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7-1 With your financial calculator, enter the following:
N = 10; I/YR = YTM = 9%; PMT = 0.08 × 1,000 = 80; FV = 1000; PV = VB =? PV = $935.82.
7-2 VB = $985; M = $1,000; Int = 0.07 × $1,000 = $70.
a. Current yield = Annual interest/Current price of bond = $70/$985. = 7.11%.
b. N = 10; PV = -985; PMT = 70; FV = 1000; YTM =? Solve for I/YR = YTM = 7.2157% ≈ 7.22%.
c. N = 7; I/YR = 7.2157; PMT = 70; FV = 1000; PV =? Solve for VB = PV = $988.46.
7-7 Percentage Price at 8% Price at 7% Change 10-year, 10% annual coupon $1,134.20 $1,210.71 6.75% 10-year zero 463.19 508.35 9. 5-year zero 680.58 712.99 4. 30-year zero 99.38 131.37 32. $100 perpetuity 1,250.00 1,428.57 14.
7-10 a. Solving for YTM:
N = 9, PV = -901.40, PMT = 80, FV = 1000 I/YR = YTM = 9.6911%.
b. The current yield is defined as the annual coupon payment divided by the current price.
CY = $80/$901.40 = 8.875%.
Expected capital gains yield can be found as the difference between YTM and the current yield.
CGY = YTM – CY = 9.691% – 8.875% = 0.816%.
Alternatively, you can solve for the capital gains yield by first finding the expected price next year. N = 8, I/YR = 9.6911, PMT = 80, FV = 1000 PV = -$908.76. VB = $908.76.
Hence, the capital gains yield is the percent price appreciation over the next year.
CGY = (P 1 – P 0 )/P 0 = ($908.76 – $901.40)/$901.40 = 0.816%.
c. As long as promised coupon payments are made, the current yield will not change as a result of changing interest rates. However, as rates change they will cause the end-of- year price to change and thus the realized capital gains yield to change. As a result, the realized return to investors will differ from the YTM.
7-11 a. Using a financial calculator, input the following to solve for YTM:
N = 20, PV = -1100, PMT = 60, FV = 1000, and solve for YTM = I/YR = 5.1849%.
However, this is a periodic rate. The nominal YTM = 5.1849%(2) = 10.3699% ≈ 10.37%.
For the YTC, input the following: N = 8, PV = -1100, PMT = 60, FV = 1060, and solve for YTC = I/YR = 5.0748%.
However, this is a periodic rate. The nominal YTC = 5.0748%(2) = 10.1495% ≈ 10.15%.
So the bond is likely to be called, and investors are most likely to earn a 10.15% yield.
b. The current yield = $120/$1,100 = 10.91%. The current yield will remain the same; however, if the bond is called the YTC reflects the total return (rather than the YTM) so the capital gains yield will be different.
c. YTM = Current yield + Capital gains (loss) yield 10.37% = 10.91% + Capital loss yield -0.54% = Capital loss yield.
This is the capital loss yield if the YTM is expected.
However, based on our calculations in part a the total return expected would actually be the YTC = 10.15%. So, the expected capital loss yield = 10.15% – 10.91% = -0.76%.
7-16 First, we must find the amount of money we can expect to sell this bond for in 5 years. This is found using the fact that in five years, there will be 15 years remaining until the bond matures and that the expected YTM for this bond at that time will be 8.5%.
N = 15, I/YR = 8.5, PMT = 90, FV = 1000 PV = -$1,041.52. VB = $1,041.52.
This is the value of the bond in 5 years. Therefore, we can solve for the maximum price we would be willing to pay for this bond today, subject to our required rate of return of 10%.
N = 5, I/YR = 10, PMT = 90, FV = 1041. PV = -$987.87. VB = $987.87.
You would be willing to pay up to $987.87 for this bond today.
