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Chapter Objectives Bond Valuation • Demonstrate how bond market prices are established and influenced by interest rate movements and Risk • Identify the factors that affect bond prices 8 • Explain how the sensitivity of bond prices to interest rates is dependent on particular bond characteristics • Explain the benefits of diversifying the bond portfolio internationally د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Valuation Process Bond Valuation Process • Bonds are debt obligations with long-term maturities • Impact of the Discount Rate on Bond Valuation issued by governments or corporations to obtain long- • Discount rate = market-determined yield that could term funds be earned on alternative investments of similar risk • Commonly purchased by financial institutions that wish and maturity to invest funds for long-term periods • Bond prices vary inversely with changes in market • Bond price (value) = present value of cash flows to be interest rates generated by the bond • Cash flows are contractual and remain the same each period • Bond prices vary to provide the new owner the market rate of return د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Risks and Prices Interest Rate Risk • Higher risk • Lower risk • Bond Prices fluctuate over Time • As interest rates in the economy change, required rates on bonds • Higher discount rates • Lower discount rates will also change resulting in changing market prices. • Lower bond prices • Higher bond prices Note Inverse Relationship Interest Between Risk, required returns Rates VB and Bond Prices د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 1 Bond Valuation Process Interest Rate Risk • Bond Prices fluctuate over Time • Bond Price = present value of cash flows • As interest rates in the economy change, required rates on bonds discounted at the market required rate of return will also change resulting in changing market prices. • C = Coupon per period (PMT) • Par = Face or maturity value (FV) • i = Discount rate (i) • n = Compounding periods to maturity Interest Rates VB Interest Rates VB PV = C + C +… C + Par (1+ i)1 (1+ i) 2 (1+ i)n د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Valuation Process Bond Valuation Process • Consider a $1000, 10% coupon (paid annually) bond that PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3 has three years remaining to maturity. Assume the prevailing annualized yield on other bonds with similar = $951.97 risk is 12 percent. Calculate the bond’s value. • The expected cash flows of a coupon bond includes periodic interest payments, and… • A final $1000 payoff at maturity N I PV PMT FV • Discounted at the market rate of return of 12% 3 12 ? 100 1000 د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Valuation Process Bond Valuation Process • Valuation of Bonds with Semiannual Payments PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3 • Most bonds pay interest semiannually = $951.97 • Double the number of compounding periods (N) and halve the annual coupon amount (PMT) and the discount rate (I) N I PV PMT FV 3 12 –951.97 100 1000 د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 2 Determining the Price of a Bond—Example Q: The AYD Corporation issued an 8%, 25-year bond 15 years ago. At • Re-work the above problem assuming the time of issue it sold for its par (face) value of $1,000. Example Comparable bonds are yielding 10% today. What must AYD’s bond semiannual compounding sell for in today’s market to yield 10% (YTM) to the buyer? Assume the bond pays interest semiannually. Also calculate the bond’s current yield. A: We need to solve for the present value of the bond’s expected cash flows at today’s interest rate. PB = PMT [PVFAk, n] + FV [PVFk, n] K represents the periodic N I PV PMT FV current market interest N represents the rate, or 10% ÷ 2. number of The payment is 8% x interest-paying $1,000 or $80 annually. 6 6 ? 