Bond yields One year ago Clark Company issued a 10-year, 12% semiannual coupon b
ID: 2776637 • Letter: B
Question
Bond yields
One year ago Clark Company issued a 10-year, 12% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 6 years at a price of $1,060, and it now sells for $1,130.
What is the bond's nominal yield to maturity? Round your answer to two decimal places.
{C}%
What is the bond's nominal yield to call? Round your answer to two decimal places.
%
Would an investor be more likely to earn the YTM or the YTC?
-Select-Since the YTM is above the YTC, the bond is not likely to be called.Since the YTC is above the YTM, the bond is not likely to be called.Since the coupon rate on the bond has declined, the bond is not likely to be called.Since the YTM is above the YTC, the bond is likely to be called.Since the YTC is above the YTM, the bond is likely to be called.Item 3
What is the current yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places.
%
Is this yield affected by whether the bond is likely to be called?
If the bond is called, the current yield and the capital gains yield will remain the same but the coupon rate will be different.
If the bond is called, the current yield will remain the same but the capital gains yield will be different.
If the bond is called, the current yield and the capital gains yield will remain the same.
If the bond is called, the capital gains yield will remain the same but the current yield will be different.
If the bond is called, the current yield and the capital gains yield will both be different.
-Select-IIIIIIIVVItem 5
What is the expected capital gains (or loss) yield for the coming year? Round your answer to two decimal places.
%
Is this yield dependent on whether the bond is expected to be called?
If the bond is not expected to be called, the appropriate expected total return is the YTC.
If the bond is expected to be called, the appropriate expected total return will not change.
The expected capital gains (or loss) yield for the coming year depends on whether or not the bond is expected to be called.
The expected capital gains (or loss) yield for the coming year does not depend on whether or not the bond is expected to be called.
If the bond is expected to be called, the appropriate expected total return is the YTM.
Explanation / Answer
YTM = 10.11%
YTC = 9.84%
Since YTM is above YTC the bond is not likely to be called
Current Yield = 10.62%
If the bond is called, the current yield and capital gains yield will both be different
Expected Capital gains yield = 3%
The yield is dependent on whether the bond is expected to be called as this changes the market price of the bond.
If the bond is expected to be called, then the appropriate expected total return is YTC.
working
Par Value =$ 1000
Coupon Rate = 12% Semi-annual
Semi-annual coupon payment = 1000 * 12% * .5 = $ 60
Current Price = $ 1130
Let r be the yield to maturity
$ 1130 = $ 60 * [ (1-(1/(1+r)^12*2))/r] + $1000/(1+r)^12*2
$1130 - $ 60 * [ (1-(1/(1+r)^24))/r] - $1000/(1+r)^24 = 0
Let r be equal to 11%, that semi annual yield is 11%/2 = 0.055.Substituting the value RHS of the above equation becomes
$1130 - $ 60 * [ (1-(1/(1.055)^24))/0.055] - $1000/(1.055)^24
= $ 1130 - $ 60 * [ (1-(1/3.6145899))/0.055] - $1000/3.6145899
= $ 1130 - $ 60 * [(1-0.2766566)/0.055] – 276.6566
= $ 1130 - $ 60 * (0.7233434/0.055) – 276.6566 =$ 1130 - $ 789.10 – 276.66
= $64.24
At r is equal to 10% the RHS of equation will become
= $1130 - $ 60 * [ (1-(1/(1.05)^24))/0.05] - $1000/(1.05)^24
= $1130 - $ 60 * [ (1-(1/(3.2250999))/0.05] - $1000/3.2250999
= $ 1130 - $ 60 * (1-0.3100679/0.05) – 310.06791 = $ 1130 – $ 827.92 - 310.07
= -$ 7.99
Therefore semi annual rate of return would be between 5% and 5.5%
Semi-annual rate of return = 0.05 + [((-7.99) (0.05-0.055))/(64.24+7.99)]
= 0.05 + [0.03995/72.23]
= 0.05 + 0.000553 = 0.050553 or 5.055% (rounded off)
Ytm = 5.055 * 2 = 10.11%
Yield to Maturity = 10.11%
Period to call = 6 years
Call Price = $1060
Let c be the yield to call, then
$ 1130 = $ 60 * [ (1-(1/(1+c)^6*2))/r] + $1060/(1+c)^6*2
Re-arranging the above equation
$ 1130 - $ 60 * [ (1-(1/(1+c)^6*2))/r] - $1060/(1+c)^6*2 = 0
At c= 10% of semi-annual rate of return of 0.05 RHS becomes
$ 1130 - $ 60 * [ (1-(1/(1.05)^12))/0.05] - $1060/(1.05)^12
= $ 1130 - $ 60 * [ (1-(1/1.7958563))/0.05] - $1060/1.7958563
= $ 1130 - $ 60 * (0.4431626/0.05) - $ 590.238 = $ 1130 - $531. 80 - $ 590.24
= 7.96
At c =9.5% or semi-annual rate of return of 4.75%, RHS will become
$ 1130 - $ 60 * [ (1-(1/(1.0525)^12))/0.0475] - $1060/(1.0525)^12
= $ 1130 - $ 60 * [ (1-(1/1.74521276))/0.0475] - $1060/1.74521276
= $ 1130 - $ 60 (0.4270039/0.0475) – 607.38 = $ 1130 - $ 539.37 - $ 607.38
= -$16.75
Semi-annual rate of return = 0.05 + ((7.96) *(0.0475-0.05)/(7.96-(-16.75))
= 0.05 + (-0.0199/24.71)
= 0.05 – 0.0008053 = 0.0491947 or 4.92% (rounded off)
YTC = 4.92% * 2 = 9.84%
Current yield = annual cash inflows / current price of the bond = $ 60 * 2 /$ 1130
= $ 120 / $ 1130 = 0.10619 or 10.62%
Capital gains yield = (Current Price – Par Value) / Par Value = (1130 – 1000)/1000
= 30/1000 = 0.03 or 3%
If the bond is expected to be called, then price of the bond would be
$ 60 * [ (1-(1/(1+c)^12))/r] + $1060/(1+c)^12 =