Question

The Faulk Corp. has a bond with a coupon rate of 7 percent outstanding. The Gonas Company has a bond with a coupon rate of 13 percent outstanding. Both bonds have 15 years to maturity, make semiannual payments, and have a YTM of 10 percent.

(A) If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
(B) What if rates suddenly fall by 2 percent instead?

Answer 1

Step-1:Calculation of current price of bonds
Price of bond is the present value of cash flow from bond.
Price of Faulk Corp. bond	=	=-pv(rate,nper,pmt,fv)	Where,
	=	$                                   769.41	pv	Present value of cash flows from bonds
			rate	YTM		5%
			nper	Number of period		30
			pmt	Coupon payment	=	$       35.00
			fv	Face value		$ 1,000.00
Price of Gonas company bond	=	=-pv(rate,nper,pmt,fv)	Where,
	=	$                               1,230.59	pv	Present value of cash flows from bonds
			rate	YTM		5%
			nper	Number of period		30
			pmt	Coupon payment	=	$       65.00
			fv	Face value		$ 1,000.00
Step-2:Calculation of change in price after rise in interest rate by 2 percent
Percentage change in the price of:
Faulk Corp. bond	=	(Price after change - Price before change)/Price before change	=	(655.88-769.41)/769.41		=	-14.76%
Price of Gonas company bond	=	(Price after change - Price before change)/Price before change	=	(1068.82-1230.59)/1230.59		=	-13.15%
Working:
After rise in interest rate of 2 percent:
Price of Faulk Corp. bond	=	=-pv(rate,nper,pmt,fv)	Where,
	=	$                                   655.88	pv	Present value of cash flows from bonds
			rate	YTM		6%
			nper	Number of period		30
			pmt	Coupon payment	=	$       35.00
			fv	Face value		$ 1,000.00
Price of Gonas company bond	=	=-pv(rate,nper,pmt,fv)	Where,
	=	$                               1,068.82	pv	Present value of cash flows from bonds
			rate	YTM		6%
			nper	Number of period		30
			pmt	Coupon payment	=	$       65.00
			fv	Face value		$ 1,000.00
Step-3:Calculation of change in price after fall in interest rate by 2 percent
Percentage change in the price of:
Faulk Corp. bond	=	(Price after change - Price before change)/Price before change	=	(913.54-769.41)/769.41		=	18.73%
Price of Gonas company bond	=	(Price after change - Price before change)/Price before change	=	(1432.30-1230.59)/1230.59		=	16.39%
Working:
After fall in interest rate of 2 percent:
Price of Faulk Corp. bond	=	=-pv(rate,nper,pmt,fv)	Where,
	=	$                                   913.54	pv	Present value of cash flows from bonds
			rate	YTM		4%
			nper	Number of period		30
			pmt	Coupon payment	=	$       35.00
			fv	Face value		$ 1,000.00
Price of Gonas company bond	=	=-pv(rate,nper,pmt,fv)	Where,
	=	$                               1,432.30	pv	Present value of cash flows from bonds
			rate	YTM		4%
			nper	Number of period		30
			pmt	Coupon payment	=	$       65.00
			fv	Face value		$ 1,000.00