Question

The Johnson Corporation sells 1,000 bonds; each bond has a face (par) valueof $1,000. The Bonds are sold on January 1, 2010. The face interest rate of each bond is 4.5%, with interest being paid twice per year, July 1st and January 1st. The bonds are 5-year bonds.

The market interest rate (yield) for these types of bonds (securities) at the time the bonds are sold (January 1, 2010) is 4% annually.

Requirements:

a. What is the total amount of interest paid to the bondholders over the life of the bonds?

b. What is the present value of the interest payments over the life of the bonds?

c. What amount is paid the bondholders to retire the bonds at the end of 10 years?

d. What is the present value of the face amount of the bonds on January 1, 2010?

e. What is the total amount the bonds sold for on January 1,2010?

Answer 1

a. Total amount of interest paid to the bondholders over the life of the bonds is $225,000

Amount repaid:
10 semi-annual Interest payment of 22,500 (1,000*1,000*4.5%*6/12)	225,000

b. Present value of the interest payments over the life of the bonds is $202,108

Particulars	Amount
Present Value of interest of (1,000*1,000*4.5%*6/12) $22,500 for 10 semi-annual years is	$202,108
22,500*8.98258 (Cumulative factor of 10 periods of 2%)

c. Amount paid to Bondholders at retirement will be $1,000,000.

d. Present value of the face amount of the bonds on January 1, 2010, is $1,000,000

e. Total amount the bonds sold for on January 1, 2010, is $1,022,456.

Particulars	Amount
Present Value of interest of (1,000*1,000*4.5%*6/12) $22,500 for 10 semi-annual years is	$202,108
22,500*8.98258 (Cumulative factor of 10 periods of 2%)
Present value of a single payment at the Maturity date
$1,000,000*.82035 (Factor at end of 10th period of 2%)	$820,348
Issue Price of bond	$1,022,456