# Bond valuation

#### What is bond valuation and how does this work?

The process of calculating a bond’s fair price is referred to as ‘bond valuation’. However, the theoretical fair price is based on the current value of the cash flow that the bond is expected to generate.

It follows suit then, that the actual valuation of a bond is calculated by discounting the anticipated cash flow to the current time by using the rate of discount that currently applies. Determining the rate, or the ‘pricing’ of the bond, is done with considerable reference to other financial instruments. This information is important to people whose goal is to make money via bond trading.

Once the bond’s price or value has been determined, the price sensitivity can be estimated. The different yields which relate to the bond’s value to the bond’s coupons can be determined as well during the valuation process. This valuation becomes more specialized if ‘embedded options’ exist (options which provide a structure to the bond) and are included in the bond. This more specialized valuation combines the cash flow based approach above with option pricing.

#### The 2 bond valuation formulas

As was mentioned above, the fair value of straight bonds, or those types of bonds which contain no embedded options, is calculated by using the current discount rate and applying it to the estimated cash flow of those bonds. The applicable formula is calculated in the following manner:

Cash Flows – C = periodic coupon payments,

n = the number of times that coupon payments occur,

F = the face or par value,

and T = the value of the bond which is paid out when it matures.

Discount Rate – r = the required rate of return or yield which is compounded annually and is the current market rate of interest for those bonds with similar risk rankings and terms,

m = the coupons which remain to be paid over the remaining bond’s lifetime (in other words like n above) multiplied by T (see above), and u = (1 + r) 1 / n) which is the accumulation of interest during each coupon period.

Taking the above into consideration, the formula is that the bond price is a combination of the above. Since the value of the bond is the present value of applicable cash flows, an inverse relationship exists between the discount rate and the actual price of the bond. The higher the rate of the discount, the lower the bond price or value that will be attained.