The bond valuation formula can be determined in different ways depending upon the data available. This data can be found through company information, financial documents and market analysis. The formula can also be adjusted to reflect different payment dates as well. Sometimes the bond is sold for less than its face value however and this is called a discount. The bond may also be sold for more than face value or at a premium.
The Data Needed to Get the Bond Valuation
In order to calculate the bond valuation formula some basic data is needed. This includes the face value of the bond (F), the contractual interest rate (iF), the periodic interest payment (C=FiF) and the number of payments (N). The market interest rate, required yield or observed yield to maturity is also needed (i) and can be found through a separate calculation. In addition the value at maturity (M) and the market price of the bond (P) may also be needed.
The Formula used for Bond Valuation
In order to find the bond valuation formula, the present value calculation is used. This is P= (C¦(1+i)+ C/(1+i)^2 +C/(1+i)^N )+M/(i+i)^N = (?_(n=1)^N¦C/?(1+i)?^n )+M/?(1+i)?^N or P=C(?1-(1+i)?^(-N)/i)+M?(1+i)?^(-N). The formula to determine the yield value can be found by taking the coupon yield (C) and dividing it by a percentage of the face value (F). Therefore, the coupon yield is C/F. The equation may also be adjusted using the Stochastic calculus approach which recognizes that discount rates are not adequately found by using a fixed number. The equation for this is 1/2 s(r)(2?^2 P)/(?r^2 )+[a®+s(r)+s(r)+f(r,t)]?P/?r+?P/?t-rP=0.
The Relative Price Approach
The relative price bond valuation formula approach is used when the bond pricing is related to a benchmark. This is often found in government securities. With this type of bond, the yield to maturity is directly related to the bond’s credit rating. The smaller the spread between the yield to maturity and the required return the better the bond. With this formula, the required return (i), calculates the discount the bond and obtain the price.
The Arbitrage Free Price Approach
The Arbitrage Free bond valuation formula the coupon or face value is discounted at the same rate as a zero-coupon bond. The credit history of the issuer is also evaluated. With this approach, the coupon dates and amounts are a known quantity. They are then compared to zero coupon bonds equal in sum to that of the discount rates. Bonds may also use short selling to meet cash flow requirements making the difference between the valuations risk free.
The cash flow of the bond is the interest payments, the principal payments and the possibility that the bond will be called soon. When these equations are used, investors are able to determine if they are willing to pay a certain price for a bond and what the cash flow will be. It also helps when deciding when to sell a bond. The equations are used to calculate the rate of return. These factors and formulas are an important component of buying and selling bonds.