Question

Market Price of a Bond

The company intends to issue 20-year bonds with a face value of $1,000. The bonds carry a coupon rate of 9%, and interest is paid semiannually. On the issue date, the market interest rate for bonds issued by companies with similar risk is 12% compounded semiannually.

Compute the market price of one bond on the date of issue.

Click here to access the PV table and the PV of an ordinary annuity table to use with this problem. Round your answer to the nearest cent.

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Answer 1

Price of bond is the present value of cash flows from bond.
	Present Value of coupon interest				$     677.08
	Present value of Par Value				$       97.22
	Present Value of cash flows				$     774.31
	So, price of bond is		$ 774.31
	Working:
# 1	Semi annnual coupon interest			=	Face Value * Semi annual coupon rate
				=	1000*4.5%
				=	$       45.00
# 2	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.06)^-40)/0.06			i	6%
				=	15.046297			n	40
# 3	Present value of 1			=	(1+i)^-n
				=	(1+0.06)^-40
				=	0.0972222
# 4	Present Value of coupon			=	Coupon Interest		*	Present Value of annuity of 1
				=	$       45.00		*	15.0463
				=	$     677.08
# 5	Present value of face value			=	Face Value		*	Present value of 1
				=	$ 1,000.00		*	0.097222
				=	$       97.22