Question

5. Suppose Hillard Manufacturing sold an issue of bonds with a 12-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 5%. At what price would the bonds sell

Answer 1

Price of bonds = $1,389.73

Step-by-step explanation:

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 for Hillard can be worked out as follows:

Step 1

Calculate the PV of interest payments

Semi annual interest payment

= 10% × 1,000 × 1/2 =50

PV of interest payment

A ×(1- (1+r)^(-n))/r

r- semi-annual yield = 5%/2 = 2.5%

n- 10× 2 = 20.

Note that the bonds now have 10 years to maturity because it was issued 2 years ago

PV on interest = 50 × (1-(1.025^(-20)/0.0425 = 779.45

Step 2

PV of redemption Value

PV = $1,000 × (1.025)^(-20) = 610.27

Step 3

Price of bond

= 779.45+ 610.27 = $1,389.73

Price of bonds = $1,389.73