Question

What is the quoted price of a 15-year 7.0% bond with semiannual coupons, a face value of $1,000, and a yield to maturity of 8.0%? A. $493.40 b. $614.82 c. $913.54 d. $914.41 e. $944.41

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 %			7.00%
	Annual Coupon Amount			$70.00
	Semi Annual Coupon Amount			$35.00
	Step 2: Calculate number of years to Maturity
	Number of years to maturity = 15 years
	Interest is paid semi annyally so total period = 15*2 = 30
	Step 3 : Caclulation of Current Market Price (intrinsic value) of the bonds
	Market rate of interest or Yield to Maturity or Required Return = 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	PVF @ 4%	PresentValue
	1	Interest	$35	0.9615	$33.65
	2	Interest	$35	0.9246	$32.36
	3	Interest	$35	0.8890	$31.11
	4	Interest	$35	0.8548	$29.92
	5	Interest	$35	0.8219	$28.77
	6	Interest	$35	0.7903	$27.66
	7	Interest	$35	0.7599	$26.60
	8	Interest	$35	0.7307	$25.57
	9	Interest	$35	0.7026	$24.59
	10	Interest	$35	0.6756	$23.64
	11	Interest	$35	0.6496	$22.74
	12	Interest	$35	0.6246	$21.86
	13	Interest	$35	0.6006	$21.02
	14	Interest	$35	0.5775	$20.21
	15	Interest	$35	0.5553	$19.43
	16	Interest	$35	0.5339	$18.69
	17	Interest	$35	0.5134	$17.97
	18	Interest	$35	0.4936	$17.28
	19	Interest	$35	0.4746	$16.61
	20	Interest	$35	0.4564	$15.97
	21	Interest	$35	0.4388	$15.36
	22	Interest	$35	0.4220	$14.77
	23	Interest	$35	0.4057	$14.20
	24	Interest	$35	0.3901	$13.65
	25	Interest	$35	0.3751	$13.13
	26	Interest	$35	0.3607	$12.62
	27	Interest	$35	0.3468	$12.14
	28	Interest	$35	0.3335	$11.67
	29	Interest	$35	0.3207	$11.22
	30	Interest	$35	0.3083	$10.79
	30	Bond Value	$1,000	0.3083	$308.32
		Total			$913.54
		Bonds Price =			$913.54
		Answer = Option C =		₹ 913.54