Lecture 2 Bond Valuation Contact: Natt Koowattanatianchai Email: - PowerPoint PPT Presentation

Lecture 2 Bond Valuation

Contact: Natt Koowattanatianchai  Email:  fbusnwk@ku.ac.th  Homepage:  http://fin.bus.ku.ac.th/nattawoot.htm  Phone:  02-9428777 Ext. 1218  Mobile:  087- 5393525  Office: 9 th Floor, KBS Building, Kasetsart University  8-1

Outline 1 Bonds and Bond Valuation 2 Calculating Bond Yields 8-2

References  Ross, S., Westerfield, R. and Jaffe, J. (2013), Corporate Finance (10 th Edition), McGraw Hill/Irvin. (Chapter 8)  Moyer, R.C., McGuigan, J.R., and Rao, R.P. (2015), Contemporary Financial Management (13 th Edition), Cengage Learning. (Chapter 6) 8-3

Bonds and Bond Valuation  A bond is a legally binding agreement between a borrower and a lender that specifies the:  Par (face) value  Coupon rate  Coupon payment  Maturity Date  The yield to maturity is the required market interest rate on the bond. 8-4

Bond Valuation  Primary Principle:  Value of financial securities = PV of expected future cash flows  Bond value is, therefore, determined by the present value of the coupon payments and par value.  Interest rates are inversely related to present (i.e., bond) values. 8-5

The Bond-Pricing Equation   1 1 -    T F (1 r)     Bond Value C  T   r (1 r)     8-6

Bond Example  Consider a U.S. government bond with as 6 3/8% coupon that expires in December 2013.  The Par Value of the bond is $1,000.  Coupon payments are made semiannually (June 30 and December 31 for this particular bond).  Since the coupon rate is 6 3/8%, the payment is $31.875.  On January 1, 2009 the size and timing of cash flows are: $ 31 . 875 $ 31 . 875 $ 31 . 875 $ 1 , 031 . 875  12 / 31 / 09 12 / 31 / 13 1 / 1 / 09 6 / 30 / 09 6 / 30 / 13 8-7

Bond Example  On January 1, 2009, the required yield is 5%.  The current value is:    $ 31 . 875 1 $ 1 , 000     1  $ 1 , 060 . 17 PV 10 10   . 05 2 ( 1 . 025 ) ( 1 . 025 ) 8-8

Bond Example  Now assume that the required yield is 11%.  How does this change the bond’s price?    $ 31 . 875 1 $ 1 , 000     1  $ 825 . 69 PV 10 10   . 11 2 ( 1 . 055 ) ( 1 . 055 ) 8-9

YTM and Bond Value When the YTM < coupon, the bond trades at a premium. 1300 Bond Value 1200 When the YTM = coupon, the 1100 bond trades at par. 1000 800 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 6 3/8 Discount Rate When the YTM > coupon, the bond trades at a discount. 8-10

Bond Concepts Bond prices and market interest rates move  in opposite directions. When coupon rate = YTM, price = par  value When coupon rate > YTM, price > par  value (premium bond) When coupon rate < YTM, price < par  value (discount bond) 8-11

Computing Yield to Maturity  Yield to maturity is the rate implied by the current bond price.  Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity.  Interpolation: lower rate −YTM lower price −market price upper rate −lower rate =  upper price −lower price 8-12

YTM with Annual Coupons  Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09.  Will the yield be more or less than 10%? 8-13

YTM with Semiannual Coupons  Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93.  Is the YTM more or less than 10%?  What is the semi-annual coupon payment?  How many periods are there? 8-14

Bond Pricing Theorems  Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate.  If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond.  This is a useful concept that can be transferred to valuing assets other than bonds. 8-15

Zero Coupon Bonds  Make no periodic interest payments (coupon rate = 0%)  The entire yield to maturity comes from the difference between the purchase price and the par value  Cannot sell for more than par value  Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs)  Treasury Bills and principal-only Treasury strips are good examples of zeroes 8-16

Pure Discount Bonds Information needed for valuing pure discount bonds:  Time to maturity ( T ) = Maturity date - today’s date  Face value ( F )  Discount rate ( r ) $ 0 $ 0 $ 0 $ F   2 0 1 1 T T Present value of a pure discount bond at time 0: F  PV (  T 1 ) r 8-17

Pure Discount Bonds: Example Find the value of a 15-year zero-coupon bond with a $1,000 par value and a YTM of 12%. $ 0 $ 0 $ 0 $ 1 , 000  30 0 2 29 1 $ 1 , 000 F   30  $ 174 . 11 PV  T ( 1 ) ( 1 . 06 ) r 8-18

Questions?