Question

Both Bond A and Bond B have 7.8 percent coupons and are priced at par value. Bond A has 9 years to maturity, while Bond B has 16 years to maturity woints a. If interest rates suddenly rise by 2.2 percent, what is the percentage change in price of Bond A and Bond B? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) eBook Print References %A in Price Bond A Bond B % b. If interest rates suddenly fall by 2.2 percent instead, what would be the percentage change in price of Bond A and Bond 87 (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) %A in Price Bond A Bond B

Answer 1

Answer: % Change in Price -12.67% -17.21% a. Bond A Bond B b. Bond A Bond B 15.23% 22.86% Workings for Part-a): Bond A Existing Proposed 7.8% 10.0% 9 9 $78 $1,000 $1,000 0 $1,000.00 $873.30 Annual yield to maturity, RATE # of Years to maturity, NPER Annual coupon receipts, PMT Maturity value at the end, FV Annual compounding type, TYPE Bond Price Bond B Existing Proposed 7.8% 10.0% [Proposed = 7.8% + 2.2% = 10.0%] 16 $78 $78 ($1000 x 7.8%] $1,000 $1,000 (Assumed Par value of the bond for both the cases] 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $1,000.00 $827.88 [Ref: NOTE-1] $78 % Change in Bond Price when interest rises by 2.2% -12.67% [($873.3 - $1000.00) / $1000.00] -17.21% [($827.88 - $1000.00) / $1000.00]

NOTE-1: For all calculations, value for pmt & fv are negative as they denote cash inflows; type = 0 because coupons paid at the end of each year only. For Bond A's Existing: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=7.8%; nper=9; pmt=-78; fv=-1000; type = 0. For Bond A's Proposed: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=10.0%; nper=9; pmt=-78; fv=-1000; type = 0. For Bond B's Existing: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=7.8%; nper-16; pmt=-78; fv=-1000; type = 0. For Bond B's Proposed: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=10.0%; nper=16; pmt=-78; fv=-1000; type = 0. D E Bond-A Existing 7.8% Proposed =B3+2.2% Bond-B Existing 7.8% 16 NM to 000 Annual yield to maturity, RATE 4 # of Years to maturity, NPER 5 Annual coupon receipts, PMT Maturity value at the end, FV Annual compounding type, TYPE 8 Bond Price Proposed =E3+2.2% 16 $1,000*7.8% $1,000 $1,000*7.8% $1,000 $1,000*7.8% $1,000 $1,000*7.8% $1,000 =PV(B3,B4,-B5,-B6,B7) =PV(C3,C4, C5,-C6,c7) =PV(E3, E4,-E5,-E6, E7) =PV(F3, F4,-F5,-F6,F7) 10 % Change in Bond Price when interest rises by 2.4% =(C8-B8)/B8 =(F8-E8)/E8

Workings for Part-(b): Bond A Existing Proposed 7.8% 5.6% 9 $78 $78 $1,000 $1,000 Annual yield to maturity, RATE # of Years to maturity, NPER Annual coupon receipts, PMT Maturity value at the end, FV Annual compounding type, TYPE Bond Price 16 Bond B Existing Proposed 7.8% 5.6% [Proposed = 7.8% - 2.2% = 5.6%] 16 $78 $78 ($1000 x 7.8%] $1,000 $1,000 (Assumed Pace value of the bond for all cases] O 0 = 0 if coupons paid at the end of each period; 1 if coupons paid at the beginning of each period. $1,000.00 $1,228.57 [Ref: NOTE-2] $1,000.00 $1,152.28 % Change in Bond Price when interest falls by 2.4% 15.23% 22.86% [($1152.28 - $1000.00) / $1000.00] [($1228.57 - $1000.00) / $1000.00] NOTE-2: For all calculations, value for pmt & fv are negative as they denote cash inflows; type = 0 because coupons paid at the end of each year only. For Bond A's Existing: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=7.8%; nper=9; pmt=-78; fv=-1000; type = 0. For Bond A's Proposed: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=5.6%; nper=9; pmt=-78; fv=-1000; type = 0. For Bond B's Existing: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=7.8%; nper=16; pmt=-78; fv=-1000; type = 0. For Bond B's Proposed: Bond Price is calculated using EXCEL FUNCTION PV(rate,nper,pmt,fv,type) where rate=5.6%; nper=16; pmt=-78; fv=-1000; type = 0.

B D G Bond-A Existing 7.8% Proposed =B3-2.2% 9 E F Bond-B Existing Proposed 7.8% =E3-2.2% 16 $1,000*7.8% $1,000*7.8% $1,000 $1,000 0 0 =PV(E3, E4, E5,-E6, E7) =PV(F3, F4,-F5,-F6,F7) 3 Annual yield to maturity, RATE 4 # of Years to maturity, NPER 5 Annual coupon receipts, PMT 6 Maturity value at the end, FV 7 Annual compounding type, TYPE 8 Bond Price 16 $1,000*7.8% $1,000*7.8% $1,000 $1,000 0 =PV(B3,B4,-B5,-B6,B7) =PV(C3,C4,-C5,-C6,c7) = (C8-B8)/B8 =(F8-E8)/E8 10 % Change in Bond Price when interest falls by 2.4% 11