On 14 March 2013 a company issued a bond with a face value of $100,000 that...

On 14 March 2013 a company issued a bond with a face value of $100,000 that matures exactly 25 years later. The coupon rate is 6% p.a. compounded half-yearly. What is the bond's value on 14 September 2018 assuming the market yield is 5% p.a. compounded half-yearly.

	a.	$100,000.00
	b.	$112,365.17
	c.	$112,174.30
	d.	$117,017.04
	e.	$112,551.39

Expert Solution

Starting from March 14th 2013, there are are 50 semiannual time periods for the next 25 years.
From March 14th 2013 to Sept 14th 2018, there are 11 semiannual time periods.
The remaining time periods till maturity equals 39 semiannual time periods.

Par/Face value	100000
Annual Coupon rate	0.06
Annual coupon	6000
semi-annual coupon	3000

Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 5%.
m is the compounding period that is 2
mt is the time period.
price of the bond = sum of present values of future cash flows
r/2	0.025
mt	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39
future cash flow	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	3000	103000
present value	2926.829	2855.443	2785.798	2717.852	2651.563	2586.891	2523.796	2462.24	2402.185	2343.595	2286.434	2230.668	2176.261	2123.182	2071.397	2020.875	1971.585	1923.498	1876.583	1830.813	1786.159	1742.594	1700.092	1658.626	1618.172	1578.704	1540.199	1502.633	1465.984	1430.228	1395.344	1361.312	1328.109	1295.716	1264.113	1233.281	1203.201	1173.855	39319.36
sum of present values	112365.17

The bond's value on 14th september 2018 is:
b) $112365.17.

jeff jeffy answered 1 year ago

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