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5-4
5.1 Definition and Example of a Bond
Consider a U.S. government bond listed as 6 3/8 of December 2009.
Time to maturity (T) = Maturity date - today’s date Face value (F) Discount rate (r)
$0
$0
$0
$F
0
1
2
T 1
T
Present value of a pure discount bond at time 0:
PV
F (1 r)T
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Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
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Pure Discount Bonds(p106)
Information needed for valuing pure discount bonds:
0
1 2…
25
|----------|---------|-------------------|
$50 PV0 = 50 ÷ (1.08)25 = $7.30
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$31.875 $31.875 $31.875
1/1/05 6/30/05 12/31/05 6/30/09
$1,031.875
12/31/09
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Estimate future cash flows:
Size (how much) and Timing (when)
Discount future cash flows at an appropriate rate:
The rate should be appropriate to the risk presented by the security.
$0
0
1
$0
$0
2
29
$1,000
$0$1,00 1202930
30
F $1,000 PV (1r)T(1.0)6 30$17.141
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Pure Discount Bonds(p106)
The pure discount bond is perhaps the simplest kind of bond. It promises a single payment at a fixed future date.
5-0CHAPTER5McGraw-Hill/Irwin Corporate Finance, 7/e
How to Value Bonds and
Stocks(p106)
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
5-1
Chapter Outline
5.1 Definition and Example of a Bond 5.2 How to Value Bonds 5.3 Bond Concepts 5.4 The Present Value of Common Stocks 5.5 Estimates of Parameters in the Dividend-Discount Model 5.6 Growth Opportunities 5.7 The Dividend Growth Model and the NPVGO Model
$C
$C
$C
$C$F
0
1
2
T 1
T
Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value
PV C r1(11r)T(1Fr)T
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Level-Coupon Bonds: Example
Find the present value (as of January 1, 2004), of a 6-3/8 coupon Tbond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent.
Specifies the principal amount of the loan. Specifies the size and timing of the cash flows:
In dollar terms (fixed-rate borrowing) As a formula (adjustable-rate borrowing)
5-5
5.2 How to Value Bonds
Identify the size and timing of cash flows.
Discount at the correct discount rate.
If you know the price of a bond and the size and timing of cash flows, the yield to maturity(YTM) is the discount rate. Yield to maturity (YTM) is bond jargon for the discount rate that equates the price of a bond with the discounted value of its coupons and face (par) value. In other words, present value = price when r =YTM. The yield to maturity represents the current market interest rate for a bond.
5-10
Example of pure discount bonds:
What is the price of a 25-year, pure discount bond that pays $50 at maturity if the current yield-to maturity is 8 percent?
The Par Value of the bond is $1,000. Coupon payments are made semi-annually (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, 2005 the size and timing of cash flows are:
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5.2 How to Value Bonds
We now consider how to value following different types of bonds: Pure discount bonds Level-coupon bonds Consols
5-2
Valuation of Bonds and Stock
First Principles:
Value of financial securities = PV of expected future cash flows
To value bonds and stocks we need to: