To determine the fair value of a security, the following variables are typically needed: time to maturity, discount rate, coupon rate, and par value.
The most common method of determining a security’s fair value is to calculate the present value of all expected future cash flows from the security. To do this, you typically need the following variables: time to maturity, discount rate, coupon rate, and face value. Essentially, time to maturity is the period of time until the bond issuer returns the money owed to the bondholder at par, which is typically a round number. The discount rate is generally the rate of return that an investor expects to receive if the bond is held to maturity, which is commonly referred to as the yield in the bond market. Finally, the coupon rate is basically the normal interest rate paid to the bondholder until maturity, when the investor receives the final coupon payment along with the par value.
When purchasing a bond, an investor normally 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 $100 US dollars (USD) per year would mean that the par value of $1,000 USD is returned to the bondholder at the end of three years along with with the last installment of the coupon. This means that the bondholder will receive three separate cash flows. That is, the investor will receive $100 USD in year one, $100 USD in year two, and the last installment will be $1,100 USD at the end of year three. To determine the fair price of such a security, it is necessary to calculate the present value of all cash flows using the discount rate and maturity period.
In finance, the fundamental principle underlying the practice of finding the present value of future cash flows is called the 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 cash flow of $100 USD received in year one is worth more than the cash flow of $100 USD received in year two, and so on. To determine the fair value of a security, it is necessary to find the present value of each cash flow separately and then add all these present values together 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 nominal value.
To illustrate, it is useful to consider a bond that has a par value of $1,000 USD, pays a coupon of $100 per year, has a 9% yield or discount rate, and has a maturity of three years. P = 100 / (1 + 0.09) + 100 / (1 + 0.09) ^ 2 + 100 / (1 + 0.09) ^ 3 + 1000 / (1 + 0.09) ^ 3, which is equal to 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. Generally, financial managers take the variables mentioned above and use a financial calculator or spreadsheet software to calculate the fair value of a security, which makes it very easy. In addition, the method described above applies to bonds known as vanilla bonds, which are the most common, although to determine the value of other types of bonds, lenders still use the above method and/or its variants.
Also, the fair value of a bond will always be above par 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 rate or yield of 8%, its value will be above $1,000 USD. On the other hand, if the discount rate is higher than the coupon rate, its value will be below par, also known as a discount bond. A bond with a yield of 12% and a coupon of 10%, for example, will have a value below $1,000 USD. Finally, the fair value of a bond with the same coupon rate and discount rate is at par, or its fair value will be $1,000 USD.