Question

You have purchased an outstanding noncallable, 12-year bond with a par value of $1,000. Assume that the bond pays interest of 7.5%, with semiannual compounding. If the going (nominal) annual rate is 8%, what price did you pay for this bond?

Answer 1

	CALCULATION OF PRESENT VALUE OF THE BOND IF THE INTEREST PAID SEMI ANNUALLY
	Step 1 : Calculation of Annual Coupon Payments
	Par value of the bond issued is   =			$1,000
	Annual Coupon %			7.50%
	Annual Coupon Amount			$75.00
	Semi Annual Coupon Amount			$37.50
	Step 2: Calculate number of years to Maturity
	Number of years to maturity = 12 years
	Interest is paid semi annyally so total period = 12 Years * 2 = 24 Periods
	Step 3 : Caclulation of Current Market Price (intrinsic value) of the bonds
	Going rate(Normal) of the bonds or Yield to maturity of bond = 8%
	Bonds interest is paid semi annualy means so discounting factor = 8 % /2= 4 %
	PVF = 1 / Discount rate = 1/ 1.04
	Result of above will again divide by 1.04 , repeat this lat period
	Period	Interest	Amount (In Million)	PVF @ 4%	PresentValue
	1	Interest	$37.50	0.9615	$36.06
	2	Interest	$37.50	0.9246	$34.67
	3	Interest	$37.50	0.8890	$33.34
	4	Interest	$37.50	0.8548	$32.06
	5	Interest	$37.50	0.8219	$30.82
	6	Interest	$37.50	0.7903	$29.64
	7	Interest	$37.50	0.7599	$28.50
	8	Interest	$37.50	0.7307	$27.40
	9	Interest	$37.50	0.7026	$26.35
	10	Interest	$37.50	0.6756	$25.33
	11	Interest	$37.50	0.6496	$24.36
	12	Interest	$37.50	0.6246	$23.42
	13	Interest	$37.50	0.6006	$22.52
	14	Interest	$37.50	0.5775	$21.66
	15	Interest	$37.50	0.5553	$20.82
	16	Interest	$37.50	0.5339	$20.02
	17	Interest	$37.50	0.5134	$19.25
	18	Interest	$37.50	0.4936	$18.51
	19	Interest	$37.50	0.4746	$17.80
	20	Interest	$37.50	0.4564	$17.11
	21	Interest	$37.50	0.4388	$16.46
	22	Interest	$37.50	0.4220	$15.82
	23	Interest	$37.50	0.4057	$15.21
	24	Interest	$37.50	0.3901	$14.63
	21	Bond Principal Value	$1,000.00	0.3901	$390.12
		Total			$961.88
		Current Bonds Price =			$961.88
		Answer = We can pay today price of the bond = $ 961.88