50 1000 periods until However, it is received in The future value is the maturity, or 10 the form of $40 every six principal repayment of years x 2 = 20. months. $1,000. د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Determining the Price of a Bond—Example Bond— Relationships Between Coupon Rate, Required Return, and Bond Price A: Substituting the correct values into the equation gives us: PB = $40 [PVFAk, n] + $1,000 [PVFk, n] Zero-Coupon Bonds = $40 [12.4622] + $1,000 [ 0.3769] = $498.49 + $376.90 = $875.39 This could also be calculated Example via a financial calculator: N 20 • No periodic coupon This is the price at which the bond must sell to yield 10%. PV -875.39 Answer • Pays face value at maturity It is selling at a discount because the current interest rate is above FV 1000 • Trade at discount from face value PMT 40 the coupon rate. The bond’s current yield is $80 ÷ $875.39, • No reinvestment risk or 9.14%. I/Y 5 • Considerable price risk د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Pricing Bond Pricing Characteristics of Bonds • Since a bond’s yield to maturity is a market Market Rate Bond Sold at interest rate: • As rates rise and fall 8% Premium • The yield rises and falls Bond • The bond price rises and falls Stated Interest 10% Face Value Rate 10% 12% Discount د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 3 Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond Price Required Return, and Bond Price • Discount bonds are bonds priced below face • Premium bond value; premium bonds above face value • Coupon > Market • Discounted bond • Rates decreased since issuance • Coupon < Market rates • Favorable risk experience • Rates have increased since issuance • Price risk—depends on maturity • Default risk might have decreased as economic activity • Adverse risks factors that may have occurred has increased • Price risk—depends on maturity • Low inflation expectations • Default risk may have increased • Fisher effect of higher expected inflation د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Value As the maturity date approaches, the price of ($) Relationships Between Coupon Rate, a bond approaches its face value. Required Return, and Bond Price 1368 Time Path of Bond Value When kd < Coupon Rate (Premium Bond) Bond Maturity and Price Variability Time Path of Bond Value When kd = Coupon Rate M=1000 M (Par Bond) • Long-term bond prices are more sensitive to given 769 Time Path of Bond Value When kd > Coupon Rate changes in market rates than short-term bonds (Discount Bond) • Changes in rates compounded many times for later coupon and maturity value, impacting price (PV) significantly • Short-term securities have smaller price 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 movements Years د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Long versus Short Maturity Bonds Interest Rate Risk Suppose YTMs decrease to 8%: Interest rate 1 year 30 years Bond values ($) 5% $1,047.62 $1,768.62 100 1 1,000 Price 2 = 1 - + 2 2 = 1,035.67 0 08 (1 08) (1 08) 10 1,000.00 1,000.00 2,000 15 956.52 671.70 100 1 1,000 $1,768.62 20 916.67 502.11 Price 15 = 1- + (1 08) = 1,171.19 0 08 15 15 (1 08) 1,500 30-year bond Suppose YTMs increase to 12%: $1,047.62 1-year bond 1,000 $916.67 100 1 1,000 Price 2 = 1 - (1 12) 2 + (1 12) 2 = 966.20 0 08 500 $502.11 100 1 1,000 Price 15 = 1 - + 15 15 = 863.78 0 12 (1 12) (1 12) 5 10 15 20 Interest rates (%) Price Change: 2 Year ($70/1000 =7%) 15 Year ($307/1000 =30.7%) Value of a Bond with a 10% Coupon Rate for Different Interest Rates and Maturities د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 4 Exhibit 8.4 Relationships Between Coupon Rate, Required Return, and Bond Price 1,800 Coupon Rates and Price Variability 1,600 1,400 1,200 1,000 • Low coupon bond prices more sensitive to change 5-Year Bond 800 10-Year Bond in interest rates 20-Year Bond 600 • PV of face value at maturity a major proportion of 400 the price 200 0 0 5 8 10 12 15 20 Required Return (Percent) د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Explaining Bond Price Movements Explaining Bond Price Movements • The price of a bond should reflect the present • Factors that affect the risk-free rate value of future cash flows discounted at a • Changes in returns on real investment required rate of return • Financial investment an alternative to real investment • The required return on a bond is primarily • Opportunity cost of financial investment is the returns available from real investment determined by • Federal Government deficits/surplus position • Prevailing risk-free rate • Inflationary expectations • Risk premium • Consumer price index • Federal Reserve monetary policy position • Oil prices and other commodity prices د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ • Exchange rate movements د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Explaining Bond Price Movements Exhibit 8.8 • Factors that affect the credit or default risk U.S. Fiscal U.S. Monetary U.S. Economic Issuer’s Industry Issuer’s Unique Policy Policy Conditions Conditions Conditions premium • Strong economic growth • High level of cash flows Long-T erm Risk-Free Risk • Investors bid up bond prices; lower default premium Interest Rate (Treasury Premium of Issuer Bond Rate) • Weak economic growth • Lower profits and cash flows Required