Question

Assume you own a bond with a 5% coupon, a 6% yield-to-maturity, 5 years to maturity, and a $1,000 par value. It is currently priced at $957.35. If the yield-to-maturity increases to 8.0%, what is the price of the bond? Select one: a. $1,043.76 b. $878.33 c. $1,000 d. $1,087.52

Answer 1

b. $878.33

Working:

Price of bond is the present value of cash flows from bond.
Cash flows are discounted at rate of of Yield to maturity.
Present value of cash flows and dicounted rate has inverse relation.
It means if discount rate increased , price of bond will be decreased and vice versa.
Face Value		$       1,000
Semi annual coupon Interest		=	face Value x Coupon rate
		=	$    1,000	x	5%	x 6/12
		=	$          25
Present Value of annuity of 1			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.04)^-10)/0.04		i	4%
			=	8.110896		n	10
Present Value of 1			=	(1+i)^-n
			=	(1+0.04)^-10
			=	0.675564
Present Value of coupon			$          25	x	8.110896	=	$ 202.77
Present Value of Par Value			$    1,000	x	0.675564	=	$ 675.56
Current Price of Bond							$ 878.34