Calculating Fair Price For Investment Bonds

If you've ever watched the business report you might see the bond report and be bewildered by what they're talking about.  Most people understand bonds as something they buy from the government and get their money back plus interest at the end of the term.  While this is still true there is a significant secondary market for these securities.  Understanding how those secondary prices are determined is not too complicated but involves some math and some understanding.  That's where this hub comes in.

Understand Bond Prices

Although bonds are issued in different denominations ($100, $1000, $5000, etc.) they are all quoted on a base 100 system to be able to make apples to apples comparisons.  Bonds that trade at 100 are said to be trading at par.  Trading below 100 is trading at a discount, while trading above 100 indicates trading at a premium.

4 Steps To Calculate Bond Prices

1. Determine the discount rate
2. Calculate present value of bond at maturity
3. Calculate present value of the interest income of the bond
4. Add the two present values together to get the price.

The discount rate is roughly equivalent to the Yield To Maturity and is determined by the marketplace based on the price paid for the bond.  It's important to note that the discount rate is not the same as the coupon rate.

Present Value Of Principal

               FV
PVP =    --------
             (1 + r)ⁿ

PVP = Present Value
FV = Future Value of the bond
r = discount rate
n = number of payment periods from present to maturity

Present Value of Interest Income

             [            1      ]
             [  1 - ----------]
PVII = C[       (1 + r)ⁿ  ]
             [---------------]
             [        r          ]

PVII = Present Value of Interest Income
C = The value of one coupon payment
r = discount rate
n = number of payment periods from present to maturity

Present Value Of Bond = PVP + PVII

Confused Yet?  Let's Try An Example

We will use a 5 year semi-annual 7% coupon bond with a discount rate of 8% (the actual price doesn't matter in this calculation).
The first thing to note is that when looking at the discount rate we have to spread it out to the same number as the number of interest payments.  So in the case we will use 4% because of the semi-annual payment schedule.
             100        the base trading value will mature at par (aka 100).
PVP = ----------
         (1+0.04)¹⁰    the 10 is derived from 5 years * 2 payments annually

             100
PVP = ----------
           1.4802

PVP = 67.5584

The coupon is paid semi-annually so much in the same way as we divided the discount rate over the number of payments per year we do the same with the coupon.  It's a percentage of the value so we can continue to use the base 100 and find that C = 3.50

                 [             1           ]
                 [  1 - ----------      ]
PVII = 3.50[       (1 + 0.04)¹⁰]
                 [--------------------]
                 [       0.04           ]

                 [             1     ]
                 [  1 -   ---------]
PVII = 3.50[         1.4802]
                 [----------------]
                 [      0.04       ]

PVII = 3.50[  0.3244 ]
                 [   -------- ]
                 [    0.04   ]

PVII = 28.385

Present Value of Bond =  67.5584 + 28.385 = 95.9434

So after all that calculation we now know that the fair price for this bond is 95.94 points.  There is a very large bond market and it would be prudent to include bonds as a part of your investing strategy but few people actually understand how they work.  Hopefully this has helped you further understand bonds.  If you'd like to learn more there are more resources here.