# Simple Valuation of Bonds using Present Value Technique

Valuation of bond can be easily done using present value technique. First, we need to understand the cash flow pattern of the bond. Secondly, the appropriate discounting factor should be decided. Lastly, discount the cash flows found in the first step using the discount rate found in the second step.

## Definition of a Bond

A bond is simply one of the main investment options available for investors to park their idle money. It is a medium to the long-term debt instrument issued by the government and corporate which offers fixed set of coupon payments based on the interest rate which is known as coupon rate and the face value of the bond i.e. principal is returned at the end of the maturity period.

A person sacrifices various pleasures of his life and saves his money. So, it is highly advisable to invest some time before investing money to achieve safe investment along with highest possible returns. Currently, we are discussing investment in a bond and its valuation using simple present value technique.

## Steps involved in Valuation of Bond

### Cash flow from a bond

Before moving forward towards valuation, let us understand a bond terminology and their cash flow patterns etc in little details. If a bond is paying 6% interest rate having the face value of \$1000 and maturity of 5 years. It means that it will pay \$60 every year till its maturity and repay \$1000 at the end of 5th year. Cash flow table will be like the below:

Cash Flows (\$):

Year1    Year2    Year3    Year4    Year5

\$60       \$60       \$60       \$60     \$1060

### Determining the appropriate discounting rate

For valuing the above bond using present value technique, it is utmost important to find the most appropriate discounting rate. For example, let’s consider the above bond is issued by a government agency and there is another government agency offering another bond at 5%. Since the bonds are issued by the government agency, they are almost risk-free or at least both of them assume the same level of risk. We can safely use 5% as our discounting rate because you can invest in 5% bond if you do not invest in the 6% bond and therefore the interest of 5% bond is your opportunity cost.

### Find Present Value of the Cash Flows i.e. Market Value of Bond

Once we have determined the most appropriate discounting rate for our situation, rest of the steps of valuation are very easy. We will now find the present value of the future cash flows or the discount the cash flows based on the discounting rate and add all of them. The result will give you the valuation of 6% bond i.e. the intrinsic value of the bond which can be construed as an ideal market price of the bond.

 Intrinsic Value of Bond = \$60.00 + \$60.00 + \$60.00 + \$60.00 + \$1,060.00 1.05^1 1.05^2 1.05^3 1.05^4 1.05^5

Intrinsic Value of Bond = \$1043.295.

The value of bond under the given conditions is \$1043.295. It can be interpreted from the calculations that the intrinsic value is more than its purchase price of \$1000. At the time of issuing the bond, an investor can get this price but once the bond opens for open market trading, the price will adjust according to the market conditions. If a bond is to be purchased from the open market, the same analysis can be done to find out the approximate value of the bond and take an informed decision.

### Using Annuity for Valuing Longer Term Bonds

One practical problem in the calculation will appear if the bond is of say 20 years. An annuity is a solution for that.

We will break the cash flows into two – the coupon payments and the principal repayment. We will find the present value of coupon payments using the annuity method and principal will be discounted using the normal method. Let’s use this method for the above calculations:

Present Value (PV) of Bond =    PV (Coupon Rate) + PV (Principal)

=          Coupon Amt. * 5 Yr. Annuity Factor + Principal * Discount Rate

=          60 * 4.3295 + 1000 * 0.7835

=          \$1043.295

Last updated on : August 31st, 2017

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