Bond and Note Valuation and Related Interest Rate Formulas

Bond Valuation - Page 15B2.n2X X X 1 XnTo simplify, multiply both sides of the equation times (1 - X)nnn1B3. 1X X X To further simplify, multiply both sides of the equation times 1n (the last two steps couldXhave been done in one step, but it is easier to see how we are getting to our results by doing it intwo steps)11B4. 1 X X XX1X nAt this point it is useful to substitute 1 r for X and VmmCto see where this is going11B5.1 r mn Vm a r p1 C mr mRearranging and solving for V (the present discounted value of the coupon payments alone)yieldsB6.VCm111rmrrmn a / p1m If we now add the present discounted value of the redemption value and the subtraction foraccrued interest, equation B6 becomes equation (23) above, which, despite its visual complexity,is easy to program into Excel, a computer program, or a calculator.The elegance of equation B6 is easier to see if we assume only one coupon interest payment per