Question

Kelly Industries issued 11% bonds, dated January 1, with a face value of $100,000 on January 1, 2018. The bonds mature in 2028 (10 years). Interest is paid semiannually on June 30 and December 31. For bonds of similar risk and maturity the market yield is 12%. What was the issue price of the bonds?

Answer 1

Price of a bond is the present value of all future cash flows receivable from the bonds discounted at market rate of return

When interest is paid semi-annually, time is multiplied by 2 and interest rate is divided by 2

So, applicable time n = 10 x 2 = 20 semi-annual periods

Interest rate for discounting r = 12 / 2 = 6% or 0.06 every 6 months

Periodic cash flows = Interest payment

= Face value x Rate of interest x Time / 12

= $100,000 x 11% x 6 / 12

= $ 5,500

Terminal cash flow is the maturity value = $100,000

Present value factor

= 1 / (1 + r) ^ n

So, PV Factor for n = 2

= 1 / (1.06 ^ 2)

= 1 / 1.1236

= 0.889996

Similarly, other calculations are shown in the following table

Calculations	A	B	C = A x B
Period	Cash Flow	PV Factor	Present value
1	5,500	0.943396	5,188.68
2	5,500	0.889996	4,894.98
3	5,500	0.839619	4,617.91
4	5,500	0.792094	4,356.52
5	5,500	0.747258	4,109.92
6	5,500	0.704961	3,877.28
7	5,500	0.665057	3,657.81
8	5,500	0.627412	3,450.77
9	5,500	0.591898	3,255.44
10	5,500	0.558395	3,071.17
11	5,500	0.526788	2,897.33
12	5,500	0.496969	2,733.33
13	5,500	0.468839	2,578.61
14	5,500	0.442301	2,432.66
15	5,500	0.417265	2,294.96
16	5,500	0.393646	2,165.05
17	5,500	0.371364	2,042.50
18	5,500	0.350344	1,926.89
19	5,500	0.330513	1,817.82
20	5,500	0.311805	1,714.93
20	100,000	0.311805	31,180.47
		Price	94,265.04