Overview
Bond valuation is a technique for determining the theoretical fair value of a particular bond. Bond valuation includes calculating the present value of a bond’s future interest payments, also known as its cash flow, and the bond’s value upon maturity, also known as its face value or par value. Because a bond’s par value and interest payments are fixed, an investor uses bond valuation to determine what rate of return is required for a bond investment to be worthwhile.
Key Takeaways
- Bond valuation is a way to determine the theoretical fair value (or par value) of a particular bond.
- It involves calculating the present value of a bond’s expected future coupon payments, or cash flow, and the bond’s value upon maturity, or face value.
- As a bond’s par value and interest payments are fixed, bond valuation helps investors figure out what rate of return would make a bond investment worth the cost.
Understanding Bond Valuation
A bond is a debt instrument that provides a steady income stream to the investor in the form of coupon payments. At the maturity date, the full face value of the bond is repaid to the bondholder. The characteristics of a regular bond include:
- Coupon rate: Some bonds have an interest rate, also known as the coupon rate, which is paid to bondholders semi-annually. The coupon rate is the fixed return that an investor earns periodically until it matures.
- Maturity date: All bonds have maturity dates, some short-term, others long-term. When a bond matures, the bond issuer repays the investor the full face value of the bond. For corporate bonds, the face value of a bond is usually $1,000; for government bonds, the face value is $10,000.
- Current price: Depending on prevailing interest rates, the investor may purchase a bond at par, below par, or above par. If interest rates increase, the value of a bond will decrease, causing it to trade at a discount.
Bond Valuation in Practice
Since bonds are an essential part of the capital markets, investors and analysts seek to understand how the different features of a bond interact in order to determine its intrinsic value. Bond valuation, in effect, is calculating the present value of a bond’s expected future coupon payments. The theoretical fair value of a bond is calculated by discounting the future value of its coupon payments by an appropriate discount rate. The discount rate used is the yield to maturity, which is the rate of return that an investor will get if they reinvested every coupon payment from the bond at a fixed interest rate until the bond matures.
Calculating Coupon Bond Valuation
Calculating the value of a coupon bond factors in the annual or semi-annual coupon payment and the par value of the bond.
The present value of expected cash flows is added to the present value of the face value of the bond using the following formula:
V_coupons = ∑ C / (1 + r)^t
V_face_value = F / (1 + r)^T
where:
C = Future cash flows (coupon payments)
r = Discount rate (yield to maturity)
F = Face value of the bond
t = Number of periods
T = Time to maturity
Example: Finding the value of a corporate bond with an annual interest rate of 5%, making semi-annual interest payments for 2 years, after which the bond matures:
- F = $1,000
- Coupon rate (semi-annual) = 5% / 2 = 2.5%
- C = 2.5% x $1,000 = $25 per period
- t = 2 years x 2 = 4 periods
- T = 4 periods
- r = YTM of 3% / 2 = 1.5%
- Present value of semi-annual payments:
25 / (1.015)^1 + 25 / (1.015)^2 + 25 / (1.015)^3 + 25 / (1.015)^4 = 96.36 - Present value of face value:
1000 / (1.015)^4 = 942.18
The value of the bond is $1,038.54.
Zero-Coupon Bond Valuation
A zero-coupon bond makes no annual or semi-annual coupon payments for the duration of the bond. Instead, it is sold at a deep discount to par when issued. The difference between the purchase price and par value is the investor’s interest earned. To calculate the value, find the present value of the face value.
Example
The value of a zero-coupon bond with a face value of $1,000, YTM of 3%, and 2 years to maturity is: 1000 / (1.03)^2 = 942.59
Comparing Bond and Stock Valuation
While both stocks and bonds are valued using discounted cash flow analysis, bonds include an interest (coupon) component and a principal component which is returning the loaned principal at maturity. Bond valuation computes the present value of each component and sums them.
Market Value vs. Face Value
A bond’s market value often differs from its face value due to factors such as interest rates, a company’s credit rating, time to maturity, call provisions, and whether the bond is secured or unsecured.
Interest Rates and Bond Prices
A bond with a fixed coupon varies inversely with interest rates. If prevailing rates rise, getting a fixed coupon becomes less attractive, leading to price discounts. Conversely, lower interest rates make fixed coupons more desirable, leading to premium prices.
Duration’s Impact on Bond Valuation
Duration measures a bond’s price sensitivity to interest rate changes. Longer-term bonds have higher durations and experience larger valuation impacts from discount rate changes.
Valuing Convertible Bonds
Convertible bonds can be converted into stock and are valued considering stock price variance, conversion ratio, and fluctuating interest rates. Essentially, their value combines the straight bond value and the conversion option value.
Related Terms: Coupon Bond, Zero-Coupon Bond, Discount Rate, Yield to Maturity, Face Value, Par Value.
References
- Treasury Direct. “Treasury Bonds: Rates and Terms”.
- Securities Industry and Financial Markets Association. “2021 Capital Markets Factbook”, Page 21.
