Akers Company sold bonds on July 1, 2017, with a face value of $100,000. These bonds are due in 10 years. The stated annual interest rate is 6% per year, payable semiannually on June 30 and December 31. These bonds were sold to yield 8%. By July 1, 2018, the market yield on these bonds had risen to 10%.

Required:
What was the bonds' market price on July 1, 2018?

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 the bond for Akers Company can be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment

= 6% × 100,000 × 1/2 = 3000

Semi-annual yield = 10%/2 = 5% per six months

Total period to maturity (in months)

= (2 × 10) = 20 periods

PV of interest =

3000 × (1- (1+0.05)^( -20)/) 0.05 = 37,386.63

Step 2

PV of Redemption Value

= 100,000 × (1.05)^(-20) = 37,688.95

Price of bond

Price of bond = 37,386.63 + 37,688.95 = 75,075.58

Price of bond= $75,075.58