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Chapter 20 - UN-15B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...

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UN-15B BASIC DURATION CALCULATION YTM 7% Year 1 70 0.0654 130 0.0855 2 70 0.1223 130 0.1598 3 70 0.1714 130 0.2240 4 70 0.2136 130 0.2791 5 70 0.2495 130 0.3260 6 70 0.2799 130 0.3657 7 70 0.3051 130 0.3987 8 70 0.3259 130 0.4258 9 70 0.3427 130 0.4477 10 1070 5.4393 1130 4.0413 Bond price Duration Bond price Duration $1,000 7.5152 $1,421 6.7535 =NPV(B3,B6:B15) =SUM(F6:F15) Excel formula 7.5152 <-- =DURATION(DATE(1996,12,3),DATE(2006,12,3),7%,B3,1) Approximating Price Changes Using Duration Actual Bond D P A -47.61 7.5152 $1,000 0.007 -49.17 <-- =-C28*D28*E28/(1.07) B -60.92 6.7535 $1,421 0.007 -62.80 Using Excel's MDuration formula: MDuration of bond A 7.0236 <-- =MDURATION(DATE(1996,12,3),DATE(2006,12,3),7%,7%,1) 0.007 Bond price $1,000.00 49.17 MDuration of bond B 6.3117 <-- =MDURATION(DATE(1999,10,31),DATE(2009,10,31),13%,7%,1) 0.007 Bond price 1,421 62.80 <-- =C42*C41*C40 (in this case--10 years). Babcock's formula N 10 Bond maturity r 7% Current market interest rate C 13% Bond coupon Price 1,421.41 <-- =PV(B51,B50,-B52*1000)+1000/(1+B51)^B50 y 9.15% Current yield PVIF(r,N) 7.02 <-- =PV(B51,B50,-1) D 6.7535 <-- =B50*(1-B54/B51)+B54/B51*B55*(1+B51) C t,A t*C t,A /P A *(1+YTM) t C t,B t*C t,B /P B *(1+YTM) t P r -DP r/(1+r) r -DP r/(1+r) Product of 3 terms above = -DP r/(1+r) r -DP r/(1+r) Note that the formulas in cells C35 and C40 use different dates! This doesn't matter in the Excel functions
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