Bond P is a premium bond with a coupon rate of 8 percent. Bond D has a coupon ra
ID: 2617941 • Letter: B
Question
Bond P is a premium bond with a coupon rate of 8 percent. Bond D has a coupon rate of 3 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 5 percent, and have seven years to maturity. What is the current yield for bond P and bond D? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Current yield Bond P % Bond D % If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P and bond D? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Capital gains yield Bond P % Bond D %
Explanation / Answer
Solution: 1st Current yield Bond P 6.82% Bond D 3.39% Working Notes: Current yield = Annual coupon / current Bond price Bond P Current Bond price P0 = $1,173.59120 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond Coupon Rate = 8% Annual coupon = Face value of bond x Coupon Rate = 1,000 x 8% = $80 YTM= 5% p.a (annual) n= no. of coupon = No. Of years x no. Of coupon in a year = 7 x 1 = 7 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond =$80 x Cumulative PVF @5% for 1 to 7th+ PVF @5% for 7th period x 1,000 =80 x 5.786373397 + 1000 x 0.71068133 =$1,173.59120 Cumulative PVF @ 5 % for 1 to 7th is calculated = (1 - (1/(1 + 0.05)^7) ) /0.05 = 5.786373397 PVF @ 5% for 7th period is calculated by = 1/(1+i)^n = 1/(1.05)^7 =0.71068133 Bond P Current yield = Annual coupon / current Bond price Current yield = $80 /$1,173.59120 Current yield = 0.068166837 Current yield = 6.8166837 % Current yield = 6.82% Bond D Current Bond price P0 = $884.27253 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond Coupon Rate = 3% Annual coupon = Face value of bond x Coupon Rate = 1,000 x 3% = $30 YTM= 5% p.a (annual) n= no. of coupon = No. Of years x no. Of coupon in a year = 7 x 1 = 7 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond =$30 x Cumulative PVF @5% for 1 to 7th+ PVF @5% for 7th period x 1,000 =30 x 5.786373397 + 1000 x 0.71068133 =$884.27253 Cumulative PVF @ 5 % for 1 to 7th is calculated = (1 - (1/(1 + 0.05)^7) ) /0.05 = 5.786373397 PVF @ 5% for 7th period is calculated by = 1/(1+i)^n = 1/(1.05)^7 =0.71068133 Bond D Current yield = Annual coupon / current Bond price Current yield = $30 /$884.27253 Current yield = 0.033926192 Current yield = 3.3926192 % Current yield = 3.39% 2nd. Capital gains yield Bond P -1.82% Bond D 1.61% Working Notes: Capital gains yield = (New price – Original price) / Original price Original price is already calculated in 1st P0 here , we have to calculate only New price P1 After one year n will be reduced by 1 ,as one year life of bond will be expired , Bond P Bond New price P1 = $1,152.27076 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond Coupon Rate = 8% Annual coupon = Face value of bond x Coupon Rate = 1,000 x 8% = $80 YTM= 5% p.a (annual) n= no. of coupon = No. Of years x no. Of coupon in a year = 6 x 1 = 6 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond =$80 x Cumulative PVF @5% for 1 to 6th+ PVF @5% for 6th period x 1,000 =80 x 5.075692067 + 1000 x 0.746215397 =$1,152.27076 Cumulative PVF @ 5 % for 1 to 6th is calculated = (1 - (1/(1 + 0.05)^6) ) /0.05 = 5.075692067 PVF @ 5% for 6th period is calculated by = 1/(1+i)^n = 1/(1.05)^6 =0.746215397 Bond P Capital gains yield = (New price – Original price) / Original price Capital gains yield = (P1 – P0) / P0 Capital gains yield = (1152.27076 - 1173.59120) / 1173.59120 Capital gains yield =-0.018166837 Capital gains yield =-1.8166837% Capital gains yield = -1.82% Bond D Bond New price P1 = $ Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond Coupon Rate = 3% Annual coupon = Face value of bond x Coupon Rate = 1,000 x 3% = $30 YTM= 5% p.a (annual) n= no. of coupon = No. Of years x no. Of coupon in a year = 6 x 1 = 6 Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond =$30 x Cumulative PVF @5% for 1 to 6th+ PVF @5% for 6th period x 1,000 =30 x 5.075692067 + 1000 x 0.746215397 =$898.48616 Cumulative PVF @ 5 % for 1 to 6th is calculated = (1 - (1/(1 + 0.05)^6) ) /0.05 = 5.075692067 PVF @ 5% for 6th period is calculated by = 1/(1+i)^n = 1/(1.05)^6 =0.746215397 Bond D Capital gains yield = (New price – Original price) / Original price Capital gains yield = (P1 – P0) / P0 Capital gains yield = (898.48616 - 884.27253) /884.27253 Capital gains yield =0.016073812 Capital gains yield =1.60738% Capital gains yield = 1.61% Please feel free to ask if anything about above solution in comment section of the question.