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. a. What is the price of each bond today

The value of the bond is the present value (PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).

Value of Bond = PV of interest + PV of RV

The value of bond Miller Corporation can be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment = 8%× 1000× 1/2 =40

Semi-annual yield = 6%/2 = 3% per six months

Total period to maturity (in months) = (2 × 18) = 36 periods

PV of interest =

40× (1- (1+0.03^(-36)/0.03)= 873.29

Step 2

PV of Redemption Value

= 1,000 × (1.03)^(-36) =345.03

Step 3:

Price of bond

= 873.29 + 345.03= $1,218.32

Modigliani Company

Step 1

PV of interest payments

Semi annul interest payment = 6%× 1000× 1/2 =30

Semi-annual yield = 8%/2 = 4% per six months

Total period to maturity (in months) = (2 × 18) = 36 periods

PV of interest =

30× (1- (1+0.04^(-36)/0.04)= 567.25

Step 2

PV of Redemption Value

= 1,000 × (1.03)^(-36) =243.66

Step 3:

Price of bond

= 567.2484586 + 243.66 = $810.92

Price of bond = $810.92