The Credit Corporation sells 900 bonds. Each bond has a par value of $1000. The

Question

The Credit Corporation sells 900 bonds. Each bond has a par value of $1000. The Bonds are sold on January 1, 2010. The interest rate listed on the bond is 8%. The bonds pay interest twice per year, June 30th and December 31st. The bonds are 15- 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% 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 to the bondholders to retire the bonds at the end of 15 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?

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? (explain)

Explanation / Answer

Since there are multiple sub-parts to the question, the first five have been answered.

________

Part A)

The total interest paid over the life of the bonds is calculated with the use of following formula:

Total Interest Paid = Number of Bonds*Face Value of Bonds*Coupon Rate*Maturity Period

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Here Number of Bonds = 900, Face Value of Bonds = $1,000, Coupon Rate = 8%/2 = 4% and Maturity Period = 15*2 = 30 [since interest is paid twice in a Year]

Using these values in the above formula for total interest paid, we get,

Total Interest Paid = 900*1,000*4%*30 = $1,080,000

_________

Part B)

The present value of interest payments can be calculated with the use of PV (present value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Market Interest Rate, Nper = Period, PMT = Interest Payment and FV = Face Value

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Here, Rate = 6%/2 = 3%, Nper = 15*2 = 30, PMT = 900*1,000*8%*1/2 = $36,000 and FV = 0 (since we are required to calculate the present value of interest payments only)

Using these values in the above function/formula for PV, we get,

Present Value of Interest Payments = PV(3%,30,36000,0) = $705,615.89

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Part C)

The total amount that will be paid to the bondholders to retire the bonds at the end of 15 years will comprise of the face value of bonds and last interest payment.

Total Amount Paid to Bondholders at Maturity = Total Face Value + Last Interest Payment = 900*1,000 + 36,000 = $936,0000

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Part D)

The present value of the face amount of bonds can be determined with the use of following formula:

Present Value of Face Amount = Face Amount/(1+Market Interest Rate/2)^n

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Here, Face Amount = 900*1,000 = $900,000, Market Interest Rate = 6%/2 = 3% and n = 15*2 = 30

Using these values in the above formula for Present Value, we get,

Present Value of Face Amount = 900,000/(1+3%)^30 = $370,788.08

_________

Part E)

The total amount at which were bonds were sold on January 1 2010 can be calculated with the use of following formula:

Total Sales Value of Bonds = Present Value of Interest Payments + Present Value of Face Amount

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Using the values calculated above, we get,

Total Sales Value of Bonds = 705,615.89 + 370,788.08 = $1,076,403.97

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