Bond Valuation FINA 320 PDF

Bond and Bond Valuation FINA 320 Dr. Lei Zhou  Learning Objectives 1. Understand basic bond terminology and apply the time value of money equation in pricing bonds. 2. Understand the difference between annual and semiannual bonds and note the key features of zero-...

Bond and Bond Valuation FINA 320 Dr. Lei Zhou  Learning Objectives 1. Understand basic bond terminology and apply the time value of money equation in pricing bonds. 2. Understand the difference between annual and semiannual bonds and note the key features of zero-coupon bonds. 3. Explain the relationship between the coupon rate and the yield to maturity. 4. Delineate bond ratings and why ratings affect bond prices. NIU FINA 320 - Dr. Lei Zhou 2  Differences Between Debt and Equity Debt Equity Not an ownership interest Ownership interest Creditors do not have voting Common stockholders vote rights for the board of directors and Interest is considered a cost of other issues doing business and is tax Dividends are not considered deductible a cost of doing business and Creditors have legal recourse if are not tax deductible interest or principal payments Dividends are not a liability are missed of the firm and stockholders Excess debt can lead to have no legal recourse if financial distress and dividends are not paid bankruptcy NIU FINA 320 - Dr. Lei Zhou 3  Bond Basics When governments or companies issue bonds, they promise to make a series of interest payments and then repay the debt. Par value : Payment at the maturity of the bond. Typically $1000 Coupon rate: Annual rate of interest paid. Coupon: Regular interest payment received by holder per year. Maturity date: Expiration date of bond when par value is paid back. Yield to maturity: Expected rate of return based on price of bond NIU FINA 320 - Dr. Lei Zhou 4  Yield to Maturity, Coupon Rate, and Current Yield A bond’s coupon rate differs from its yield to maturity (YTM) as well as current yield. Coupon rate is set by the company at the time of issue and is fixed (except for newer innovations which have variable coupon rates). YTM is dependent on market, economic, and company-specific factors and is therefore variable. Current yield – relation between coupon payment and price of bond. NIU FINA 320 - Dr. Lei Zhou 5  Coupon Rate The coupon rate on a bond is set by the issuing company at the time of issue It represents the annual rate of interest that the firm is committed to pay over the life of the bond. If the rate is set at 7%, the firm is committed to pay.07*$1000 = $70 per year on each bond, It is paid either in a single check or two checks of $35 paid six months apart. NIU FINA 320 - Dr. Lei Zhou 6  Yield to Maturity Expected rate of return on a bond if held to maturity. The price that willing buyers and sellers settle at determines a bond’s YTM at any given point. Changes in economic conditions and risk factors will cause bond prices and their corresponding YTMs to change. NIU FINA 320 - Dr. Lei Zhou 7  Current Yield Current yield is defined as the annual coupon payment divided by the price of the bonds. Current yield ignores the potential capital gain or capital loss due to changes in the price of bond NIU FINA 320 - Dr. Lei Zhou 8 Bond X makes an annual coupon payment of $80 and has a par value of $1,000. The bond is currently trading at $950. Which of the following statements is true? A. The coupon rate of X is higher than its current yield. B. The coupon rate of X is the same as its current yield. C. The coupon rate of X is lower than its current yield. D. Without bond maturity date, we cannot tell the relation between its coupon rate and current yield. NIU FINA 320 - Dr. Lei Zhou 9  Bond Basics – An Example Let’s say you see the following price quote for a corporate bond: Issue Price Coupon(%) Maturity YTM% Current Yld. Rating Hertz Corp. 91.50 6.35 15-Jun-2030 7.5% 6.94 B Price = 91.5% of $1000 = $915; Annual coupon = 6.35% *1000 = $63.50 Maturity date = June 15, 2030; If bought and held to maturity, then yield to maturity = 7.50% Current Yield = $ Coupon/Price = $63.5/$915 = 6.94% NIU FINA 320 - Dr. Lei Zhou 10  Application of the Time Value of Money Tool: Bond Pricing Provide periodic interest income – annuity series Return of the principal amount at maturity – future lump sum Prices can be calculated by using present value techniques i.e. discounting of future cash flows. Combination of present value of an annuity and of a lump sum NIU FINA 320 - Dr. Lei Zhou 11  Pricing a Bond in Steps Since bonds involve a combination of