One of the Most Important Uses of Discounting

The present value of a bond is the sum of all the future cash flows that can be derived from it. In this sense, the valuation of bonds really becomes simple, isn’t it? All we need to do is find out the future stream of payments that are due on the bond and then find out their present value and we call find out what the valuation of that bond is. Well, this may be theoretically this simple.

However, in practical life estimating the parameters like discount rate which go into the calculation can be very difficult. Also, using different discount rates can cause us to come up with very different valuations. So, bond valuation really is a game about guessing what the future discount rate will be.

Now, let’s have a look at a theoretical example of bond valuation. Here is a step by step procedure of how the calculation must be done:

Two Components

The calculation of the present value of the bond is done in two components. They are as follows:

• Annuity: Bonds have a series of coupon payments that are due. Coupon payments are interest payments that are made periodically. Usually the frequency of paying interest is semi-annual. Corporations all over the world pay interest twice a year because it is a bond market convention.

  Also, it must be understood that bonds can have 2 values. The face value is the original issue value of the bond whereas the market value is its current market price. So, if the interest payments are not directly given, we need to compute them using the face value. Remember that interest payments are always computed using face value and not market value!

  Hence, the annual interest rate needs to be converted into a semi-annual rate or whatever rate is appropriate. Then, it must be plugged into the annuity formula along with the other details to derive the present value of the coupon payments that are due.

• Lump sum: Bonds usually pay interest throughout their lives. However, they pay back the principal at the end of their lives. The principal therefore is a lump sum payment that may have to be discounted many years into the future. Now, even though this payment is not being received twice a year, we will still consider the semi-annual interest rates to find out the present value of the lump sum payment.

The final step is to add the present value of the annuity as well as of the lump sum payment. This adds the present values of the interest payments as well as the principal payments. Hence, we get the present value of the bond.

Example:

Let’s find the present value of a bond whose face value is $100. Interest rate is 12% on an annual basis. The bond will make semi-annual interest payments for 10 years after which the principal has to be repaid and the bond expires.

Present Value of Interest Payments

Number of periods = 20 periods (10 years, however the payment is semi-annual)

Discount Rate = 6% per period (Since we have doubled the number of periods, we need to cut the discount rate into half)

Payment: $6 per period (6% * face value of $100)

Therefore, present value of the annuity equals $68.82. This is the present value of the interest payments due.

Present Value of Principal Due

The principal that needs to be repaid is $100. It needs to be repaid after 20 periods and the discount rate we are considering is 6% per period. The present value of the principal therefore is $31.18

To find the present value of the bond we need to add $68.82 + $31.18. In this case, this adds up to $100. Therefore the present value of the bond is $100.

It must, however be noted that in real life bond values swing based on the expectation of what the future discount rate will be like. It is not really the current discount rate which determines the bond value!