The Debit Corporation sells 1000 bonds; each bond has a face (par) value of $1,0
ID: 2444636 • Letter: T
Question
The Debit Corporation sells 1000 bonds; each bond has a face (par) value of $1,000. The Bonds are sold on January 1, 2010. The fact interest rate of each bond is 8%, with interest being paid twice per year, June 30 and December 31. The bonds are 20-year bonds.
The market interest rate (yield) for these types of bonds (securities) at the time the bonds are sold (January 1, 2010) is 6% anually.
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 to the bondholders to reture the bonds at the end of 20 years?
d. What is the present value of the face amount of the bonds of January 1, 2010?
e. What is the total amount of the bonds sold for on January 1, 2010?
f. What is the present value of the bond issue if the market rate was 10% per year at date of issue?
g. Does the increase or decrease in interest rates in the market over the life of the bonds impact your calculations in "f" above? Why or why not?
Explanation / Answer
a. No. of bonds sold = 1,000
Face value per bond = $1,000
Total value of bonds issued = $1,000,000
Interest rate = 8% per annum
Total interest paid over 20 years = $1,000,000 * 8% *20 = $1,600,000
b.
Interest are paid twice a year.
Interest payment per half year = ($1,000,000 * 8%)/2 = $40,000
This interest payments have to discounted at the market rate of 6% per annum for a period of 20 years. Since, interest is paid twice a year the period shall be 40 and discount rate shall be 3%.
Present value of interest payments = $40,000 (1-1/1.0340)/0.03 =$40,000(1-0.3066)/0.03 = $924,533.33
c.
Amount to be paid to retire the bonds at the end of 20 years is the face vaue of the bonds and the interest payments for the second half of the 20thh year
Hencce, amount to be paid = $1,000,000 + $40,000 = $1,040,000
d.
Present value of face amount of bonds = $1,000,00/1.0340 = $1,000,000 / 3.2620 = $306,560.40
e. Total amount of bonds sold for = $1,000 * 1000 bonds = $1,000,000
f. If the market rate is 10% then the present value of the bonds issue shall be calulcated as the sum of present value of interest payments and present value of face amount of bonds
Present value of bonds issue = Present value of interest payments + Present value of face amount
= $40,000(1-1/1.0540)/0.05 + $1,000,000/1.0540
= $40,000(1-0.1420)/0.05 + $1,000,000/7.040
= $686,400 + $142,045.45 = $828,445.45
g. We have calculated the present value of interest payments and present value of face amount of bonds at 6% market rate in part b and part c.
At market rate 6%, present value of bonds issue = $924,533.33 + $306,560.40 = $1,231,093.73
At market rate 10% present value of bonds issue = $686,400 + $142,045.45 = $828,445.45
As we can see, if the market rate increases the present value of bonds issue decreases. This is because, if the coupon rate of bonds is greater than the market rate, the investor will be willing to pay premium to get the advantage of the coupon rate. In the opposite case, if the market rate is more than coupon rate, the bonds have to be sold at discount as the investors can get the higher return through other inveestments in market.
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