an annuity (coupons) and a lump sum (par value) its price is best calculated by using the following steps: NIU FINA 320 - Dr. Lei Zhou 12  Pricing a Bond in Steps – An Example Calculate the price of an AA-rated, 20-year, 8% coupon (paid annually) corporate bond (Par value = $1,000) which is expected to earn a yield to maturity of 10%. Year 0 1 2 3 18 19 20 $80 $80 $80 … $80 $80 $80 $1,000 Annual coupon = Coupon rate * Par value =.08 * $1,000 = $80 = PMT YTM = r = 10% Maturity = n = 20 Price of bond = Present Value of coupons + Present Value of par value NIU FINA 320 - Dr. Lei Zhou 13 Pricing a Bond in Steps – An Example  1   1  PMT  1  r n  Present value of coupons =   r      1   1  $80  1  0.10  20  =  0.10      = $80 x 8.51359 = $681.09 NIU FINA 320 - Dr. Lei Zhou 14 Pricing a Bond in Steps – An Example Present Value of Par Value = = = $148.64 Price of bond = PV of coupons + PV of par value = $681.09 + $148.64 = $829.73 NIU FINA 320 - Dr. Lei Zhou 15  Pricing a Bond in Steps – An Example Using a financial calculator Input: N I/Y PV PMT FV Key: 20 10 ? 80 1000 CPT PV = -829.73 Note that PV has opposite sign of PMT and FV Think from an investor’s point: paying $829.73 for the bond today (cash outflow) and receive annual payment of $80 (cash inflow) and $1,000 at the end of maturity (cash inflow). NIU FINA 320 - Dr. Lei Zhou 16 How much should you pay for a $1,000 bond with 10% coupon, annual payments, and 5 years to maturity if the interest rate is 12%? A) 927.90 B) 981.40 C) 1000 D) 1075.82 NIU FINA 320 - Dr. Lei Zhou 17  Pricing a Bond – More Discussion Suppose the yield to maturity on the bond changes from 10% to 6%. What would happen to the price of the bond? N=20, I/Y=6, PMT=80, FV=1000 CPT PV= -1,229.40 What happens if the yield to maturity is 8% N=20, I/Y=8, PMT=80, FV=1000 CPT PV= -1,000 NIU FINA 320 - Dr. Lei Zhou 18 Graphical Relationship Between Price and Yield-to- maturity 2000 1800 1600 1400 1200 1000 800 600 2% 4% 6% 8% 10% 12% 14% 16% NIU FINA 320 - Dr. Lei Zhou 19 Relationship of Yield to Maturity and Coupon Rate NIU FINA 320 - Dr. Lei Zhou 20 You are evaluating a corporate bond, X. The bond has a par value of $1,000 and makes $100 annual coupon payment. However, you do not know the maturity date of the bond. The current market price of the bond is $1,000. What is the yield to maturity of this bond? A) Less than 10% B) Exactly 10% C) More than 10% D) Cannot be determined because we do not have the maturity NIU FINA 320 - Dr. Lei Zhou 21  Semiannual Bonds and Zero- Coupon Bonds Most corporate and government bonds pay coupons on a semiannual basis. Some companies issue zero-coupon bonds by selling them at a deep discount. For computing price of these bonds, the values of the inputs have to be adjusted according to the frequency of the coupons (or absence thereof). For example, for semi-annual bonds, the annual coupon is divided by 2, the number of years is multiplied by 2, and the YTM is divided by 2. NIU FINA 320 - Dr. Lei Zhou 22 Semiannual Bonds – An Example On Feb. 1, 1992, Coca-Cola issued a 30-year bond with maturity on Feb. 1, 2022. The bond has a par value of $1,000 and a coupon rate of 8.5%, paid semiannually. The yield to maturity at the issuance date is 8.8%. Find the price of the bond. NIU FINA 320 - Dr. Lei Zhou 23 Semiannual Bonds – An example NIU FINA 320 - Dr. Lei Zhou 24  Semiannual Bonds – An example Using a financial calculator Input: N I/Y PV PMT FV Key: 60 4.4 ? 42.5 1000 CPT PV = -968.48 NIU FINA 320 - Dr. Lei Zhou 25 A six-year bond, ABS has a face value of $1,000 and coupon rate of 10%, paid semiannually. The yield to maturity on the bond is 8%. What is bond price? A) 1000.00 B) 1092.46 C) 1093.85 D) 1203.24 NIU FINA 320 - Dr. Lei Zhou 26  Zero-Coupon Bonds Known as “pure” discount bonds and sold at a discount from face value Do not pay any interest over the life of the bond. At maturity, the investor receives the par value, usually $1000. Price of a zero-coupon bond is calculated by merely discounting its par value at the prevailing discount rate or yield to maturity. NIU FINA 320 - Dr. Lei Zhou 27  Zero-Coupon Bond – An Example John wants to buy a 20-year, AAA-rated, $1000 par value, zero-coupon bond being sold by Diversified Industries Inc. The yield to maturity on similar bonds is estimated to be 9%. How much would he have to pay for it? It is important to note that we treat zero-coupon bond as semi-annual coupon bond, even if it does not pay any coupon. The number of years is multiplied by 2, and the YTM is divided by 2. NIU FINA 320 - Dr. Lei Zhou 28  Zero-Coupon Bond – An Example Method 1: Using TVM equation Bond Price = Par Value /(1+r)n Bond Price = $1000/(1.045)40 = $171.93 Method 2: Using a financial calculator Input: N I/Y PV PMT FV Key: 40 4.5 ? 