Question

Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of 8 percent, a YTM of 6 percent, and 18 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of 6 percent, a YTM of 8 percent, and also has 18 years to maturity. Both bonds have a par value of $1,000.
Required:
a. What is the price of each bond today?
b. If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 9 years? In 13 years? In 17 years? In 18 years?

Answer 1

Answer:

The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = YTM, Nper = Period, PMT = Coupon Payment and FV = Face Value of Bonds.

a. Miller Bond  

Here, Rate = 6%/2 = 3%, Nper = 18*2 = 36, PMT = 1,000*8%*1/2 = $40 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(3%,36,40,1000)

Bond Price = $1,218.32

 

Modigliani Bond

Here, Rate = 8%/2 = 4%, Nper = 18*2 = 36, PMT = 1,000*6%*1/2 = 30 and FV = $1,000 [we use 2 since the bond is semi-annual]

Bond Price = PV(4%,36,30,1000)

Bond Price = $810.92

b.   1 Year from Now

Miller Bond

Here, Rate = 6%/2 = 3%, Nper = 18*2 = 34, PMT = 1,000*8%*1/2 = $40 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(3%,34,40,1000)

Bond Price = $1,211.32

Modigliani Bond  

Here, Rate = 8%/2 = 4%, Nper = 17*2 = 34, PMT = 1,000*6%*1/2 = 30 and FV = $1,000 [we use 2 since the bond is semi-annual]

Bond Price = PV(4%,34,30,1000)

Bond Price = $815.89

9 Years from Now  

Miller Bond

Here, Rate = 6%/2 = 3%, Nper = 9*2 = 18, PMT = 1,000*8%*1/2 = $40 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(3%,18,40,1000)

Bond Price = $1,137.54

 

Modigliani Bond

Here, Rate = 8%/2 = 4%, Nper = 9*2 = 18, PMT = 1,000*6%*1/2 = 30 and FV = $1,000 [we use 2 since the bond is semi-annual]

Bond Price = PV(4%,18,30,1000)

Bond Price = $873.41  

13 Years from Now

Miller Bond

Here, Rate = 6%/2 = 3%, Nper = 5*2 = 10, PMT = 1,000*8%*1/2 = $40 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(3%,10,40,1000)

Bond Price = $1,085.30

Modigliani Bond

Here, Rate = 8%/2 = 4%, Nper = 5*2 = 10, PMT = 1,000*6%*1/2 = 30 and FV = $1,000 [we use 2 since the bond is semi-annual]

Bond Price = PV(4%,10,30,1000)

Bond Price = $918.89  

17 Years from Now  

Miller Bond

Here, Rate = 6%/2 = 3%, Nper = 1*2 = 2, PMT = 1,000*8%*1/2 = $40 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(3%,2,40,1000)

Bond Price = $1,019.13  

Modigliani Bond  

Here, Rate = 8%/2 = 4%, Nper = 1*2 = 2, PMT = 1,000*6%*1/2 = 30 and FV = $1,000 [we use 2 since the bond is semi-annual]

Bond Price = PV(4%,2,30,1000)

Bond Price = $981.14

18 Years  

Miller Bond

Here, Rate = 6%/2 = 3%, Nper = 1*2 = 2, PMT = 1,000*8%*1/2 = $40 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(3%,0,40,1000)

Bond Price = $1,000

Modigliani Bond

Here, Rate = 8%/2 = 4%, Nper = 0, PMT = 1,000*6%*1/2 = 30 and FV = $1,000 [we use 2 since the bond is semi-annual]  

Bond Price = PV(4%,0,30,1000)

Bond Price = $1,000