Question

Miller Corporation has a premium bond making semiannual payments. The bond pays a coupon of 10 percent, has a YTM of 8 percent, and has 16 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond pays a coupon of 8 percent, has a YTM of 10 percent, and also has 16 years to maturity.

What is the price of each bond today? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Price of Miller Corporation bond	$
Price of Modigliani Company bond	$

If interest rates remain unchanged, what do you expect the prices of these bonds to be 1 year from now? In 7 years? In 12 years? In 14 years? In 16 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Price of bond	Miller Corporation Bond	Modigliani Company Bond
1 year	$	$
7 years	$	$
12 years	$	$
14 years	$	$
16 years	$	$

Answer 1

A1	B	C	D	E	F	G	H	I	J	K
2		Calculation of price of Miller Corporation Bond:
3		Par value (F)	$1,000
4		Coupon rate	10.00%
5		Yield to maturity	8.00%
6		Time to maturity	16	Years
7
8		Interest is paid twice a year i.e. semiannual.
9		Semiannual coupon (C)	$50.00
10		Semiannual Period (n)	32
11		Semiannual YTM (i)	4.00%
12		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
13		Cash Flow of Bonds can be written as follows:
14		Semiannual Period	0	1	2	3	…	32
15		Cash Flow of Bonds		$50.00	$50.00	$50.00	$50.00	$1,050.00
16
17		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
18		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
19
20		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
21			=50*(P/A,4%,32)+1,000*(P/F,4%,32)
22			$1,178.74	=D9*PV(D11,D10,-1,0)+D3*(1/((1+D11)^D10))
23		Hence current market value of bond is	$1,178.74
24
25		Alternative method:
26		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:
27		RATE	4.00%
28		NPER	32
29		PMT	$50.00
30		FV	$1,000
31		TYPE	0	(End of the period Cash Flow)
32
33		Price of the Bond	$1,178.74	=-PV(D27,D28,D29,D30,0)
34
35		Hence Price of Miller Bond is	$1,178.74
36
37		Calculation of price of discount bond:
38		Par value (F)	$1,000
39		Coupon rate	8.00%
40		Yield to maturity	10.00%
41		Time to maturity	16	Years
42
43		Interest is paid twice a year i.e. semiannual.
44		Semiannual coupon (C)	$40.00
45		Semiannual Period (n)	32
46		Semiannual YTM (i)	5.00%
47		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
48		Cash Flow of Bonds can be written as follows:
49		Semiannual Period	0	1	2	3	4	…
50		Cash Flow of Bonds		$40.00	$40.00	$40.00	$40.00	$40.00
51
52		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
53		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
54
55		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
56			=40*(P/A,5%,32)+1,000*(P/F,5%,32)
57			$841.97	=D44*PV(D46,D45,-1,0)+D38*(1/((1+D46)^D45))
58		Hence current market value of bond is	$841.97
59