💳Principles of Finance Unit 10 – Bonds and Bond Valuation

What Are Bonds?

• Financial instruments that represent 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, providing an alternative to equity financing
• Investors purchase bonds to receive regular interest payments and the return of principal when the bond matures
• Bonds are generally considered less risky than stocks but offer lower potential returns
• The price of a bond is influenced by factors such as interest rates, credit quality of the issuer, and time to maturity
• Bonds play a crucial role in the capital markets, allowing entities to borrow money and investors to earn a predictable stream of income

Types of Bonds

• Government bonds issued by national governments (U.S. Treasury bonds) and considered low-risk investments
• Municipal bonds issued by state and local governments to fund public projects (infrastructure) and often offer tax advantages
• Corporate bonds issued by companies to raise capital for various purposes (expansion, acquisitions) and offer higher yields but greater risk compared to government bonds
• High-yield bonds (junk bonds) issued by companies with lower credit ratings and offer higher interest rates to compensate for the increased risk of default
• Zero-coupon bonds do not pay regular interest but are sold at a deep discount and pay face value at maturity
• Convertible bonds can be converted into a predetermined number of the issuer's equity shares under certain conditions
• Callable bonds give the issuer the right to redeem the bond before maturity, typically when interest rates fall

Bond Features and Terminology

• Face value (par value) represents the amount the bondholder will receive when the bond matures
• Coupon rate is the annual interest rate paid on the bond's face value, expressed as a percentage
• Coupon payments are the periodic interest payments received by the bondholder, typically paid semi-annually
• Maturity date is the date on which the principal amount of the bond is repaid to the bondholder
• Credit rating is an assessment of the creditworthiness of the bond issuer, provided by credit rating agencies (Moody's, Standard & Poor's)
• Yield to maturity (YTM) is the total return anticipated on a bond if it is held until maturity, expressed as an annual rate
• Duration measures the sensitivity of a bond's price to changes in interest rates, expressed in years
• Convexity is a measure of how the duration of a bond changes as interest rates change, providing a more precise measure of interest rate risk

How Bond Pricing Works

• Bond prices are quoted as a percentage of the face value (par value) and can be above (premium) or below (discount) par
• The price of a bond is determined by the present value of its expected future cash flows, which include coupon payments and the repayment of principal
• Interest rates and bond prices have an inverse relationship: when interest rates rise, bond prices fall, and vice versa
• The price of a bond is influenced by factors such as the bond's coupon rate, time to maturity, credit quality of the issuer, and prevailing market interest rates
• Newly issued bonds are typically priced at or near par value, with the coupon rate set to match prevailing market interest rates
• As interest rates change, the price of a bond will adjust to maintain its yield relative to other investment alternatives
• The market price of a bond can be calculated using the present value formula, which discounts future cash flows at the appropriate discount rate

Calculating Bond Yields

• Current yield is the annual interest payment divided by the bond's current market price, expressed as a percentage
  • Current yield = Annual coupon payment / Market price
• Yield to maturity (YTM) is the total return anticipated on a bond if it is held until maturity, taking into account the present value of future cash flows
  • YTM is calculated using a trial-and-error process or a financial calculator, as it requires solving for the discount rate that equates the present value of future cash flows with the bond's current price
• Yield to call (YTC) is the total return anticipated on a bond if it is called by the issuer prior to maturity, taking into account the present value of cash flows until the call date and the call price
• Realized yield is the actual return earned on a bond, taking into account the price paid, coupon payments received, and the price at which the bond is sold or matures
• Nominal yield is the coupon rate on a bond, which does not take into account the time value of money or inflation
• Real yield is the nominal yield adjusted for inflation, representing the true increase in purchasing power that an investor receives

Interest Rates and Bond Prices

• Interest rates and bond prices have an inverse relationship: when interest rates rise, bond prices fall, and vice versa
• This relationship exists because the coupon rate on a bond is fixed at issuance, so as market interest rates change, the price of the bond must adjust to provide a competitive yield
• The sensitivity of a bond's price to changes in interest rates depends on factors such as the bond's coupon rate, time to maturity, and the prevailing market interest rates
• Bonds with longer maturities and lower coupon rates are more sensitive to interest rate changes, as a greater portion of their total return comes from the repayment of principal at maturity
• The duration of a bond is a measure of its price sensitivity to interest rate changes, with longer-duration bonds experiencing greater price fluctuations for a given change in interest rates
• Convexity measures the rate of change of a bond's duration as interest rates change, providing a more precise measure of interest rate risk
• Investors can manage interest rate risk by diversifying their bond holdings across different maturities and adjusting their portfolio's duration based on their expectations for future interest rate movements

Bond Valuation Methods

• The present value approach discounts a bond's future cash flows (coupon payments and principal repayment) at the appropriate discount rate to determine its theoretical fair value
  • The discount rate used is typically the yield to maturity (YTM) of the bond, which represents the total return an investor would receive by holding the bond to maturity
• The yield to maturity approach calculates the total return an investor would receive by holding a bond to maturity, taking into account the bond's current price, coupon payments, and face value
  • YTM is calculated using a trial-and-error process or a financial calculator, as it requires solving for the discount rate that equates the present value of future cash flows with the bond's current price
• The yield to call approach calculates the total return an investor would receive if a callable bond is called by the issuer prior to maturity, taking into account the bond's current price, coupon payments, and call price
• The nominal spread approach compares the yield on a bond to the yield on a benchmark security (U.S. Treasury bond) of similar maturity to determine the bond's relative value
  • The nominal spread represents the additional yield an investor receives for taking on the credit risk associated with the bond issuer
• The option-adjusted spread approach takes into account the value of embedded options (call, put) in a bond when comparing its yield to that of a benchmark security
• The credit spread approach compares the yield on a bond to the yield on a risk-free security of similar maturity to determine the additional yield an investor receives for taking on credit risk

Risks and Rewards of Bond Investing

• Interest rate risk is the risk that changes in interest rates will cause bond prices to fluctuate, with rising interest rates leading to falling bond prices and vice versa
• Credit risk (default risk) is the risk that the bond issuer will fail to make coupon payments or repay the principal when the bond matures
  • Credit risk is assessed by credit rating agencies (Moody's, Standard & Poor's), which assign ratings to bond issuers based on their creditworthiness
• Liquidity risk is the risk that an investor will not be able to sell a bond quickly or at a fair price due to a lack of market demand
• Inflation risk is the risk that the purchasing power of a bond's coupon payments and principal repayment will be eroded by inflation over time
• Reinvestment risk is the risk that an investor will have to reinvest coupon payments or the principal repayment at a lower interest rate than the bond's original coupon rate
• Bonds offer several advantages to investors, including regular income through coupon payments, preservation of capital (principal repayment at maturity), and diversification benefits when combined with other asset classes (stocks)
• Bonds are generally considered less risky than stocks, as they offer a predictable stream of income and the repayment of principal at maturity, but they also provide lower potential returns over the long term
• Investors can manage the risks associated with bond investing by diversifying their holdings across different bond types, maturities, and credit qualities, and by actively managing their portfolio's duration and credit exposure based on their investment objectives and risk tolerance