Question

Jason Greg is a recent retiree who is interested in investing some of his savings in corporate bonds. Listed below are the bonds he is considering adding to his portfolio. 2. Bond A has a 7.5% semiannual coupon, matures in 12 years, and has a S 1,000 face value. Bond B has a 10% semiannual coupon, matures in 12 years, and has a $1,000 face value. Bond C has an 11.5% semiannual coupon, matures in 12 years, and has a $1,000 face value. Each bond has a YTM of 10%. a. Before calculating the prices of the bonds, indicate whether each bond is trading at a premium, discount or par. b. Calculate the price of each of these bonds. c. Calculate the current yield for each bond. d. If the yield to maturity for each bond remains at 9%, what will be the price of each bon years from now? Mr. Greg is considering another bond, Bond D. It has an 8% semiannual coupon and a $1,000 face value. Bond D is scheduled to mature in 9 years and has a price of $1,150 also callable in 5 years at a call price of $1,040. What is the bond's YTM? What is th bond's YTC? If Mr. Greg were to purchase this bond, would he be more likely to rec the YTM or YTC? Explain your answer Price each bond and explain how the number of years to maturity and the coupon rate the current price of bonds. Assume a YTM of 7%. 1, A 4-year bond with a 9% annual coupon e, f. A 4-year bond with a zero coupon A 15-year bond with a 9% annual coupon A 15-year bond with a zero coupon 2. 3, 4.

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K
2
3
4		a)
5		The Bond is said to be selling at premium when it is selling above its face value and
6		it is said to be selling at discount when the bond is selling at price lower than than the face value.
7		When bond selling price is equal to the face value of the bond, then it is said to be selling on par.
8
9		Bond price is the present value of future cash flows discounted at yield to maturity.
10		Thus higher the Yield to maturity lower is the price of the bond.
11		When YTM is equal to the coupon price, the bond price equals par value of the bond.
12		When YTM is higher than the coupon rate then the bond will sell at discount and
13		when YTM is lower than the coupon rate then the bond will sell at premium.
14
15		Yield to maturity	0.1
16
17		Bond	Coupon Rate	Selling At
18		A	0.075	Premium
19		B	0.1	Par
20		C	0.115	Discount
21
22		b)
23
24		Calculation of Price of Bond A:
25		Par value (F)	1000
26		Interest rate (Coupon rate)	0.075
27		Yield to maturity	=D15
28		Time to maturity	12	Years
29
30		Interest is paid twice a year i.e. semiannual.
31		Semiannual coupon (C)	=D25*D26/2
32		Semiannual Period (n)	=D28*2
33		Semiannual YTM (i)	=D27/2
34		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
35		Cash Flow of Bonds can be written as follows:
36		Semiannual Period	0	1	2	3	4	…	=D32
37		Cash Flow of Bonds		=$D31	=$D31	=$D31	=$D31	=$D31	=$D31+D25
38
39		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
40		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
41
42		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
43			=37.5*(P/A,5%,24)+1,000*(P/F,5%,24)
44			=D31*PV(D33,D32,-1,0)+D25*(1/((1+D33)^D32))	=D31*PV(D33,D32,-1,0)+D25*(1/((1+D33)^D32))
45		Hence price of bond A is	=D44
46
47		Alternative method:
48		Price of the bond can also be calculated by finding the present value of cash flows of the bond using PV formula of excel as follows:
49		RATE	=D33
50		NPER	=D32
51		PMT	=D31
52		FV	=D25
53		TYPE	0	(End of the period Cash Flow)
54
55		Price of the Bond	=-PV(D49,D50,D51,D52,0)	=-PV(D49,D50,D51,D52,0)
56
57		Hence Bond Price is	=D55
58
59		Simillarly for other bonds, price can be calculated as follows:
60		Bond	Coupon Rate	Maturity	YTM	Bond Price
61		A	0.075	12	0.1	=-PV(F61/2,E61*2,1000*D61/2,1000)	=-PV(F61/2,E61*2,1000*D61/2,1000)
62		B	0.1	12	0.1	=-PV(F62/2,E62*2,1000*D62/2,1000)
63		C	0.115	12	0.1	=-PV(F63/2,E63*2,1000*D63/2,1000)
64
65		c)
66
67		Current Yield is calculated as annual coupon divided by bond price.
68
69		Bond	Coupon Rate	Maturity	YTM	Annual Coupon	Bond Price	Current Yield
70		A	0.075	12	0.1	=1000*D70	=-PV(F70/2,E70*2,1000*D70/2,1000)	=G70/H70	=G70/H70
71		B	0.1	12	0.1	=1000*D71	=-PV(F71/2,E71*2,1000*D71/2,1000)	=G71/H71
72		C	0.115	12	0.1	=1000*D72	=-PV(F72/2,E72*2,1000*D72/2,1000)	=G72/H72
73
74		d)
75
76		Bond	Coupon Rate	Maturity	YTM	Bond Price
77		A	0.075	12	0.09	=-PV(F77/2,E77*2,1000*D77/2,1000)	=-PV(F77/2,E77*2,1000*D77/2,1000)
78		B	0.1	12	0.09	=-PV(F78/2,E78*2,1000*D78/2,1000)
79		C	0.115	12	0.09	=-PV(F79/2,E79*2,1000*D79/2,1000)
80