Valuation of Bonds Bond Key Features Bond - a term promissory note - loan agreement - a contract- specifying loan amount, methods of payment and interest if any. Most common Bond features: Par value: Face amount; paid at maturity. Assume $1,000. Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed. Maturity: Years until bond is repaid. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Special Features Call feature: Issuer can refund if rates decline (will pay a call premium). That helps the issuer but hurts the investor. Most bonds have a deferred call and a declining call premium. Conversion feature: Lender (bond holder) can exchange the bond with a pre-specified number of stocks. Since it provide an equity option, the interest rate on such a bond might be lower, reducing the Cash Flow drain. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Asset Valuation Asset Value as Present Value of the Cash Flows it will produce: 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Pure Discount Bonds A pure discount bond (also called Zero Coupon or Zeroes) is a security that promises to pay a specified single cash payment (face value or par value) at a specified date called its maturity date Note There is no cash flow associated with interest Pure discount bonds are purchased at a discount from their face or par value 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Pure Discount Bond The pure discount bond is an example of the present value of a lump sum equation we analyzed previously. Let i be the appropriate discount rate, n number of periods to maturity. When we observe a price, we can compute the discount rate used to set that price: The yield-to-maturity is the discount rate that makes the present value of the cash flows from the bond equal to the current price of the bond. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Determinants of Rates of Return “Real” vs “Nominal” rates r* - real risk free rate, T-bill rate when there is no inflation rf - risk free rate, free of any risk including inflation risks r - Nominal rate, as rate required by assets holders IP – Inflation premium Short Term T-Bill rate of return (3) r = rf = r* + IP 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Determinants of Rates of Return For other assets (long term government, foreign government, municipal, corporate) add all or some of the following: DRP - Default Risk Premium LP - Liquidity Premium MRP – Maturity Risk Premium So that: (4) r = r* + IP +DRP + LP + MRP 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Yield Curve Term Structure: the relationship between interest rates (or yields) and maturities. A graph of the term structure is called the Yield Curve. We use pure discount bonds yield to maturity as the different period rates, called also pure discount rate June 17 2003 data. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Coupon Bonds A coupon bond obligates the issuer to make periodic payments of interest (called coupon payments) to the bond holder until the bond matures at maturity the face value of the bond is also paid to the bond holder and the contract is satisfied The coupon rate is the interest rate applied to the face value to compute the coupon payment A bond with a face value of $1,000 and a coupon rate of 10% pays an annual coupon of $100 At maturity, the payment is $1,000+$100 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Coupon Bond Price We can always analyze any fixed income contract into a sum of pure discount bonds Let i0,t be the t years pure discount rate. Such that i0,1 is a one year pure rate and i0,10 is the 10 years pure discount rate A bond with F par value and that pays $C coupon every period and is maturing in T periods. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg The YTM of a Coupon Bond We have the price of the coupon bond, and the timing and magnitude of its future cash flows, so we can determine its YTM The yield-to-maturity is the (one equal) discount rate that makes the present value of the cash flows from the bond equal to the current price of the bond. i that solves for the price is the YTM If we are provided a bond YTM, we can use it to price the bond. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Par, premium, and Discount Bonds A coupon bond with its current price equal to its par value is a par bond If it is trading below par it is a discount bond If it is trading above par it is a premium bond At maturity, the value of any bond must equal its par value. If a bond is currently valued at a premium (discount), as it approached maturity its value will decline (appreciate) towards par value. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Bond Yields YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.” 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Bond Risks Reinvestment Risk: The risk that Cash Flows will have to be reinvested in the future at lower rates, reducing income. Interest rate risk: Rising discount rates cause bond’s price to fall. Long-term bonds: High interest rate risk, low reinvestment rate risk. Short-term bonds: Low interest rate risk, high reinvestment rate risk. 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Bond Default Risk If issuer defaults, investors receive less than the promised return. Bond Ratings Services Provide One Measure of Default Risk Investment Grade Junk Bonds Moody’s Aaa Aa A Baa Ba B Caa C S&P AAA AA A BBB BB B CCC D 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg

Fin 301- Bond Valuation | Dr. Menahem Rosenberg Bond Default Risk Financial performance Debt ratio TIE ratio Current ratios Provisions in the bond contract Secured vs. unsecured debt Senior vs. subordinated debt Guarantee provisions Sinking fund provisions Debt maturity Other factors Earnings stability Regulatory environment Potential product liability Accounting policies 4/17/2019 Fin 301- Bond Valuation | Dr. Menahem Rosenberg