Chapter 5 Bonds Bond Valuation and Interest Rates

Chapter 5 Bonds, Bond Valuation, and Interest Rates Essentials of Managerial Finance by S. Besley & E. Brigham Slide 1 of 20

Copyright © 2014 by Nelson Education Ltd. Essentials of Managerial Finance by S. Besley & E. Brigham 6 -2 Slide 2 of 20

Basic Valuation • The (market) value of any investment asset is simply the present value of expected cash flows. • The interest rate that these cash flows are discounted at is called the asset’s required return. • The higher expected cash flows, the greater the asset’s value. • It makes sense that an investor is willing to pay (invest) some amount today to receive future benefits (cash flows). Essentials of Managerial Finance by S. Besley & E. Brigham Slide 3 of 20

Basic Valuation Model V 0 = CF 1 + (1 + k)1 CF 2 + … + (1 + k)2 CFn (1 + k)n Where: V 0 = value of the asset at time zero CFt = cash flow expected at the end of year t k = appropriate required return (discount rate) n = relevant time period Essentials of Managerial Finance by S. Besley & E. Brigham Slide 4 of 20

Raise funds with debt: Bonds • A bond is a long-term debt where the amount borrowed is repaid at maturity—that is, the end of the bond’s life – principal amount, face value, maturity value, and par value (all the above terminology refers to the amount that must be repaid by the borrower) – coupon interest rate - coupon payment divided to the par value – maturity date - date in which the par value must be repaid – call provision - the issuer can pay them prior to maturity – new issues - the coupon rate on a bond is approximately equal to the rate at which similar risk bonds are trading in the financial markets when the bond is issued Essentials of Managerial Finance by S. Besley & E. Brigham Slide 5 of 20

Retractable Bonds • Allow investors to sell the bonds back before maturity to the issuer at a pre-set price • Protect investors from the rising interest rates or the event risk Essentials of Managerial Finance by S. Besley & E. Brigham Slide 6 of 20

Sinking Fund Provision • Provision to pay off a loan over its life rather than all at maturity • Similar to amortization on a term loan • Reduces risk to investor, shortens average maturity • But not good for investors if rates decline after issuance Essentials of Managerial Finance by S. Besley & E. Brigham Slide 7 of 20

Two Ways to Handle Sinking Fund 1. Call x% at par per year for sinking fund purposes. 2. Buy bonds on the open market. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 8 of 20

Other Bond Features • Convertible bonds: Bondholders have a right to convert the bond into shares of common stock, at a fixed price. • Income bonds: Pay interest only when the issuer can afford to do so. • Real return bonds: Principal and interests are indexed and protected against inflation. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 9 of 20

Zero Coupon Bond Prices • With no interest payments, the price of a zero is the present value of the principal payment at maturity. 0 1 rd% Value Essentials of Managerial Finance by S. Besley & E. Brigham N 2 . . . M Slide 10 of 20

The basic bond valuation model B 0 = I 1 + (1+k)1 I 2 + … + (1+k)2 (In + Mn) (1+k)n Using the above model, find the (market) price of a 10% coupon bond, 3 years to maturity if market interest rates are currently 10%(par value= 100). B 0 = € 10 + (1+. 10)1 € 10 + (1+. 10)2 (€ 10 + € 100) (1+. 10)3 It can also be calculated by finding the present value of the annuity B 0 = 10 * (1 - [1/(1+. 10)3]) + 100 * [1/(1+. 10)3] =. 10 Essentials of Managerial Finance by S. Besley & E. Brigham Slide 11 of 20

Valuation of a bond using Excel For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%. Note: the equation for calculating price is =PV(rate, nper, pmt, fv) Essentials of Managerial Finance by S. Besley & E. Brigham Slide 12 of 20

Changes in bond values over time In the previous example, what would happen to the bond’s price if interest rates drop from 10% to 8%? When interest rate falls below the coupon rate, then the bond would sell at a premium When the interest rate goes down, the bond price will always go up Essentials of Managerial Finance by S. Besley & E. Brigham Slide 13 of 20

Changes in bond values over time In the previous example, what would happen to the bond’s price if interest rates increase from 10% to 12%? When interest rate increases above the coupon rate, then the bond would sell at a discount When the interest rate goes up, the bond price will always go down Essentials of Managerial Finance by S. Besley & E. Brigham Slide 14 of 20

Bond value–interest rate relationship Essentials of Managerial Finance by S. Besley & E. Brigham Slide 15 of 20

Bond Return kd Rate of return = INT Vd = Current yield Essentials of Managerial Finance by S. Besley & E. Brigham + Vd 1 – Vd 0 + Capital gains yield Slide 16 of 20

