Bonds are often quoted with the price showing the percentage of notional value or face value that an investor must pay for the bond at any given moment.
So bond prices play a critical role for market participants.
But how exactly is a bond priced? Well, the answer lies in a fundamental concept in finance known as the time value of money.
This principle suggests that the present value of a cashflow is different from its future value because money available today has the potential to earn interest or investment returns while future money is not immediately available for us.
From a technical point of view, a bond is essentially a series of cash flows In the case of fixed coupon bonds, these cash flows, which include coupon payments and the final redemption payments, they are all known from the outset of the bond's life.
However, because these payments occur in the future, we cannot simply add them all together to calculate the bond's price.
This is where the time value of money comes into play.
To calculate the bond's price, we need to discount all of the future coupon payments as well as the final redemption payment to today.
This is done by dividing each of these future payments by one plus the required rate of return per period raised to the power of the period number.
The formula for this is shown here.
C represents the coupon amount per period.
Fee is the face value of the bond, which will be repaid at maturity.
R is the required rate of return or discount rates per period, and N is the number of periods to maturity.
So the bond price is the sum of the present value of all the coupon payments and the redemption payment each discounted back to the present using the required rate of return.
Why do we use the required rate of return for this calculation? Well, the required rate of return reflects the return investors expect for the level of risk they are taking by buying the bond.
At issuance, the bond price is set so that based on the bond's, coupon, payments and final redemption value investors achieve their required rate of return.
In other words, the bond price ensures that the investor will receive the rate of return they require, assuming they hold the bond maturity.
If this weren't the case, investors would not be motivated to invest in the bond in the first place once the bond is trading in The the secondary market. However, the price is no longer determined solely by this formula.
Instead, it's driven by supply and demand factors, including changes in interest rates and perceptions of the issuers credit worthiness.
Investors may buy the bond at a premium above face value or at a discounts below face value, depending on how these market factors influence the bond's appeal.
However, at issuance pricing the bond using the required rate of return ensures that it offers the return that investors buying the bond consider appropriate for the level of risk.
