Valuation of Bonds

Valuation of Bonds Bus 512- Bond Valuation | Dr. Menahem Rosenberg

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. Bus 512- 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. Bus 512- Bond Valuation | Dr. Menahem Rosenberg

Asset Valuation • Asset Value as Present Value of the Cash Flows it will produce: Bus 512- 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 Bus 512- 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. Bus 512- 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 Bus 512- 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 Bus 512- 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. Bus 512- Bond Valuation | Dr. Menahem Rosenberg

Yield Curve • October 10 2002 data. Bus 512- 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 Bus 512- 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,tbe the t years pure discount rate. • Such that i0,1is a one year pure rate and i0,10is 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. Bus 512- 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. Bus 512- 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. Bus 512- Bond Valuation | Dr. Menahem Rosenberg

Bond Yields • YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.” Bus 512- 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. Bus 512- 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 Bus 512- 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 Bus 512- Bond Valuation | Dr. Menahem Rosenberg

Valuation of Bonds