# Bonds

Tutorials Long term Debt Finance Questions and Answers

Using present value to value bonds

A bond, from the perspective of the person issuing the bond is a form of long term debt.

In the hands of the person who has acquired the bond it is an asset.

The agency issuing the bond agrees to pay a fixed sum of money to the holder of the bond for a period of years and then, at the end of that period, to pay back the face value of the bond.

Bonds can be issued by a variety of agencies/companies:

1.Municipal bonds: issued by cities, states and other local agencies

2.Government bonds: issued by the department of finance/treasury department of a government

3.Corporate bonds: issued by companies

Our main interest in relation to bonds is in corporate bonds. Why do companies issue bonds? •Raise finance

•Often cheaper than bank borrowings

Terminology relevant to bond valuation

•Nominal/Face value/Principal – This is the amount on which interest payments are based. It is normally a round sum such as €1,000.

•Redemption value – This is the amount that will be paid out by the issuer of the bond when he comes to repay/redeem it.

•Coupon – The amount of interest paid on the bond is referred to as the coupon and the rate (%) is the coupon rate.

Premium/Discount - When you buy a bond you may pay a premium to acquire that bond or alternatively you may buy the bond at a discount. Where this occurs, the amount actually paid for the bond is greater (where it is acquired at a premium) or less (where it is acquired at a discount) than the face value of the bond. Whether you can acquire a bond at a discount or will have to pay a premium to acquire it will depend on how the coupon/interest rate being paid on the bond compares to the interest rate being paid on new issues of bonds. A premium bond is therefore one where the bond value is more than its face value. A discount bond is one where the value is less than its face value.

Valuing a fixed coupon and redemption date bond

Where we are dealing with this type of bond the valuation involves considering firstly the cash flows that are payable in respect of this type of bond.

In the same way as we considered the returns from an amount invested in earlier lectures, we can use the cash flows arising from the bond to arrive at a present value of the bond.

1.Consider a €1,000 bond which pays an annual coupon rate of 8% for five years after which period it will be redeemed. This bond will generate the following cash flows:

End year 1€80

End year 2€80

End year 3€80

End year 4€80

End year 5€1,080

What is the value of this bond?

1.Answer

The answer depends on the discount rate applicable to similar bonds. Once we know the appropriate discount rate we can calculate the present value of these cash flows and work out the value of the bond. If the redemption yield for similar bonds is 10% what is the value of the bond? Is it a premium or a discount bond? What would your answers be if the appropriate interest rate for this type of bond was 7%. 10% - Answer:

€80 x 3.791 = €303.28

€1,000 x .621 = €621

€303.28+€621 = €924.28

This would therefore be a discount bond

7% - Answer:

€80 x 4.1 = €328

€1,000 x 0.713 = €713

€328+€713= €1,041

This would therefore be a premium bond.

As we can see from the example above, the value of the bond is lower where redemption yields are high – therefore in a situation where current rates of interest are 10% and the bond is only paying out a return of 8%, the bond value is lower than its face value as it is no longer a very attractive investment. On the other hand where prevailing rates of interest are lower than the return being paid out by the bond its value increases and it becomes a much more attractive investment and investors would be willing to pay a premium on the bond in order to acquire it.

Question 3.

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