Bonds and Bonds Valuation PDF

Bonds and Bonds Valuation 1  Topics of Discussion Key features of bonds Bond valuation Measuring yield Assessing risk 2 3 Bond 4 5 6 7 Bond Terminology  Key Features of a Bond Par value: Face amount; pa...

Bonds and Bonds Valuation 1  Topics of Discussion Key features of bonds Bond valuation Measuring yield Assessing risk 2 3 Bond 4 5 6 7 Bond Terminology  Key Features of a Bond Par value: Face amount; paid at maturity. Assume $1,000/$100 or Rs 1000. Coupon interest rate: Stated interest rate. Multiply by par value to get dollars/rupees of interest. Generally fixed. (More…) 9  Key Features of a Bond Maturity: Years until the bond must be repaid. Declines. Issue date: Date when bond was issued. Default risk: Risk that issuer will not make interest or principal payments or both. 10 Sample Bond Issue – NTPC Ltd. https://www.icicidirect.com/fd-and-bonds/ntpc-ltd-891/ine733e07jj9 11 12 Municipal Bonds in India 13 Sr. Date of Date of Amount (Rs. Coupon Tenure (in No. Name of Municipality Issue Maturity In crs.) (%) years) June 20, 1 Pune Municipal Corporation 2017 20-06-2027 200 7.59 10 Greater Hyderabad Municipal 2 Corporation Feb 16, 2018 16-02-2028 200 8.9 10 June 28, 3 Indore Municipal Corporation 2018 29-06-2028 139.9 9.25 10 Greater Hyderabad Municipal 4 Corporation Aug 14, 2018 14-08-2028 195 9.38 10 5 Bhopal Municipal Corporation Sept 25, 201826-09-2028 175 9.55 10 Greater Vishakhapatnam Municipal 6 Corporation Dec 21, 2018 21-12-2028 80 10 10 7 Ahmedabad Municipal Corporation Jan 11, 2019 15-01-2024 200 8.7 5 8 Surat Municipal Corporation Feb 27,2019 01-03-2024 200 8.68 5 Greater Hyderabad Municipal August 20, 9 Corporation 2019 21-08-2029 100 10.23 10 November 13, 10 Lucknow Municipal Corporation 2020 18-11-2024 200 8.5 4 14  Call Provision Issuer can refund if rates decline. That helps the issuer but hurts the investor. Therefore, borrowers are willing to pay more, and lenders require more on callable bonds. Most bonds have a deferred call 15  Bond Issue in India https://www.dezerv.in/bonds/corporate-bon ds/ https://www.moneycontrol.com/bonds/ 16  Class Problem -1 Consider a 10 year bond with a face value of Rs 1000 that has a coupon rate of 5.5% with semi-annual payment. Required (a) What is the coupon payment for this bond? (b) Draw a cash flows for the bond on a timeline. 17 Class Exercise -2 18  Zero-Coupon Bond Cash Flows Following cash flow occurs:- Can you identify those cash flows? https://www.wintwealth.com/bonds/zero-co upon-bonds/ https://www.dezerv.in/bonds/icici-jan-2002 -bonds/ine005a11ba8/ 19 Cash flow at T0(Purchase date) and T1(Maturity) 20  Yield to maturity (YTM) The rate of return of an investment in a bond that is held to its maturity date, Or the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond. 21 the yield to maturity for a zero-coupon bond is the return you will earn as an investor by buying the bond at its current market price, holding the bond to maturity, and receiving the promised face value payment. 22 23 Example 24 Class Exercise-3 25 Solution 26  Class Problem -2 The following table summarises prices of various default-free zero coupon bonds (expressed as a percentage of face value) 27 Zero-Coupon Yield Curve 28  Computing the Price of a Zero-Coupon Bond Given the yield curve shown in last Figure, what is the price of a five-year risk-free zero-coupon bond with a face value of $100? 29 We can compute the bond’s price as the present value of its face amount, where the discount rate is the bond’s yield to maturity. 30 Yield to Maturity of a Coupon Bond Cash flow of a Coupon Bond? 31 Cash Flow of Coupon Bond 32 Price of a Coupon Bond Where: P = Bond Price C= Coupon Payment r= market interest rate n= number of years to maturity FV= Face value of bond 33 Price of a Coupon Bond 34  Class example Consider a five year bond with 2.2% coupon rate paid seminally. Suppose interest rate is 2%. Face value 1000 of the bond. What price of the bond trading now? 35 P= 11 x 9.4713+ 1000/1.1046 = 104.18+905.30 = 1009.48 36  Example Let’s say a Bond has a maturity of 15 years and pay 9% Coupons. It has a face value of 1000 and redeemed at par. What is current MP or price of the bond? 37  OR P= 90 x 8.0607+ 1000/3.6425 = 725.46+274.53 = 1000 38 Finding our current price/MP of the Bond. 39 What would happen if inflation goes up, and rd increases to 14 %? ₹ 692.89. This means that as Interest Rate increases Bond prices (market price) will go down What's going on here? 40 What would happen if inflation fell, and rd declined to 7%? =PV(RATE, NPER, PMT, FV) If coupon rate > rd, price rises above par, and bond sells at a premium. ₹ 1,182.16. Bond Price gone up from Market price (₹ 1000) 41  Bond Value ($) vs. Years remaining to Maturity At maturity, the value of any bond must equal its par value. The value of a premium bond would decrease to $1,000. The value of a discount bond would increase to $1,000. A par bond stays at $1,000 if rd remains constant. 