Question

2. I am considering investing in an A-rated five year zero coupon corporate bond with a par value of $10,000. Five year government bonds are trading at a yield of 3.8% (semi-annual) and corporate bonds spreads are:

​​AA​​ 100

​​A 140

BB 190

​

a) What would the purchase price of the bond be ?

b) What would be my total percentage capital gain or loss at the end of five years ?

c) What would be my capital gain or loss if I sold the bond at the end of year 4 for at a yield of 4.4%?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I
2
3		Par Value of Bond (P)	10000
4		Government Bond Yield	0.038	(Semi-annual)
5		Spread for A rate bond	140	Basis points
6		Time to maturity (n)	5	Years
7
8		Effective annual rate for government bond	=((1+D4/2)^2)-1	=((1+D4/2)^2)-1
9
10		Yield for corporate bond (y)	=D8+(D5/10000)	=D8+(D5/10000)
11
12		a)
13
14		Price of zero coupon corporate bond	=Par Value / (1+y)n
15			=D3/((1+D8)^D6)	=D3/((1+D8)^D6)
16
17		Hence purchase price of bond will be	=D15
18
19		b)
20		Price of Bond at the end of 5 year	=Par Value
21			=D3
22
23		Capital gain at the end of 5 year	=(Price at the end of 5 year - Purchase Price)/Purchase Price
24			=(D21-D17)/D17	=(D21-D17)/D17
25
26		Hence capital gain	=D24
27
28		c)
29
30		Yield	0.044
31		Time to maturity at the end of 4th year	=5-4	Year
32
33		Price of Bond at the end of Year 4	=Par Value / (1+y)n
34			=D3/((1+D30)^D31)	=D3/((1+D30)^D31)
35
36		Capital gain at the end of 5 year	=(Price at the end of 5 year - Purchase Price)/Purchase Price
37			=(D34-D17)/D17	=(D34-D17)/D17
38
39		Hence capital gain	=D37
40