Return on the • Impact on specific industries varied Bond • Investors flee from risky bonds to Treasury bonds • Bond prices fall; default premiums increase Bond Price د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 5 Sensitivity of Bond Prices to Interest Rate Movements Sensitivity of Bond Prices to Interest Rate Movements • Calculate the price sensitivity of a zero-coupon • Bond Price Elasticity = Bond price sensitivity for any bond with 10 years until maturity if interest rates % change in market interest rates go from 10% to 8%. • Bond Price Elasticity = • First, calculate the price of the bond for both rates (% Change In Price)/(% Change In Interest Rates) • When k = 10%, PV = ? • Increased elasticity means greater price risk • When k = 8%, PV = ? • Hint: Remember zero-coupon or no PMT in this calculation • The price of a zero-coupon bond is the present value of a single future value cash flow. د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Sensitivity of Bond Prices to Interest Rate Movements Sensitivity of Bond Prices to Interest Rate Movements • Calculate the price sensitivity of a zero-coupon Calculate the bond elasticity: bond with 10 years until maturity if interest rates go from 10% to 8%. $ 463 − $ 386 • First, calculate the price of the bond for both rates percent ∆ P $ 386 P = e = = − . 997 • When k = 10%, PV = $386 percent ∆ k 8 % − 10 % • When k = 8%, PV = $463 10 % Bond elasticity or price sensitivity to changes in interest rates approaches the limit at –1 for zero-coupon bonds. Price sensitivity is lower for coupon bonds. The inverse relationship between k and p causes the negative numbers د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Sensitivity of Bond Prices to Interest Rate Movements Sensitivity of Bond Prices to Interest Rate Movements • Price-Sensitive Bonds • Longer maturity—more price variation for a change Duration in interest rates • Lower coupon rate bonds are more price sensitive (the PV is a greater % of current value) • Zero-coupon bonds most sensitive, approaching –1 • Measure of bond price sensitivity price elasticity • Measures the life of bond on a PV basis • Greater for declining rates than for increasing rates • Duration = Sum of discounted, time-weighted cash flows divided by price د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 6 Sensitivity of Bond Prices to Interest Rate Movements Sensitivity of Bond Prices to Interest Rate Movements • Modified duration is an easily calculated Duration approximate of the duration measure DUR • The longer a bond’s duration, the greater its DUR * = sensitivity to interest rate changes (1 + k ) • The duration of a zero-coupon bond = bond’s term to maturity • The duration of any coupon bond is always less DUR* is a linear approximation of DUR which measures the convex relationship between bond yields and prices than the bond’s term to maturity د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Investment Strategies Used by Investors Bond Investment Strategies Used by Investors Matching Strategy Laddered Strategy • Create bond portfolio that will generate income that • Funds are allocated evenly to bonds in several will match their expected periodic expenses different maturity classes • Used to provide retirement income from savings • Example: ¼ funds invested in bonds with 5 years accumulation until maturity, ¼ in10-year bonds, ¼ in 15-year • Estimate cash flow needs then select bond portfolio bonds, and ¼ in 20-year bonds that will generate needed income • Investor receives average return of yield curve over time as maturing bonds are reinvested د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bond Investment Strategies Used by Investors Comparison of laddered and barbell maturity strategies Percent of Portfolio A dobe Sy stems Maturing Laddered Maturity Strategy 10 Barbell Strategy • Allocated funds to short-term bonds and long-term bonds 1 2 3 4 5 6 7 8 9 10 Percent of Portfolio • Short-term bonds provide liquidity from maturity Maturing Maturity in Years 40 Barbell Maturity Strategy • Long-term bonds provide higher yield (assuming up-sloping yield curve) 30 20 10 د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 1 2 3 4 ... ... 