SECTION 4.3 4.3.1 A 10% bond with face amount 100 is callable on any coupon date
ID: 2469640 • Letter: S
Question
SECTION 4.3 4.3.1 A 10% bond with face amount 100 is callable on any coupon date from 15% years after issue up to the maturity date which is 20 years from issue. (a) Find the price of the bond to yield a minimum nominal annual rate of (i) 12%, (ii) 10%, and (iii) 8%. (b) Find the minimum annual yield to maturity if the bond is pur- chased for (i) 80, (ii) 100, and (iii) 120. 4.3.2.Repeat Exercise 4.3.1 assuming that the bond is callable at a re- demption amount of 110, including the redemption at maturity.Explanation / Answer
Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Callable between the period Nper =15.5 x 2 31 Nper = 20 x 2 40 PMT = $100 x 5% $5 Yield =12%/2 6.00% Bond's Price (PV) @ 20 Years PV(6%,31,-5,-100) $86.07 Bond's Price (PV) @ 15.5 Years Pv(6%,40,-5,-100) $84.95 Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Callable between the period Nper =15.5 x 2 31 Nper = 20 x 2 40 PMT = $100 x 5% $5 Yield =10%/2 5.00% Bond's Price (PV) @ 20 Years PV(5%,31,-5,-100) $100 Bond's Price (PV) @ 15.5 Years Pv(5%,40,-5,-100) $100 Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Callable between the period Nper =15.5 x 2 31 Nper = 20 x 2 40 PMT = $100 x 5% $5 Yield =8%/2 4.00% Bond's Price (PV) @ 20 Years PV(5%,31,-5,-100) $117.59 Bond's Price (PV) @ 15.5 Years Pv(5%,40,-5,-100) $119.79 a) Nominal Rate Price 12.00% $84.95 10.00% $100 8.00% $117.59 a) Nominal Yield Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Nper = 15.5 x 2 31 Nper = 20x 2 40 Pmt $5 price of bond $80 Rate (nper,pmt,pv,fv) =Rate(31,-5,80,-100) 6.52% Rate (nper,pmt,pv,fv) =Rate(40,-5,80,-100) 6.40% Annual yield @ 15.5 years 13.04% Annual yield @ 20 years 12.8% Nominal Yield Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Nper = 15.5 x 2 31 Nper = 20x 2 40 Pmt $5 price of bond $100 Rate (nper,pmt,pv,fv) =Rate(31,-5,100,-100) 5.00% Rate (nper,pmt,pv,fv) =Rate(40,-5,100,-100) 5.00% Annual yield @ 15.5 years 10.00% Annual yield @ 20 years 10.0% Nominal Yield Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Nper = 15.5 x 2 31 Nper = 20x 2 40 Pmt $5 price of bond $120 Rate (nper,pmt,pv,fv) =Rate(31,-5,100,-100) 3.88% Rate (nper,pmt,pv,fv) =Rate(40,-5,100,-100) 3.99% Annual yield @ 15.5 years 7.76% Annual yield @ 20 years 8.0% Price Nominal Yield $80 12.8% $100 10.00% $120 7.76% b) Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Callable between the period Nper =15.5 x 2 31 Nper = 20 x 2 40 PMT = $100 x 5% $5 Yield =12%/2 6.00% Bond's Price (PV) @ 20 Years PV(6%,31,-5,-110) $87.71 Bond's Price (PV) @ 15.5 Years Pv(6%,40,-5,-110) $85.93 Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Callable between the period Nper =15.5 x 2 31 Nper = 20 x 2 40 PMT = $100 x 5% $5 Yield =10%/2 5.00% Bond's Price (PV) @ 20 Years PV(5%,31,-5,-110) $102.2 Bond's Price (PV) @ 15.5 Years Pv(5%,40,-5,-110) $101.42 Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Callable between the period Nper =15.5 x 2 31 Nper = 20 x 2 40 PMT = $100 x 5% $5 Yield =8%/2 4.00% Bond's Price (PV) @ 20 Years PV(5%,31,-5,-100) $120.55 Bond's Price (PV) @ 15.5 Years Pv(5%,40,-5,-100) $121.88 a) Nominal Rate Price 12.00% $85.93 10.00% $101.42 8.00% $120.55 a) Nominal Yield Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Nper = 15.5 x 2 31 Nper = 20x 2 40 Pmt $5 price of bond $80 Rate (nper,pmt,pv,fv) =Rate(31,-5,80,-110) 6.64% Rate (nper,pmt,pv,fv) =Rate(40,-5,80,-110) 6.47% Annual yield @ 15.5 years 13.29% Annual yield @ 20 years 12.93% Nominal Yield Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Nper = 15.5 x 2 31 Nper = 20x 2 40 Pmt $5 price of bond $100 Rate (nper,pmt,pv,fv) =Rate(31,-5,100,-110) 5.14% Rate (nper,pmt,pv,fv) =Rate(40,-5,100,-110) 5.08% Annual yield @ 15.5 years 10.28% Annual yield @ 20 years 10.16% Nominal Yield Face Value (FV) $100 Coupon Rate semiannual = 10%/2 5.00% Nper = 15.5 x 2 31 Nper = 20x 2 40 Pmt $5 price of bond $120 Rate (nper,pmt,pv,fv) =Rate(31,-5,100,-100) 4.03% Rate (nper,pmt,pv,fv) =Rate(40,-5,100,-100) 4.08% Annual yield @ 15.5 years 8.05% Annual yield @ 20 years 8.16% Price Nominal Yield $80 12.93% $100 10.16% $120 8.05%
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