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

Bond Valuation

Lecture 2

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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:



9th Floor, KBS Building, Kasetsart University

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Outline

1 Bonds and Bond Valuation 2 Calculating Bond Yields

8-3

References

 Ross, S., Westerfield, R. and Jaffe, J.

(2013), Corporate Finance (10th Edition), McGraw Hill/Irvin. (Chapter 8)

 Moyer, R.C., McGuigan, J.R., and Rao,

R.P. (2015), Contemporary Financial Management (13th Edition), Cengage

• Learning. (Chapter 6)

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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.

8-5

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.

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The Bond-Pricing Equation

T T

r) (1 F r r) (1 1

• 1

C Value Bond                

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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:



09 / 1 / 1

875 . 31 $

09 / 30 / 6

875 . 31 $

09 / 31 / 12

875 . 31 $

13 / 30 / 6

875 . 031 , 1 $

13 / 31 / 12

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Bond Example

 On January 1, 2009, the required yield is 5%.  The current value is:

17 . 060 , 1 $ ) 025 . 1 ( 000 , 1 $ ) 025 . 1 ( 1 1 2 05 . 875 . 31 $

10 10

          PV

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Bond Example

 Now assume that the required yield is 11%.  How does this change the bond’s price?

69 . 825 $ ) 055 . 1 ( 000 , 1 $ ) 055 . 1 ( 1 1 2 11 . 875 . 31 $

10 10

          PV

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YTM and Bond Value

800 1000 1100 1200 1300 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Discount Rate Bond Value

6 3/8

When the YTM < coupon, the bond trades at a premium. When the YTM = coupon, the bond trades at par. When the YTM > coupon, the bond trades at a discount.

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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)

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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 upper rate −lower rate = lower price −market price upper price −lower price

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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%?

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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?

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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

• f the second bond.

 This is a useful concept that can be transferred

to valuing assets other than bonds.

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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

• riginal issue discount bonds (OIDs)

 Treasury Bills and principal-only Treasury strips are

good examples of zeroes

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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) T

r F PV ) 1 (  

Present value of a pure discount bond at time 0:



$

1

$

2

$

1  T

F $

T

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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%.

11 . 174 $ ) 06 . 1 ( 000 , 1 $ ) 1 (

30 

  

T

r F PV



$

1

$

2

$

29

000 , 1 $

30

Questions?