Company has a 11.4 percent callable bond outstanding on the market with 25 years to maturity, call protection for the next 10 years, and a call premium of $25. What is the yield to call (YTC) for this bond if the current price is 103 percent of par value?
2) Consider a 5.4 percent coupon bond with nine years to maturity and a current price of $1,055.40. Suppose the yield on the bond suddenly increases by 2 percent. Find the duration to estimate the new price of the bond. And Calculate the new bond price.
Explanation / Answer
1) Current Price of bond = 103% * 1000 = $1030
Coupon = 11.4% * 1000 = $114
Callable Period = 10 yeas
Call Premium = $25
Call Price = 1000 + 25 = $1025
Yield to call can be calculated using the rate function excel. The syntax for the same is
=RATE(10,114,-1030,1025)
= 11.04%
2) Current Price of bond = $1055.40
Coupon = 5.4% * 1000 = $54
Period = 9 years
Duration
= (Price of bond with 1% decrease in yield - Price of bond with 1% increase in yield) / (2 * Current Price * 1%)
Current yield =RATE(9,54,-1055.4,1000) = 4.63%
Price with yield of 3.63% =PV(3.63%,9,54,1000) = $1133.85
Price with yield of 5.63% =PV(5.63%,9,54,1000) = $984.10
Duration = (1133.85 - 984.10)/(2 * 1055.40 * 0.01) = 7.09 years
Decrease in price of bond = Duration * Increase in YTM = 7.09 * 2% = 14.18%
New Price of the bond using duration measure = (1 - 0.1418) * 1055.40 = $905.74
Actual Price of the bond with 2% increase in yield = =PV(6.63%,9,54,1000) = $918.59
This difference is coming because duration assumes a linear relationship between the yield and the price. However, actually the relationship is convex. Thus, in case of the case of increase in yield, decrease in the price of the bond using the duration measure is more than the actual decrease in the price of the bond. To correct this, we have to use an additional convexity measure to estimate the new price of the bond. Duration can be used to estimate the new price of the bond for extremely small changes in the yield.
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