0 1000 CPT PV= -171.93 NIU FINA 320 - Dr. Lei Zhou 29 RC Inc. just issued zero-coupon bonds with a par value of $1,000. If the bond has a maturity of 15 years and a yield to maturity of 10%, what is the current price of the bond ? A) 231.38 B) 239.39 C) 909.09 D) 0 because a bond without coupon payment is worthless NIU FINA 320 - Dr. Lei Zhou 30  Calculating Yield to Maturity Suppose we know the current price of a bond, its coupon rate, and its time to maturity. How do we calculate the YTM? We can use the straight bond formula, trying different yields until we come across the one that produces the current price of the bond. This is tedious. So, to speed up the calculation, financial calculators are often used. NIU FINA 320 - Dr. Lei Zhou 31  Calculating Yield to Maturity – An Example 20-year bond, 10% coupon, face value $1,000, annual payments. The price is $945. What is the yield to maturity (i)?  20 100  1000 945   t   20  t 1 (1  i )  (1  i ) i 10.68% or , with calculator: PMT 100, PV -945, N  20, FV  1000, I  ? I 10.68% NIU FINA 320 - Dr. Lei Zhou 32  Calculating Yield to Maturity It is very important to remember the sign convention in calculating yield to maturity. PV has opposite sign from the PMT and FV If PMT and FV are entered as positive numbers (cash inflows for investors), then PV must be entered as a negative number (cash outflow when investors buy the bond). If PMT and FV are entered as negative numbers (cash outflows for issuing firms), then PV must be entered as a positive number (cash inflow when firms sell the bond). NIU FINA 320 - Dr. Lei Zhou 33  YTM with Semiannual Coupons For bonds paying semiannual coupons (and zero coupon bonds), the output from financial calculator is six-month yield. Annualize it by multiplying it by two. Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93. Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? N = 40; PV = -1197.93; PMT = 50; FV = 1000; I/YR = 4% (Is this the YTM?) YTM = 4%*2 = 8% NIU FINA 320 - Dr. Lei Zhou 34 The Bonsai Nursery Corporation has $1,000 par value bonds with a coupon rate of 8% per year making semiannual coupon payments. If there are twelve years remaining prior to maturity and these bonds are selling for $876.40, what is the yield to maturity for these bonds? A) 8.00% B) 8.33% C) 9.77% D) 9.80% NIU FINA 320 - Dr. Lei Zhou 35 One Equation and Five Variables The bond valuation model has five variables: PV, FV, I/Y, N and PMT Given four variables, we can always solve for the one remaining variable For bond valuation, we solve for PV given FV, I/Y, N and PMT We have also solved for I/Y given FV, PV, N, and PMT Similarly, we can solve for PMT, N, or FV In using financial calculator, watch out for the sign convention. NIU FINA 320 - Dr. Lei Zhou 36  The Bond Indenture Contract between the company and the bondholders and includes The basic terms of the bonds The total amount of bonds issued Collaterals Seniority Sinking fund provisions Call provisions Details of protective covenants NIU FINA 320 - Dr. Lei Zhou 37  Default Risk Default is defined as a violation of any part of the bond indenture Default risks are usually measured by bond ratings. – Moody’s, Standard & Poor and several other small rating agencies Most often, issuing firms pay to have their bonds rated Smaller bonds are usually not rated – Interpretation of ratings Proxy for default risk Not a recommendation to sell or buy NIU FINA 320 - Dr. Lei Zhou 38 NIU FINA 320 - Dr. Lei Zhou 39 Bond A is rated BBB- by S&P and has a yield to maturity of 5%. Bond B is rated BB+ by S&P and has a yield to maturity of 7%. Which of the following statements must be true? A. Bond A is a better investment because of its higher rating. B. Bond B is a better investment because of its higher yield to maturity. C. Bond A has a lower probability of default than bond B. D. The other three statements are all false. NIU FINA 320 - Dr. Lei Zhou 40  Bond Ratings Investment grade bond: bonds rated BBB- or above. Lower default risk and suitable for prudent investment Junk bonds: bonds that are rated below BBB-. High default risk and speculative in nature and Carry higher yields to compensate for high risk Also known as high-yield bonds or noninvestment grade bonds Two types of junk bonds: fallen angels and original issued junk bonds. NIU FINA 320 - Dr. Lei Zhou 41