💰Intro to Finance Unit 5 – Bond Valuation

What's a Bond?

• Financial instrument that represents a loan made by an investor to a borrower, typically a corporation or government entity
• Bonds are debt securities where the issuer owes the holder a debt and is obligated to pay interest (coupon) and/or repay the principal at a later date (maturity)
• Bonds are used by companies and governments to finance projects and operations
• Key features of a bond include the coupon rate, face value, maturity date, and issuer
  • Coupon rate determines the amount of interest paid annually
  • Face value (par value) is the amount paid to the bondholder at maturity
• Bondholders are creditors of the issuer and have priority over stockholders in the event of bankruptcy
• Bonds offer a predictable income stream and are generally considered less risky than stocks
• Bond prices have an inverse relationship with interest rates; when interest rates rise, bond prices fall, and vice versa

Types of Bonds

• Government bonds are issued by national governments and backed by the full faith and credit of the issuing country (U.S. Treasury bonds)
• Municipal bonds are issued by states, cities, and other local government entities to fund public projects (infrastructure, schools)
  • Interest on municipal bonds is often exempt from federal income tax and may be exempt from state and local taxes for residents of the issuing state
• Corporate bonds are issued by companies to raise capital for various purposes (expansion, acquisitions)
  • Corporate bonds typically offer higher yields than government bonds due to increased risk of default
• Zero-coupon bonds do not pay regular interest but are issued at a discount and redeemed at face value upon maturity
• Convertible bonds give bondholders the right to convert their bonds into a predetermined number of shares of the issuer's common stock
• Callable bonds allow the issuer to redeem the bond before the maturity date at a predetermined price
• Junk bonds (high-yield bonds) are issued by companies with lower credit ratings and offer higher yields to compensate for the increased risk

Bond Pricing Basics

• Bond prices are quoted as a percentage of the bond's face value (par value)
  • A bond trading at 100 is selling at its face value (100% of par)
  • A bond trading at 95 is selling at a discount (95% of par)
  • A bond trading at 105 is selling at a premium (105% of par)
• Bond prices are influenced by various factors, including interest rates, credit quality, and time to maturity
• The price of a bond is the present value of its future cash flows, which include coupon payments and the repayment of principal at maturity
• The relationship between bond prices and yields is inverse; when bond prices rise, yields fall, and vice versa
• Duration is a measure of a bond's sensitivity to changes in interest rates
  • Bonds with longer durations are more sensitive to interest rate changes than bonds with shorter durations
• Convexity is a measure of how the duration of a bond changes as interest rates change
  • Bonds with higher convexity experience smaller price changes for a given change in interest rates compared to bonds with lower convexity

Yield and Interest Rates

• Coupon rate is the annual interest rate paid by the bond issuer on the bond's face value
• Current yield is the annual return earned on a bond based on its current market price and coupon rate, calculated as: $Current Yield = \frac{Annual Coupon Payment}{Current Bond Price}$
• Yield to maturity (YTM) is the total return expected on a bond if held until maturity, taking into account the current price, coupon rate, and time to maturity
  • YTM assumes that all coupon payments are reinvested at the same rate and is calculated using a trial-and-error process or a financial calculator
• Nominal yield is the stated interest rate on a bond, while real yield takes inflation into account
• Yield curve is a graphical representation of the relationship between bond yields and their maturities
  • A normal yield curve slopes upward, indicating that longer-term bonds have higher yields than shorter-term bonds
  • An inverted yield curve slopes downward, indicating that shorter-term bonds have higher yields than longer-term bonds
• The Federal Reserve influences interest rates through monetary policy, which can impact bond yields and prices

Calculating Bond Value

• The value of a bond is the present value of its future cash flows, which include coupon payments and the repayment of principal at maturity
• The bond valuation formula is: $Bond Value = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$
  • $C$ = Coupon payment
  • $F$ = Face value (par value)
  • $r$ = Required rate of return (discount rate)
  • $n$ = Number of periods until maturity
  • $t$ = Time period
• The required rate of return (discount rate) is the minimum rate of return an investor demands for investing in the bond, taking into account the bond's risk and opportunity cost
• The time value of money concept is crucial in bond valuation, as it accounts for the fact that money received in the future is worth less than money received today
• Bond valuation calculations can be performed using a financial calculator, spreadsheet software (Microsoft Excel), or online bond calculators
• The bond valuation formula assumes that coupon payments are made annually; for bonds with semi-annual coupon payments, the formula should be adjusted accordingly

Bond Valuation Methods

• Discounted cash flow (DCF) method values a bond by discounting its future cash flows (coupon payments and principal repayment) at the required rate of return
  • The DCF method is the most comprehensive and accurate approach to bond valuation
• Relative value method compares a bond's yield and other characteristics to similar bonds in the market to determine its relative value
  • This method is useful for identifying mispriced bonds and making investment decisions based on relative value
• Yield-based method values a bond based on its yield to maturity (YTM) and compares it to the yields of other bonds with similar risk and maturity
  • This method is a quick way to assess a bond's value but does not provide a precise valuation
• Matrix pricing method values a bond based on a matrix of yields for bonds with similar credit ratings and maturities
  • This method is often used by bond dealers and pricing services to provide indicative prices for less actively traded bonds
• Option-adjusted spread (OAS) method values a bond with embedded options (callable or putable) by considering the value of the option and the bond's cash flows
  • The OAS method is more complex than the DCF method but provides a more accurate valuation for bonds with embedded options

Risk Factors in Bond Valuation

• Interest rate risk is the risk that changes in interest rates will cause bond prices to fluctuate
  • When interest rates rise, bond prices generally fall, and vice versa
• Credit risk (default risk) is the risk that the bond issuer will fail to make coupon payments or repay the principal at maturity
  • Higher credit risk leads to higher yields and lower bond prices
• Liquidity risk is the risk that an investor may not be able to sell a bond quickly or at a fair price due to a lack of market demand
  • Less liquid bonds typically offer higher yields to compensate investors for the increased risk
• Inflation risk is the risk that the purchasing power of a bond's cash flows will decline due to inflation
  • Inflation-linked bonds (TIPS) can help mitigate inflation risk by adjusting the principal and coupon payments based on changes in the Consumer Price Index (CPI)
• Call risk is the risk that a callable bond will be redeemed by the issuer before maturity, potentially forcing the investor to reinvest at a lower yield
• Extension risk is the risk that a bond's expected maturity will be extended due to falling interest rates, causing the investor to miss out on the opportunity to reinvest at higher yields
• Sovereign risk is the risk that a government issuer will default on its debt obligations due to political or economic instability

Real-World Applications

• Bond valuation is essential for making informed investment decisions and managing bond portfolios
  • Investors use bond valuation to identify undervalued or overvalued bonds and make buy, sell, or hold decisions
• Financial advisors and portfolio managers use bond valuation to construct and optimize client portfolios based on risk tolerance, investment goals, and market conditions
• Companies and governments use bond valuation to determine the fair value of their outstanding debt and make decisions about issuing new bonds
• Bond valuation is crucial for assessing the creditworthiness of issuers and determining the appropriate yield spread over risk-free rates (credit spread)
• Central banks and monetary policy authorities use bond valuation to gauge market expectations and assess the effectiveness of their policies
• Bond valuation plays a key role in the development and functioning of capital markets, enabling the efficient allocation of resources and the pricing of risk
• Actuaries and pension fund managers use bond valuation to estimate the present value of future liabilities and ensure that pension plans are adequately funded
• Bond valuation is an important component of financial modeling and analysis, used in a variety of applications (mergers and acquisitions, capital budgeting)