Question

The Change Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,300 every six months over the subsequent eight years, and finally pays $2,600 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 12 percent compounded semiannually. What is the current price of Bond M and Bond N?

Answer 1

Semi Annual Rate = 12%/2 = 6%

Periods(Half Years) remaining = 20*2 = 40

Period	Cash Flow	Discounting Factor [1/(1.0365^year)]	PV of Cash Flows (cash flows*discounting factor)
1		0.964785335	0
2		0.930810743	0
3		0.898032555	0
4		0.86640864	0
5		0.83589835	0
6		0.80646247	0
7		0.778063164	0
8		0.750663931	0
9		0.724229552	0
10		0.698726051	0
11		0.674120648	0
12		0.650381715	0
13	2300	0.627478741	1443.201104
14	2300	0.605382287	1392.379261
15	2300	0.584063953	1343.347092
16	2300	0.563496337	1296.041575
17	2300	0.543653002	1250.401905
18	2300	0.524508444	1206.369421
19	2300	0.506038055	1163.887527
20	2300	0.488218095	1122.901617
21	2300	0.471025658	1083.359014
22	2300	0.454438647	1045.208889
23	2300	0.438435743	1008.402208
24	2300	0.422996375	972.8916628
25	2300	0.4081007	938.631609
26	2300	0.39372957	905.5780116
27	2300	0.379864515	873.6883855
28	2300	0.366487714	842.921742
29	2600	0.353581972	919.313127
30	2600	0.341130701	886.9398234
31	2600	0.329117898	855.7065349
32	2600	0.317528122	825.5731162
33	2600	0.306346475	796.5008357
34	2600	0.295558587	768.4523258
35	2600	0.28515059	741.3915348
36	2600	0.275109108	715.2836804
37	2600	0.265421233	690.0952054
38	2600	0.256074513	665.7937341
39	2600	0.247056935	642.348031
40	2600	0.238356908	619.7279604
40	20000	0.238356908	4767.138157	= Price of Bond N
		Sum of PVs	31783.47509	= Price of Bond M

Price of Bond will be the Present Value of All the Cash Flows. For Bond N, as there are No Coupons, the Present Value of Maturity Value will be the Price.

Therefore,

Price of Bond M = $31783.48

Price of Bond N = $4767.14