What are the individual YTMs of the following bonds? Also, what is the weighted
ID: 2792029 • Letter: W
Question
What are the individual YTMs of the following bonds? Also, what is the weighted average YTM of the bond table?
Bond Prices as of December 20, 2016
Issue
Price
April 2019 4.75%
100.50
March 2020 7.75%
105.25
May 2021 6.13%
105.28
Dec 2021 8.75%
106.13
March 2022 5.75%
94
Oct 2022 6%
94
Jan 2023 6.13%
95.34
March 2025 7.50%
98.80
May 2034 7.45%
87.75
Dec 2026 7.35%
90
Issue
Price
April 2019 4.75%
100.50
March 2020 7.75%
105.25
May 2021 6.13%
105.28
Dec 2021 8.75%
106.13
March 2022 5.75%
94
Oct 2022 6%
94
Jan 2023 6.13%
95.34
March 2025 7.50%
98.80
May 2034 7.45%
87.75
Dec 2026 7.35%
90
Explanation / Answer
Computation of Individual YTM . c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-Y + B(1 + r)-Y = P where c = annual coupon payment (in dollars, not a percent) Y = number of years to maturity B = par value P = purchase price OR YTM = C+F-P/N F+P/2 C=coupan rate F=face value P=price N=maturity Bond Prices as of December 20, 2016 Issue Price YTM April 2019 4.75% 100.5 4.57% 4.75(1+r)^-1+4.75(1+r)^-2+4.75(1+r)^-3+100(1+r)^-3=100.5 r=4.57% OR 4.57% March 2020 7.75% 105.25 6.21% May 2021 6.13% 105.28 4.91% Dec 2021 8.75% 106.13 7.25% March 2022 5.75% 94 7.01% Oct 2022 6% 94 7.27% Jan 2023 6.13% 95.34 7.00% March 2025 7.50% 98.8 7.69% May 2034 7.45% 87.75 8.83% Dec 2026 7.35% 90 8.90% Computation of weighted avg. YTM of bond table YTM Maturity(yrs) Product 4.57% 3 13.70% 6.21% 4 24.85% 4.91% 5 24.55% 7.25% 5 36.26% 7.01% 6 42.05% 7.27% 6 43.61% 7.00% 7 48.97% 7.69% 9 69.21% 8.83% 18 159.01% 8.90% 10 89.01% 69.64% 73 551.23% weighted avg. YTM of bond table = 7.55%
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