The fair value of a bond is determined by calculating the present value of all expected future cash flows, using variables such as time to maturity, discount rate, coupon rate, and face value. The time value of money principle is used, and the formula is P = C / (1 + r) + C / (1 + r) ^ 2 +…+ C / (1 + r) ^ n + M / (1 + r) ^ n. The fair value will be above face value for a premium bond and below for a discount bond.
The most common method of determining the fair value of a bond is to calculate the present value of all expected future cash flows from the bond. To do so, the following variables are typically needed: time to maturity, discount rate, coupon rate, and face value. Essentially, time to maturity is the time it takes for the bond issuer to return the money owed to the bondholder at face value, which is generally a round number. The discount rate is generally the rate of return an investor expects to receive if the bond is held to maturity, commonly known as the yield in the bond market. Finally, the coupon rate is basically the regular interest rate paid to the bondholder until maturity, where the investor receives the final coupon payment along with the face value.
When purchasing a bond, an investor generally expects to receive a series of cash flows until the bond matures. For example, a bond that has a maturity of three years and pays a coupon of US$100 per year would mean that the face value of US$1,000 is returned to the bondholder at the end of three years along with the last coupon fee. . This means that the bondholder will receive three separate cash flows. That is, the investor will receive $100 USD in the first year, $100 USD in the second year, and the last installment will be $1,100 USD at the end of the third year. To determine the fair price of such a bond, one needs to calculate the present value of all cash flows using the discount rate and the maturity period.
In finance, the fundamental principle underlying the practice of finding the present value of future cash flows is called time value of money (TVM). This concept states that a dollar earned today is more valuable than one earned in the future. For example, the $100 cash flow received in the first year is worth more than the $100 cash flow received in the second year, and so on. To determine the fair value of a bond, one needs to find the present value of each cash flow separately, and then add all of these present values to arrive at the fair price. The formula used to do this is as follows: P = C / (1 + r) + C / (1 + r) ^ 2 +. . . + C / (1 + r) ^ n + M / (1 + r) ^ n, where P is the fair value, C is the coupon, r is the discount rate, n is the number of full years to maturity , and M is the face value.
To illustrate, it is useful to consider a bond that has a face value of $1,000 USD, pays a coupon of $100 per year, with a yield of 9% or discount rate, and will mature in three years. P = 100 / (1 + 0.09) + 100 / (1 + 0.09)^2 + 100 / (1 + 0.09)^3 + 1000 / (1 + 0.09)^3, which equals the fair value of $1025.31 USD . It is important to note that the discount rate is expressed in decimals unless a financial calculator is used. In general, financial managers take the variables mentioned above and use a financial calculator or spreadsheet software to calculate the fair value of a bond, which makes it easy. Also, the method described above is applied to bonds known as vanilla bonds, which are the most common, although to determine the value of other types of bonds, financiers still use the above method and/or its variants.
Also, the fair value of a bond will always be above face value if the coupon rate is higher than the discount rate, which is called a premium bond. For example, if a bond has a coupon rate of 10% and a discount or yield rate of 8%, then its value will be greater than $1,000 USD. Conversely, if the discount rate is higher than the coupon rate, then its value will be less than par, also known as a discount bond. A bond with a yield of 12% and a coupon of 10%, for example, will be worth less than $1,000 USD. Finally, the fair value of a bond with the same coupon rate and discount rate is at face value, or its fair value will be $1,000.
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