Question

Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 5 years to maturity, whereas Bond Dave has 18 years to maturity. (Do not round your intermediate calculations.)

   

Requirement 1:

(a)	If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Sam?
	(Click to select) -20.71% 21.90% -17.16%1 7.95% -17.14%

    

(b)	If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Dave?
	(Click to select)-44.65%-30.87%-30.85%58.91%37.06%

    

Requirement 2:

(a)	If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Sam be then?
	(Click to select)21.93%21.86%17.95%21.88%-17.11%

    

(b)	If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Dave be then?
	(Click to select)58.87%58.94%-30.82%37.06%58.89%

Answer 1

Solution:
1.	If interest rate suddenly rise by 5%
a.	% change in price of Bond Sam	=-17.16%
	[Answer is 3rd option ]
b.	% change in price of Bond Dave	= -30.87%
	[Answer is 2nd option ]
2.	If interest rate suddenly fall by 5%
a.
	% change in price of Bond Sam	=21.88%
	[Answer is 4th option ]
b.
	% change in price of Bond Dave	=58.89%
	[Answer is 5th option ]
Working Notes:
	AS both the bonds priced at par value, YTM of both bonds is equal to Coupon Rate that is 10%
1st case is of interest rate suddenly rise by 5% means YTM becomes 10%+5%=15%
	then price of both bond will fall
Bond Sam price =$828.39798
	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 = 10%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 10% = $100
	Semi annual coupon = Annual coupon / 2 = $100/2=$50
	YTM= 15% p.a (annual)
	Semi annual YTM= 15%/2 = 7.50%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 5 x 2 = 10
	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
	= $50 x Cumulative PVF @ 7.5% for 1 to 10th + PVF @ 7.5% for 10th period x 1,000
	= 50 x 6.864080956 + 1000 x 0.485193928
	=$828.39798
Cumulative PVF @ 7.5 % for 1 to 10th is calculated = (1 - (1/(1 + 0.075)^10) ) /0.075 = 6.864080956
PVF @ 7.5% for 10th period is calculated by = 1/(1+i)^n = 1/(1.075)^10 =0.485193928
Bond Dave price =$691.33694
	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 = 10%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 10% = $100
	Semi annual coupon = Annual coupon / 2 = $100/2=$50
	YTM= 15% p.a (annual)
	Semi annual YTM= 15%/2 = 7.5%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 18 x 2 = 36
	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
	= $50 x Cumulative PVF @ 7.5% for 1 to 36th + PVF @ 7.5% for 36th period x 1,000
	= 50 x 12.34652224 + 1000 x 0.074010832
	=$691.33694
Cumulative PVF @ 7.5 % for 1 to 36th is calculated = (1 - (1/(1 + 0.075)^36) ) /0.075 = 12.34652224
PVF @ 7.5% for 36th period is calculated by = 1/(1+i)^n = 1/(1.075)^36 =0.074010832
	Percentage change in price = (New price – Original price) / Original price
	% change in price Bond Sam=($828.39798 -1000)/1000		=-17.16%
	= -0.17160202
	% change in price Bond Dave=($691.33694 -1000)/1000		= -30.87%
	=-0.30866306
2nd case If interest rate suddenly fall by 5%
Working Notes:
	2nd case is of interest rate suddenly fall by 5% means YTM becomes 10%-5% =5%
	then price of both bond will rise
Bond Sam price =$1,218.80160
	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 = 10%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 10% = $100
	Semi annual coupon = Annual coupon / 2 = $100/2=$50
	YTM= 5% p.a (annual)
	Semi annual YTM= 5%/2 = 2.5%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 5 x 2 = 10
	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
	= $50 x Cumulative PVF @ 2.5% for 1 to 10th + PVF @ 2.5% for 10th period x 1,000
	= $50 x   8.752063931 + 1000 x 0.781198402
	=$1,218.80160
Cumulative PVF @ 2.5 % for 1 to 10th is calculated = (1 - (1/(1 + 0.025)^10) ) /0.025 = 8.752063931
PVF @ 2.5% for 10th period is calculated by = 1/(1+i)^n = 1/(1.025)^10 =0.781198402
Bond Dave price =$1,588.90628
	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 = 10%
	Annual coupon = Face value of bond x Coupon Rate = 1,000 x 10 % = $100
	Semi annual coupon = Annual coupon / 2 = $100/2=$50
	YTM= 5% p.a (annual)
	Semi annual YTM= 5%/2 = 2.5%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 18 x 2 = 36
	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
	= $50 x Cumulative PVF @ 2.5% for 1 to 36th + PVF @ 2.5% for 36th period x 1,000
	= 50 x 23.55625107 + 1000 x 0.411093723
	=$1,588.90628
Cumulative PVF @ 2.5% for 1 to 36th is calculated = (1 - (1/(1 + 0.025)^36) ) /0.025 = 23.55625107
PVF @ 2.5% for 36th period is calculated by = 1/(1+i)^n = 1/(1.025)^36 =0.411093723
Percentage change in price = (New price – Original price) / Original price
% change in price Bond Sam=($1,218.80160-1000)/1000
	=0.2188016	=21.88%
% change in price Bond Dave=($1,588.90628-1000)/1000
	=0.58890628	=58.89%
Please feel free to ask if anything about above solution in comment section of the question.