Understanding Bonds: Key terms, Face Value and Maturity

• Debt is when a company borrows money and repays it later.
• A bill is a short-term debt with promised principal payments within a year.
• A bond is a long-term debt issued by governments/corporations with future payments and a maturity date.
• Bond owners receive periodic interest payments and get back the amount at maturity.
• Bond trustee can classify the issuer as insolvent and force it into bankruptcy if the firm fails to make payments.

Bond Terminology

• Face value (or Par Value) is the notional amount of principal borrowed.
• Face value is used to compute interest payments.
• Face value is typically repaid at the loan's end.
• Assume the face value is $1000 for corporate bonds unless specified.
• Maturity is where the final repayment date of bond, including the principal amount borrowed.
• Interest payments on bonds are called "coupons".
• The coupon rate is the rate at which coupons are paid, expressed as an APR.
• The coupon amount is calculated as: Coupon Rate x Face Value / Number of Coupon Payments per Year
• Assume bonds pay coupons twice per year and coupon rate is an APR that compounds semi-annually if not stated.
• Yield to maturity (YTM) is the market required rate of return for bonds of similar risk and maturity.
• YTM is sometimes called the "yield".
• YTM is used as the discount rate to value a bond, and is quoted as an APR.

Bond Pricing

• Bond value equals the present value of interest payments and contractually promised principal, discounted using the market's required yield to maturity.
• Bonds are a type of fixed-income security.
• Cost of debt: rd = (1 + YTM/m)^(m*n) - 1
• Semi-annual bonds example
• An 8-year, $1,000 bond with a 7% semi-annual coupon has a market yield to maturity of 8% compounded semi-annually.
• Number of CPN payments = 2 x 8 years = 16
• Semiannual CPN = (7% x 1000 )/2 = $35
• Semiannual yield (rd) = 8%/2 = 4%
• P0 = 35 x [1 - (1 + 0.04)^-16 / 0.04] + [1000/(1 + 0.04)^16] = $941.74

Zero-Coupon Bonds

• Some companies issue bonds with no coupon payments, only one payment at maturity.
• To price it, calculating present value with a single cash flow formula: Bond Value = Face Value / (1 + rd)^n
• Zero coupon bonds sell below face value because they offer no coupons.

Bond Yields

• A bond's yield to maturity is the discount rate that makes the present value of coupon and principal payments equal to the bond price.
• YTM is the yield that the investor earns if the bond is held to maturity, and all coupon and principal payments are made as promised.
• A bond's yield to maturity changes daily as interest rates increase or decrease.
• Zero-Coupon Bond example
• A one-year, risk-free, zero-coupon bond with a $100,000 face value has an initial price of $96,618.36.
• The bond’s YTM is calculated as: rd = (Face Value / Bond Price)1/n - 1
• YTM of the zero coupon bond is 3.5%.
• Coupon Bond example
• An investor bought a three-year 6% coupon bond for $960.99, paying coupons annually.
• Investor's yield to maturity = rd =7.5%

Bond Relationships

• There is an inverse relationship between the market's required yield and bond prices.
• Bond prices fall as interest rates and bond yields rise.
• Bond prices rise as interest rates and bond yields fall.
• Coupon rate equals yield to maturity, the bond is sold at a price equal to its face value; these are par bonds.
• Coupon rate is less than yield to maturity, the bond is sold at a price less than its face value; these are discount bonds.
• Coupon rate is greater than yield to maturity. Then the bond is sold at a price more than its face value; these are premium bonds.
• Holding all other things constant, as the maturity date approaches, the market value of a bond approaches its face value.

Bond Risks and Characteristics

• Bond Price is inversely related to the market yield.
• When interest rates increase by 1% (100 basis points), bond prices decrease.
• Prices of long-term bonds change more than prices of short-term bonds with a given change in interest rates.
• Long-term bonds have greater price volatility than short-term bonds.
• Long-term bonds are riskier, all other things being equal.
• Interest rate risk increases as maturity increases, but at a decreasing rate.
• Prices of lower-coupon bonds change more than the prices of higher-coupon bonds with a given change in interest rates.
• The lower the bond's coupon rate, the greater the proportion of the bond's cash flow investors receive at maturity.
• A given change in interest rates will have a greater impact on the price of a low-coupon bond than a higher-coupon bond with the same maturity, all other things being equal.
• The lower a bond's coupon rate, the greater its price volatility. Lower coupon bonds have greater interest rate risk.

Bond Theorem Applications

• If rates are expected to increase, portfolio managers should avoid investing in long-term and/or low coupon bonds, as they could see a significant decline in value.
• If an investor expects interest rates to decline, you may want to invest in and/or low coupon bonds.
• The price of long-term zero-coupon bonds will increase more than any other bond type as interest rates decline.
• Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond.
• Default Risk is the risk that the lender may not receive payments as promised.
• The yield of bonds with credit risk will be higher than otherwise identical default-free bonds.
• Individuals and small businesses must rely on outside agencies for information on the potential that a bond issuer may default.
• The two most prominent credit rating agencies are Moody's Investors Service (Moody's) and Standard & Poor's (S&P).
• Highest grade bonds, those with the lowest default risk, are rated Aaa (or AAA).
• "Investment grade bonds", are in the top four rating categories, rated from Aaa (AAA) to Baa (BBB).
• Some laws require banks, insurance companies, superannuation funds, other financial institutions, government agencies to purchase only investment grade securities
• Speculative Bonds (BB - D) are also known as Junk Bonds or High-Yield Bonds.