Valuation of Corporate Securities
SelfPaced Overview
Bond Yields
In the previous example the market rate of discount was 8%. That did not mean that all bonds sold in the market had coupon rates of 8%. Rather it meant that all bonds of similar quality went through the same auction price as the bond in the example. If the bond sold for a discountDiscount:Selling below par., that would increase the yield. If it sold at a premiumPremium:Selling in excess of par., that would decrease the yield, all other things being equal. The yield to maturityYield to Maturity:Return on bond if held to maturity. Reflects premium/discount and price and maturity of bond. is actually the internal rate of returnInternal Rate of Return:Rate of return that causes net present value to equal 0. on a bond. To find the internal rate of return, use a financial calculator, a bond yield table, or a spreadsheet program. However, an approximation of the yield to maturity may be found by employing the following formula.
YTM Approx = 



where: I =
FV =
MP =
n =
Annual Interest in Dollars
Face Value of Bond
Market Price of Bond
Number of Years Until Maturity
An example shows the approximate yield to maturity for a 5%, $1000 bond selling for $990 with 6 years to maturity.
YTM Approx = 

= 5.19%  

Note that in using this approximation formula that the semiannual payments are not adjusted. In an efficient market, the yield, market rate of discount, and investors' required rate of return are all equal.