Question

Assume that an investor is looking at two​ bonds: Bond A is a 10​-year, 12​% ​(semiannual pay) bond that is priced to yield 13.5 %. Bond B is a 10​-year, 11​% ​(annual pay) bond that is priced to yield 10.5​%. Both bonds carry 5​-year call deferments and call prices​ (in 5 ​years) of ​$1,075.

a. Which bond has the higher current​ yield?

b. Which bond has the higher​ YTM?

c. Which bond has the higher​ YTC?

Answer 1

A	B	C	D	E	F	G	H	I	J	K
2
3		a)
4
5		Current Yield can be calculated as follows:
6		Current Yield	=Annual Interest / Current Price
7
8		Calculation of price Bond A:
9		Par value (F)	$1,000
10		Coupon rate	12.00%
11		Yield to maturity	13.50%
12		Time to maturity	10	Years
13
14		Interest is paid twice a year i.e. semiannual.
15		Semiannual coupon (C)	$60.00	=D9*D10/2
16		Semiannual Period (n)	20	=D12*2
17		Semiannual YTM (i)	6.75%	=D11/2
18		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
19		Cash Flow of Bonds can be written as follows:
20		Semiannual Period	0	1	2	3	4	…	20
21		Cash Flow of Bonds		$60.00	$60.00	$60.00	$60.00	$60.00	$1,060.00
22
23		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
24		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
25
26		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
27			=60*(P/A,6.75%,20)+1,000*(P/F,6.75%,20)
28			$918.98	=D10*PV(D12,D11,-1,0)+D4*(1/((1+D12)^D11))
29		Hence current price of bond A is	$918.98
30
31		Alternative method:
32		Price of the bond can also be calculated using PV formula of excel as follows:
33		RATE	6.75%
34		NPER	20
35		PMT	$60.00
36		FV	$1,000
37		TYPE	0	(End of the period Cash Flow)
38
39		Price of the Bond	$918.98	=-PV(D28,D29,D30,D31,0)
40
41		Hence Price of Bond A is	$918.98
42
43		Current Yield for Bond A	=Annual Coupon / Current Price
44			=(2*$60)/$918.98
45			13.06%	=(2*D15)/D41
46
47		Hence Current Yield for Bond A is	13.06%
48
49
50		Similarly, the price of bond B can be calculated as follows:
51		Bond	Coupon rate	Time until maturity	Current Market Rate	Par Value	Price
52		B	11%	10	10.5%	$1,000	$1,030.07
53
54		Current Yield for Bond B	=Annual Coupon / Current Price
55			=(1000*11%)/$1030.07
56			10.68%	=(G52*D52)/H52
57
58		Hence Current Yield for Bond B is	10.68%
59