Bond Valuation – Change in value over time Bond Characteristics: M = € 1, 000. 00, INT = € 60. 00, kd = 8% Years to End of Year Maturity Value, Vd Capital Gain = (Vd 1 -Vd 0)/Vd 0 Current Yield = INT/Vd 0 Total Return 5 € 920. 15 4 2 933. 76 948. 46 964. 33 1. 48% 1. 57 1. 67 6. 52% 6. 43 6. 33 8. 00% 8. 00 1 981. 48 1. 78 6. 22 8. 00 0 1, 000. 00 1. 89 6. 11 8. 00 3 Essentials of Managerial Finance by S. Besley & E. Brigham Slide 17 of 20

Market value converges at par value to maturity Essentials of Managerial Finance by S. Besley & E. Brigham Slide 18 of 20

Finding the Yield to Maturity on a Bond • The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. PV = I 1 (1+k)1 + I 2 + … + (1+k)2 (In + Mn) (1+k)n Note that this is the same equation of the Basic Valuation Model. The only difference now is that we know the market price but are solving for return. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 19 of 20

Valuation with semi-annual compounding Example: M = € 1, 000, C = 5%, Yrs to maturity = 8, kd = 6% 16 3 ? 25 1000 N I PV PMT FV -931, 23 • Adjustments to computations – N = # years x m; m = # of interest payments per year – i = kd/m – INT = interest payment period = Annual INT/m Essentials of Managerial Finance by S. Besley & E. Brigham Slide 20 of 20

Callable Bonds and Yield to Call • Expected rate of return earned on a callable bond assuming it is to be called at the first call date • The company must pay a price (call price) higher than the par value to call the bond. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 21 of 20

Yield To Call (YTC): An Example • A 10 -year, 10% annual coupon, $1, 000 par value bond is selling for $1, 494. 93 with an 5% yield to maturity. • It can be called after 1 year at $1, 100. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 22 of 20

Yield To Call (YTC) if the Bond is Called 9 Years After Purchase Essentials of Managerial Finance by S. Besley & E. Brigham Slide 23 of 20

If You Bought Bonds, Would You Be More Likely to Earn YTM or YTC? • Coupon rate = 10% vs. YTC = rd = 4. 21%. Firm could raise money by selling new bonds that pay 4. 21%. • Could thus replace bonds that pay $100/year with bonds that pay only $42. 1/year. • Investors should expect a call, hence YTC = 4. 21%, not YTM = 5%. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 24 of 20

If You Bought Bonds, Would You Be More Likely to Earn YTM or YTC? (cont'd) • In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is likely. • So, expect to earn: – YTC on premium bonds – YTM on par & discount bonds Essentials of Managerial Finance by S. Besley & E. Brigham Slide 25 of 20

Current Yield A measure of the amount of cash income to be generated in a given year. Not an accurate measure of the bond's total expected return (consider a zero coupon bond with a current yield of zero). Current yield = Essentials of Managerial Finance by S. Besley & E. Brigham Annual coupon pmt Current price Slide 26 of 20

Current Yield: An Example 10% coupon, 14 -year bond, P = $1, 494. 93, and YTM = 5. 0% Current yield Essentials of Managerial Finance by S. Besley & E. Brigham = $100 $1, 494. 93 = 0. 0669 = 6. 69% Slide 27 of 20

Determinants of Market Interest Rates • Rate of return (interest) = k = Risk-free rate + Premium for risk = k. RF + RP Return Risk Premium = RP k. RF Risk-Free Return = k. RF 0 Essentials of Managerial Finance by S. Besley & E. Brigham k RP = k. RF + Risk Slide 28 of 20

Determinants of Market Interest Rates • Quoted rate = k. RF + RP = [k* + IP] + [DRP + LP + MRP] k* IP = real risk-free rate = inflation premium = k. RF DRP = default risk premium LP = liquidity (marketability) premium MRP = maturity risk premium Essentials of Managerial Finance by S. Besley & E. Brigham = RP Slide 29 of 20

Essentials of Managerial Finance by S. Besley & E. Brigham Slide 30 of 20

The Term Structure of Interest Rates Relationship between yields and bond maturities Yield (%) Upward sloping (normal) Flat Downward sloping (inverted) Term to Maturity (years) Essentials of Managerial Finance by S. Besley & E. Brigham Slide 31 of 20

The term structure of interest rates Explanations for the shape of the yield curve • Expectations theory – The shape of the yield curve is based on expectations about inflation in the future, i. e. inflation increases => yield curve upward sloping • Liquidity preference theory – Long-term bonds are considered less liquid than short-term bonds, i. e. long-term bonds must have higher yields to attract investors • Market segmentation theory – Borrowers and lenders prefer bonds with particular maturities. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 32 of 20

Interest rate Levels and Stock Prices Effects on corporate profits • Interest is a cost to business, so interest rate changes have a direct impact on business profits • Interest rates affect investment behavior, so when rates on bonds increase, money is taken out of the stock markets to invest in the bond markets => general prices of stocks are pushed down and the prices of bonds are pushed up Essentials of Managerial Finance by S. Besley & E. Brigham Slide 33 of 20

