Question

Ryan company issues a $100,000 on 8/31/17, 10%, bond that mature in 5 years. Intrest paid on August 31 of each year. How much would you pay to yield:

8%

10%

14%

Answer 1

			At 8% Yield		At 10% Yield		At 14% Yield
Current Price			$ 1,07,985.42		$ 1,00,000.00		$     86,267.68
Working:
Price of bond is the present value of cash flow from bond.
Face Value							1,00,000
Annual coupon			1,00,000	x	10%	=	10,000
at 8%
Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.08)^-5)/0.08			i	8%
			=	3.99271			n	5
Present Value of 1			=	(1+i)^-n
			=	(1+0.08)^-5
			=	0.68058
Present Value of Coupon			10,000	x	3.99271	=	$     39,927.10
Present Value of Face Value			1,00,000	x	0.68058	=	$     68,058.32
Price of Bond							$ 1,07,985.42
at 10%
Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.10)^-5)/0.10			i	10%
			=	3.790787			n	5
Present Value of 1			=	(1+i)^-n
			=	(1+0.10)^-5
			=	0.620921
Present Value of Coupon			10,000	x	3.79079	=	$     37,907.87
Present Value of Face Value			1,00,000	x	0.62092	=	$     62,092.13
Price of Bond							$ 1,00,000.00
at 14%
Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.14)^-5)/0.14			i	14%
			=	3.433081			n	5
Present Value of 1			=	(1+i)^-n
			=	(1+0.14)^-5
			=	0.519369
Present Value of Coupon			10,000	x	3.43308	=	$     34,330.81
Present Value of Face Value			1,00,000	x	0.51937	=	$     51,936.87
Price of Bond							$     86,267.68