42  What’s “yield to maturity”? YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.” It assumes the bond will not default. 43  YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887 0 1 9 10 rd=?... 90 90 90 PV1 1,000... PV10 PVM 887 Find rd that “works”! 44  Find rd INT... + INT M VB = + N + 1 (1 + rd) (1 + rd) (1 + rd)N 90... 90 1,000 887 = 1+ + N+ (1 + rd) (1 + rd) (1 + rd)N INPUT 10 -887 90 1000 S N rd PV PMT FV OUTPU T 45 Finding our Rate? Rate 11% 46 Find YTM if price were $1,134.20. INPUT S10 -1134.2 90 1000 N rd OUTPU PV PMT FV T 7.08 Sells at a premium. Because coupon = 9% > rd = 7.08%, bond’s value > par. 47 YTM on Coupon Bond Where: C – Interest/coupon payment FV – Face value of the security PV – Present value/price of the security t – How many years it takes the security to reach maturity 48  YTM on a Coupon Bond Assume that there is a bond on the market priced at Rs 850 and that the bond comes with a face value of Rs 1,000 (a fairly common face value for bonds). The coupon rate for the bond is 15% and the bond will reach maturity in 7 years. Compute YTM? 49 The approximated YTM on the bond is 18.53%. 50  Problem 2 Face Value of Bond (FV) = $1,000 Annual Coupon Rate (%) = 6.0% Number of Years to Maturity = 10 Years Price of Bond (PV) = $1,050 Coupon is paid semi annually. Calculate YTM? 51  Semi-Annual Yield to Maturity (YTM) = [$30 + (($1,000 – $1,050) ÷ 20)] [($1,000 + $1,050) ÷ 2] Semi-Annual YTM = 2.7% Annual YTM = 5.4% 52  Example ( Practice) Consider at Five year, Rs 1000 bond with a 2.2% coupon rate and paid semi-annually. Current selling price is 963.11 What is YTM of the Bond? 53  Using Short cut method =(11+(1000-963.11)/10)/((1000+963.11)/2) =1.50% 54  YTM for the bond. Current Yield = PMT/Current Price = 11/963.11= 1.14 % 55 Why Bond Prices Change 56  Determining the Discount or Premium of a Coupon Bond Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate. If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value? Which bond trades at a premium, which trades at a discount, and which trades at par? 57 Solution 58 Bond Prices Immediately After a Coupon Payment 59 Effect of Time on Bond Price 60  Class Problem You have purchased a 10% coupon bond for Rs 1040. What will happen to the bond price if the market interest rate increases? 61 Class Problem 62  Definitions Annual coupon pmt Current yield = Current price Capital gains yield = Change in price Beginning price Exp total Exp Exp cap = YTM = + return Curr yld gains yld 63 9% coupon, 10-year bond, P = $887, and YTM = 10.91% Find out the current yield. $90 Current yield = $887 = 0.1015 = 10.15%. 64  Semiannual Bonds 1. Multiply years by 2 to get periods = 2N. 2. Divide nominal rate by 2 to get periodic rate = rd/2. 3. Divide annual INT by 2 to get PMT = INT/2. INPUT S 2N r d /2 OK INT/2 OK N I/YR PV PMT FV OUTPU T 65  Value of 10-year, 10% coupon, semiannual bond if rd = 13%. INPUT2(10) 13/2 100/2 S 20 6.5 50 1000 N rd PV PMT FV OUTPU -834.72 T 66 Class Problem 67 Solution 68 Class Problems Problem 1: 69 Class Exercise 70 Class Exercise 71 Exercise for practice 72 Callable Bonds and Yield to Call A 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1,135.90 with an 8% yield to maturity. It can be called after 5 years at $1,050. Compute YTC? 73 Nominal Yield to Call (YTC) INPUT 10 -1135.9 50 1050 S N I/YR PV PMT FV OUTPU 3.765 x 2 = 7.53% T 74 What factors affect default risk and bond ratings? Financial ratios Debt ratio Coverage ratios, such as interest coverage ratio or EBITDA coverage ratio Profitability ratios Current ratios 75 Other Factors that Affect Bond Ratings Provisions in the bond contract Secured versus unsecured debt Senior versus subordinated debt Guarantee provisions Sinking fund provisions Debt maturity (More…) 76 Other Factors that Affect Bond Ratings Other factors Earnings stability Regulatory environment Potential product liability Accounting policies 77  What is reinvestment rate risk? The risk that CFs will have to be reinvested in the future at lower rates, reducing income. Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%. 78 What is reinvestment rate risk? Year 1 income = $50,000. At year-end get back $500,000 to reinvest. If rates fall to 3%, income will drop from $50,000 to $15,000. Had you bought 30-year bonds, income would have remained constant. 79  Term Structure Yield Curve Term structure of interest rates: the relationship between interest rates (or yields) and maturities. A graph of the term structure is called the yield curve. 80