Question

Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 7 percent, a YTM of 5 percent, and 19 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 5 percent, a YTM of 7 percent, and also has 19 years to maturity. Both bonds have a par value of $1,000.

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

Price of Miller bond	$
Price of Modigliani bond	$

If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 10 years? In 14 years? In 18 years? In 19 years? (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16.)

Price of bond in:	Miller bond		Modigliani bond
1 year	$		$
10 years	$		$
14 years	$		$
18 years	$		$
19 years	$		$

Answer 1

Miller bond

Price today

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =19x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^19x2

k=1

Bond Price = 1243.49

1 year

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =18x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^18x2

k=1

Bond Price = 1235.56

10 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =9x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^9x2

k=1

Bond Price = 1143.53

14 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^5x2

k=1

Bond Price = 1087.52

18 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =1x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^1x2

k=1

Bond Price = 1019.27

19 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =0x2

Bond Price =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^0x2

k=1

Bond Price = 1000

Modigliani bond

Price today

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =19x2

Bond Price =∑ [(5*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^19x2

k=1

Bond Price = 791.59

1 year

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =18x2

Bond Price =∑ [(5*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^18x2

k=1

Bond Price = 797.1

10 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =9x2

Bond Price =∑ [(5*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^9x2

k=1

Bond Price = 868.1

14 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(5*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^5x2

k=1

Bond Price = 916.83

18 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =1x2

Bond Price =∑ [(5*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^1x2

k=1

Bond Price = 981

19 years

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =0x2

Bond Price =∑ [(5*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^0x2

k=1

Bond Price = 1000