Valuation of Bonds
The value of a bond can be determined by adding up the present value of all the cash flows associated with the bond.
Present value is the amount that must be invested today in order to receive a given amount in the future. In an inflationary environment, present value is lower than future value.
For instance, if you buy a one-year $100 U.S. Treasury note with no coupons for $90, you pay $90 today for the right to receive $100 in one year. The present value of the one-year note is $90.
Let’s look at a more detailed example.
An investor wants to purchase a debt instrument that will pay $10 million in 10 years, with an annual interest rate of 5%.
The following equation can be used to calculate the present value:
Present value is indicated by PV, while future value is represented by FV. R is the interest rate, and n is the number of times (periods) the interest rate will be accrued.
So:
PV = $10,000,000 x (1 / (1 + 0.05)10)
PV = $10,000,000 x (1 / (1.63))
PV = $10,000,000 x 0.61
PV = $6,100,000
So $6.1 million invested today at a 5% interest rate will yield $10 million after ten years. This process of finding the present value is sometimes called discounting, so the present value is often called the discounted value.
Municipal bonds offer interest payments in addition to the principal amount, so how do we determine the present value of a municipal bond? Assuming the interest rate is fixed, the bond can be broken down into each of its individual cash flows, then the present value of each cash flow can be calculated, and if they are all added together, we have the present value of the bond.
Let’s say you buy a five-year $1,000 municipal bond that pays 5% at the end of each year. The cash flows are the interest payments. So you have a $50 cash flow at the end of the first year, then another $50 cash flow at the end of the second year, and