A bond’s yield to maturity (YTM) is the percentage return that it is expected to
ID: 2744493 • Letter: A
Question
A bond’s yield to maturity (YTM) is the percentage return that it is expected to generate if the bond is assumed to be held until it matures. Calculating a bond’s YTM requires you to make several assumptions. Which of the following is one of these assumptions? A. The bond is callable or B. The probability of default is zero.
Consider the following case of Blue Moose Home Builders Inc.: Blue Moose Home Builders Inc. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1160.35. However, Blue Moose Home Builders Inc. may call the bonds in eight years at a call price of $1,060.
What are the YTM and yield to call (YTC) on bonds? Blue Moose Home Builders Inc.’s bonds have a yield-to-maturity (YTM) of A. 8.24%, B. 6.84%, C. 9.35%, D. 7.36%, E. 9.23%, F. 6.05%, G. 7.83%?
and a yield-to-call (YTC) of A. 9.23%, B. 7.36%, C. 7.83%, D. 6.91%, E. 6.05%, F. 9.35%, 6.84%, G. 8.24%?
If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Blue Moose Home Builders Inc.’s bonds? A. 5 years, B. 8 years, C.18 years, D. 10 years
If Blue Moose Home Builders Inc. issued new bonds today, what coupon rate must the bonds have to be issued at par? A. 8.24%, B. 6.84%, C. 9.23%, D. 6.91%, E. 9.35%, F. 6.05%, G. 7.83%, H. 7.36%
Explanation / Answer
Answer 1
Option B - the probability of default is zero.
Answer - case of Blue Moose Home Builders Inc
YTM can be calculated by the following formula
1160.35 = 90PVIFA(18,X%)+1090PVIF(18,X%)
For the calculation of X , we have to take the help of the hit and trial method
Assume X = 8%
therefore = 90 PVIFA (18,8%) = 90/0.08 {1-1/(1.08)^18} = 1125{1-0.25} = 843.75
1000PVIF(18,8%) = 1090 {1/(1.08)^18} = 1000 { 0.25} =250.25
total value at X = 8% = 843.75+250.25 = 1094
Assume X = 7%
therefore = 90 PVIFA (18,7%) = 90/0.07 {1-1/(1.07)^18} = 1285.71{1-0.296} = 905.31
1090PVIF(18,7%) = 1090 {1/(1.07)^18} = 1090 { 0.212} =295.86
total value at X = 7% = 905.31+295.86 = 1201.67
By interpolation we get = 8+1201.67-1160.35 / 1201.67-1094 = 7+(41.32/107.67) = 7.38
Therefore YTM will be option D
YTC can be calculated by the following formula
1160.35 = 90PVIFA(8,X%)+1060PVIF(8,X%)
For the calculation of X , we have to take the help of the hit and trial method
Assume X = 6%
therefore = 90 PVIFA (8,6%) = 90/0.06 {1-1/(1.06)^8} = 1500{1-0.627} = 558.88
1060PVIF(8,6%) = 1060 {1/(1.06)^8} = 665.06
total value at X = 6% = 1223.94
Assume X = 7%
therefore = 90 PVIFA (8,7%) = 90/0.07 {1-1/(1.07)^8} = 537.42
1060PVIF(8,7%) = 1060 {1/(1.07)^8} = 616.93
total value at X = 7% = 1154.35
By interpolation we get = 6+(1223.94-1160.35 / 1223.94-1154.35) = 6.91
Therefore YTC will be option D
Answer For calculation of duration of the bond
duration = Rc/Rd*PVIFA(Rd,n)*(1+Rd)+{1-(Rc/Rd)*n where as Rc= current yeild Rd= yeild to maturity n= term to maturity Durartion = 0.077/0.0736* 9.8 *1.0736 + {1-(0.077/0.0736)} *18 = 0.077/0.0736* 9.8 *1.0736 + {1-(0.077/0.0736)} *18 10.1758 or 10 years = option D Last Answer The coupon rate is equal to the YTM if the Bond is issued at the par , so the corrent answer is option H i.e. 7.36%Related Questions
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