Question

  

4)Consider two $27,000 face value corporate bonds. Bond A is

currently selling for $26,946 and matures in 18 years.

Bond B sells for $25,245 and matures in 3 years. Calculate

the current yield for both bonds if both have a coupon rate

equal to 4%. (Assume a yearly coupon payment). 1)Current yield Bond A to 2 decimal places 2)Current yield Bond B to 2 decimal places 3)YTM Bond A to 2 decimal places 4)YTM Bond B to 2 decimal places 5)Which current yield is a better approximation of the yield to maturity, A or B?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K	L	M
2
3		4)
4
5		Bond A:
6		Face value	27000
7		Current Price Bond A	26946
8		Current Price Bond B	25245
9
10		Maturity of Bond A	18
11		Maturity of Bond B	3
12
13		Coupon rate of Bond A	0.04
14		Coupon rate of Bond B	0.04
15
16		1)
17
18		Annual Coupon of A	=D6*D13
19
20		Current yield Bond A	= Annual Coupon of Bond A / Current Price of Bond A
21			=D18/D7	=D18/D7
22
23		Hence Current yield Bond A	=D21
24
25		2)
26
27		Annual Coupon of Bond B	=D6*D14
28
29		Current yield Bond B	= Annual Coupon of Bond B / Current Price of Bond B
30			=D27/D8	=D27/D8
31
32		Hence Current yield Bond B	=D30
33
34		3)
35
36		Calculation of Yield to maturity of Bond A:
37		Face value	=D6
38		Coupon rate	=D13
39		Current Price	=D7
40		Years to Maturity	=D10	years
41		Annual Coupon	=D37*D38	=D37*D38
42		Cash flow to investor will be as follows:
43		Year	0	1	2	3	4	5	..	=D40
44		Cash flow	=-D39	=D41	=E44	=F44	=G44	=H44	=I44	=J44+D37
45
46		Yield to maturity is the rate at which if future NPV to Investor will be zero.
47		Let r be the yield to maturity then,
48
49
50
51
52
53
54
55		By solving above equation, yield to maturity r can be found.
56		Hit and trial method can be used to find the solution of above equation.
57
58		Rate(nper,pmt,PV, [fv],type) function of excel can be used to find the yield to maturity as follows:
59		NPER	=D40
60		PMT	=D41
61		PV	=-D39
62		FV	=D37
63
64		Yield to maturity	=RATE(D59,D60,D61,D62)	=RATE(D59,D60,D61,D62)
65
66		Thus yield to maturity of Bond A is	=D64
67
68		4)
69
70		Calculation of Yield to maturity of Bond B:
71		Face value	=D6
72		Coupon rate	=D14
73		Current Price	=D8
74		Years to Maturity	=D11	years
75		Annual Coupon	=D71*D72	=D37*D38
76		Cash flow to investor will be as follows:
77		Year	0	1	2	3	4	5	..	=D74
78		Cash flow	=-D73	=D75	=E78	=F78	=G78	=H78	=I78	=J78+D71
79
80		Yield to maturity is the rate at which if future NPV to Investor will be zero.
81		Let r be the yield to maturity then,
82
83
84
85
86
87
88
89		By solving above equation, yield to maturity r can be found.
90		Hit and trial method can be used to find the solution of above equation.
91
92		Rate(nper,pmt,PV, [fv],type) function of excel can be used to find the yield to maturity as follows:
93		NPER	=D74
94		PMT	=D75
95		PV	=-D73
96		FV	=D71
97
98		Yield to maturity	=RATE(D93,D94,D95,D96)	=RATE(D93,D94,D95,D96)
99
100		Thus yield to maturity of Bond B is	=D98
101
102		5)
103			Bond A	Bond B
104		Current Yield	=D23	=D32
105		Yield to maturity	=D66	=D100
106
107		Hence for Bond A, current yield is a better approximation of the yield to maturity.
108