10 11 د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 12 13 14 15 Maturity in Years 7 Bond Investment Strategies Used by Investors Foreign Exchange Rates and Interest Rates • Country interest rate differences reflect expected future Interest Rate Strategy spot foreign exchange rates • Expected future spot foreign exchange rates (forward • Funds are allocated in a manner that capitalizes on forex rates) reflect expected inflation differences interest rate forecasts between countries • Example: if rates are expected to decline, move • Expected return on foreign bond portfolio related to into longer-term bonds return on bonds adjusted for expected changes in forex rates • Problems: • High transaction costs because of higher trading • Difficulty in forecasting interest rates د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Diversifying Bonds Internationally Bond Ratings Low Quality, speculative, Investment-Quality Bond Ratings and/or “Junk” • Investor may diversify by: High Grade Medium Grade Low Grade Very Low Grade • Credit risk Standard & Poor’s AAA AA A BBB BB B CCC CC C D Moody’s Aaa Aa A Baa Ba B Caa Ca C C • Country risk Moody’s S&P • Foreign exchange risk Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong. • Interest rate risk Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rating, this group • Seek lower total variability of returns per level A A comprises the high-grade bond class. Debt rated A has a strong capacity to pay interest and repay of risk assumed principal, although it is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than debt in high rated categories. د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ Bonds- Trading Bonds-How Ratings Work Bonds- Trading Bonds-How Ratings Work In general, higher ratings are associated with: It is important to note that more profitable companies *bond rating are given to issues not companies relying less on debt as a form of financing same can have different rating assigned to different more liquid issues stronger cash flows *bond rating can change with changes in conditions no trouble servicing their debt in a timely fashion *bond rating capture on default risk *more highly rated issues are more interest sensitive AAA through BBB is considered “investment grade” indicating financially strong, well run companies Below BBB (i.e. BB or Ba) denotes junk bonds - default risk is considered to be high. د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 8 DETERMINING COST OF DEBT CAPITAL DETERMINING COST OF DEBT CAPITAL rdebt or rd = RR + IP + DRP +LP + MP rdebt or rd = RR + IP + DRP+LP + MP • Determinants of Market Interest Rates • Nominal interest rate - observed or stated interest • Determinants of Market Interest Rates rate >Inflation premium (IP) – average expected • Real interest Rate (RR) – rate in addition to the inflation rate over the life of a risk-free loan inflation rate expected on a risk-free loan Inflation – rising prices not offset by increasing Risk-Free Rate or rf = RR + IP quality of the goods or services being purchased • Risk-free interest rate – interest rate on debt capital that is virtually free of default risk د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ DETERMINING COST OF DEBT CAPITAL DETERMINING COST OF DEBT CAPITAL rdebt or rd = RR + IP + DRP +LP + MP rdebt or rd = RR + IP + DRP +LP + MP • Determinants of Market Interest Rates • Determinants of Market Interest Rates >Default Risk Premium (DRP) – additional >Liquidity Premium (LP) – charged when a debt interest rate premium required to compensate the instrument cannot be converted to cash quickly and at lender for the probability that a borrower will its existing value default on a loan • Prime rate – interest rate charged by banks to their highest >Maturity Premium (MP) – premium to reflect in- quality (lowest default risk) business customers creased uncertainty associated with long-term debt • Bond rating – reflects the default risk of a firm’s bonds as judged • Term structure of interest rates – relationship between nominal by a bond rating agency interest rates and time to maturity when default risk is held constant • Senior debt – debt secured by a venture’s assets • Yield curve – graph of the term structure of interest rates • Subordinated debt – debt with an inferior claim (relative to senior debt) to venture assets اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ .د د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ DETERMINING MARKET INTEREST RATES The Term Structure of Interest Rates A. Upward-sloping term structure B. Downward-sloping term structure Interest Interest rdebt or rd = RR + IP + DRP+LP + MP rate Nominal rate interest rate Nominal • Real interest rate = 3% Interest rate Interest rate interest rate risk premium risk premium • Inflation expectation = 3% • Default risk = 5% Inflation Inflation premium • Liquidity premium = 3% premium • Maturity premium = 2% Real rate Real rate Time to Time to rd = 3% + 3% + 5% + 3% + 2% = 16% maturity maturity د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ د. اﺣﻤﺪ ﻳﻮﺳﻒ دﺷﺘﻲ 9