Bond Valuation

Bond Arithmetic

Bond Valuation

1. In theory, the value of a bond is simply the present value of the EXPECTED payments. However, in practice, bond values are estimated by calculating the PV of the PROMISED payments which are the coupon payments and par value. The expected payments are the same as the promised payments for bonds that have no chance of default. However, if there is a chance that the promised payments won’t be made in full, the promised payment is the maximum possible amount (no one pays more than promised) and the expected payment must be less than the promised payment.

2. Here is the basic bond valuation equation:

Bond Value = C/(1+k)1 + C/(1+k)2 + ……+ C/(1+k)n + ParValue/(1+k)n

Where:

C is the coupon payment

n is the number of years to maturity

k is the appropriate annual discount rate

Note:

Most bonds make semi-annual payments and this requires some changes to the above expression. The payments must be halved, the discount rate must be halved, and the half-year intervals must be included.

For a bond with semi-annual payments,

Bond Value = .5C/(1+k/2)1 + .5C/(1+k/2)2 + ……+ .5C/(1+k)2n + ….

+ ParValue/(1+k/2)2n

3. The above equation is very easy to use within Excel. Just put the coupon payments and principal payments in a string of consecutive cells. Put the numbers 1 through n in a parallel string of cells and then calculate the PV of each single cash payment. Bond value is just the sum of these PVs. It is easy to check this calculation with the number produced using Excel’s PV formula.

4. Notice that the same rate is used to discount each cash payment in the formulas above. When we study the term