Question

Compute the price of a 7.2 percent coupon bond with 15 years left to maturity and a market interest rate of 10.0 percent. (Assume interest payments are semiannual.) (Do not round intermediate calculations. Round your final answer to 2 decimal places.) IS this a Discount or Premium Bond?

Answer 1

Price of Bond			$ 784.79
This is a Discount Bond.
Working:
Price of Bond is the present value of cash flows from bond.
To find present value of cash flows, first of all we calculate discount factor.
Present Value of annuity of 1			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.05)^-30)/0.05		i	10.0%/2	=	0.05
			=	15.3725		n	15*2	=	30
Present Value of 1			=	(1+i)^-n
			=	(1+0.05)^-30
			=	0.2314
Now, we can use above discount factor to find present value of cash flows.
Suppose Par Value is 1000.
Semi annual coupon			=	Par Value x Semi annual coupon rate
			=	$ 1,000.00	x	7.2% x 6/12
			=	$       36.00
Present Value of coupon interest				$       36.00	x	15.3725	=	$ 553.41
Present value of Par Value				$ 1,000.00	x	0.2314	=	$ 231.38
Total Present value								$ 784.79
So,
Price of bond is		$ 784.79
Market interest rate is higher than bond. It means interest on bonds are lower than market interest.So, price
of such bond will lower than market and It is lower than par value of bond.Hence, It is a discount bond.