Question

Bond Dave has a 8 percent coupon rate, makes semiannual payments, a 8 percent YTM, and 27 years to maturity. If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave? Enter the answer with 4 decimals (e.g. 0.0123).

Answer 1

Solution:
	Change in the price of Bond Dave =-0.3190
Working Notes:
	Currently coupon rate is 8 % and YTM is also 8% which means bond current price is at par value that is $1000
	But when interest rate rise by 4 % means YTM becomes = 8%+4% =12%
	Now YTM becomes higher than Coupon rate of 8%, bond price will fall
Bond Dave price =$681.00048860
	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
	Semi annual coupon = Annual coupon / 2 = $80/2=$40
	YTM= 12% p.a (annual)
	Semi annual YTM= 12%/2 = 6%
	n= no.of coupon = No. Of years x no. Of coupon in a year
	= 27 x 2 =54
	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
	= $40x Cumulative PVF @ 6% for 1 to 54th + PVF @ 6% for 54th period x 1,000
	= 40 x 15.94997554 + 1000 x 0.043001467
	=$681.00048860
Cumulative PVF @ 6 % for 1 to 54th is calculated = (1 - (1/(1 + 0.06)^54) ) /0.06 = 15.94997554
PVF @ 6% for 54th period is calculated by = 1/(1+i)^n = 1/(1.06)^54 =0.043001467
	Percentage change in price = (New price – Original price) / Original price
	% change in price Bond Dave=(681.00048860-1000)/1000
	=-0.318999511
	=    -0.3190
Please feel free to ask if anything about above solution in comment section of the question.