Interest rates and business decisions A firm’s decision concerning what types of financing should be used for investments in assets is based on forecasts of future interest rates • Suppose that interest rates are expected to fall over the next period, then the firm would borrow short-term and “lock” into lower long-term rates when the rates fall Essentials of Managerial Finance by S. Besley & E. Brigham Slide 34 of 20

Self – test problems Term structure of interest rates • If you have information that a recession is ending, and the economy is about to enter a boom, and your firm needs to borrow money, it should probably issue longterm rather than short-term debt – (a) TRUE – (b) FALSE Essentials of Managerial Finance by S. Besley & E. Brigham Slide 35 of 20

Self – test problems Term structure of interest rates • And the right answer is…. . (a) Essentials of Managerial Finance by S. Besley & E. Brigham Slide 36 of 20

Self – test problems Risk and return • Your uncle would like to restrict his interest rate risk and his default risk, but he still would like to invest in corporate bonds. Which of the possible bonds listed below best satisfies your uncle’s criteria? • (a) AAA bond with 10 years to maturity • (b) BBB bond with 10 years to maturity • (c) AAA bond with 5 years to maturity • (d) BBB bond with 5 years to maturity Essentials of Managerial Finance by S. Besley & E. Brigham Slide 37 of 20

Self – test problems Risk and Return • And the right answer is…. . (c) Essentials of Managerial Finance by S. Besley & E. Brigham Slide 38 of 20

Exam – type problems • Problem 1 – Suppose the annual yield on a two-year Treasury bond is 11. 5 percent, while that on a one-year bond is 10 percent; k* is 3 percent, and the maturity risk premium is zero. • Using the expectations theory, forecast the interest rate on a oneyear bond during the second year • What is the expected inflation rate in Year 1? Year 2? Essentials of Managerial Finance by S. Besley & E. Brigham Slide 39 of 20

Problem 1 Solution Given: One-year bond yield Two-year bond yield k*3. 0% MRP 0. 0% 11. 5% One-year rate In Year 2 Essentials of Managerial Finance by S. Besley & E. Brigham Slide 40 of 20

Exam – type problems • Problem 2 – Today is January 1, 2005, and according to the results of a recent survey, investors expect the annual interest rates for the years 2008 – 2010 to be: Year One-Year Rate 2008 5% 2009 4% 2010 3% – The rates given here include the risk-free rate, k. RF , and appropriate risk premiums. Today a three – year bond – that is, a bond that matures on December 31, 2007, has an interest rate equal to 6%. What is the yield to maturity for bonds that mature at the end of 2008, 2009 and 2010? Essentials of Managerial Finance by S. Besley & E. Brigham Slide 41 of 20

Problem 2 – Solution Year One-Year Rate 2008 5% 2009 4% 2010 3% Essentials of Managerial Finance by S. Besley & E. Brigham Today = 1/1/05 3 -yr yield = 6% Slide 42 of 20

Bankruptcy and Reorganization • A business is declared insolvent when it cannot meet its financial obligations. • Two options to deal with insolvency: – dissolve through liquidation (bankruptcy) – reorganize and stay alive Essentials of Managerial Finance by S. Besley & E. Brigham Slide 43 of 20

Bankruptcy and Reorganization (cont'd) • Two main chapters of the federal Bankruptcy Act: – Bankruptcy and Insolvency Act (BIA), bankruptcy – Companies' Creditors Arrangement Act (CCAA), reorganization Essentials of Managerial Finance by S. Besley & E. Brigham Slide 44 of 20

Reorganization • If a company can't meet its obligations, it files under CRA, which stops creditors from foreclosing, taking assets, and shutting down the business. • Company has 120 days to file a reorganization plan. – Court appoints a "trustee" to supervise reorganization. – Management usually stays in control. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 45 of 20

Reorganization (cont'd) • Company must demonstrate in its reorganization plan that it is "worth more alive than dead. " • Otherwise, judge will order liquidation under the Bankruptcy and Insolvency Act. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 46 of 20

Priority of Claims in Case of Liquidation • Suppliers can repossess goods delivered within 30 days prior to bankruptcy • Costs for environmental damage • Trustee expenses • Unremitted payroll taxes and deductions • Unpaid wages, up to $2, 000 per worker. • Secured creditors from sales of secured assets • Expenses incurred after bankruptcy filing Essentials of Managerial Finance by S. Besley & E. Brigham Slide 47 of 20

Priority of Claims in Case of Liquidation (cont'd) • Municipal taxes • Claims for rent, up to 3 months prior to bankruptcy • Creditor costs who first filed a claim • Injury claim costs to employees not covered under Workers' Compensation • Other unsecured creditors • Preferred stockholders • Common stockholders Essentials of Managerial Finance by S. Besley & E. Brigham Slide 48 of 20

Bankruptcy and Reorganization • In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back. • Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, the company "emerges" from bankruptcy with lower debts, reduced interest charges, and a chance for success. Essentials of Managerial Finance by S. Besley & E. Brigham Slide 49 of 20