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 $3000 every six months over the subsequent eight years, and finally pays $3,300 every six months over the last 6 years. bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coipon payments over the life of the bond. the required return on both these binds is 10 percent compounded semiannually. what is the current price of Bond M and Bond N?

Answer 1

Price of Bond M:

Price of Bond = C/(1+r) + C/(1+r)² + C/(1+r)³ + C/(1+r)⁴ ….. C/(1+r)^t + F/(1+r)^t

Where, C is Coupon payment

r is discount rate

F is par value

t is time to maturity

r= 10% semi-annually compounding

Time (t)	Coupon (C)	Discount factor (D) = 1/(1+10%/2)^t	PV(t) = (C)*(D)
1	0	0.95	0.00
2	0	0.91	0.00
3	0	0.86	0.00
4	0	0.82	0.00
5	0	0.78	0.00
6	0	0.75	0.00
7	0	0.71	0.00
8	0	0.68	0.00
9	0	0.64	0.00
10	0	0.61	0.00
11	0	0.58	0.00
12	0	0.56	0.00
13	3000	0.53	1590.96
14	3000	0.51	1515.20
15	3000	0.48	1443.05
16	3000	0.46	1374.33
17	3000	0.44	1308.89
18	3000	0.42	1246.56
19	3000	0.40	1187.20
20	3000	0.38	1130.67
21	3000	0.36	1076.83
22	3000	0.34	1025.55
23	3000	0.33	976.71
24	3000	0.31	930.20
25	3000	0.30	885.91
26	3000	0.28	843.72
27	3000	0.27	803.54
28	3000	0.26	765.28
29	3300	0.24	801.72
30	3300	0.23	763.55
31	3300	0.22	727.19
32	3300	0.21	692.56
33	3300	0.20	659.58
34	3300	0.19	628.17
35	3300	0.18	598.26
36	3300	0.17	569.77
37	3300	0.16	542.64
38	3300	0.16	516.80
39	3300	0.15	492.19
40	23300	0.14	3309.66

Price of Bond M = Sum of PV(t) = $28,406.71

Price of Bond N

Price of Zero coupon Bond = F/(1+r)^t

Where,

r is discount rate

F is par value

t is time to maturity

r= 10% semi-annually compounding

Price of Bond N = 20000/(1+10%/2)^20*2

Price of Bond N = $2,840.91