1. Chapter 3 Valuing Bonds Principles of Corporate Finance Tenth Edition
Slides by
Matthew Will
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. 1 1 1 1 1 2

2. Topics Covered Using The Present Value Formula to Value Bonds
How Bond Prices Vary With Interest Rates
The Term Structure of Interest Rates
Explaining the Term Structure
Real and Nominal Rates of Interest
Corporate Bonds and the Risk of Default 2 2 2 2 3 2

3. Valuing a Bond

4. Valuing a Bond Cash Flows Sept 11 12 13 14 15 115 115 115 115 1115
Example
If today is October 1, 2010, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
Cash Flows
Sept

5. Valuing a Bond Example continued
If today is October 1, 2010, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)

6. Valuing a Bond Example - France
In December 2008 you purchase 100 Euros of bonds in France which pay a 8.5% coupon every year. If the bond matures in 2012 and the YTM is 3.0%, what is the value of the bond?

7. Valuing a Bond Another Example - Japan
In July 2010 you purchase 200 Yen of bonds in Japan which pay a 8% coupon every year. If the bond matures in 2015 and the YTM is 4.5%, what is the value of the bond?

8. Valuing a Bond Example - USA
In February 2009 you purchase a 3 year US Government bond. The bond has an annual coupon rate of 4.875%, paid semi-annually. If investors demand a % semiannual return, what is the price of the bond?

9. Valuing a Bond Example continued - USA
Take the same 3 year US Government bond. If investors demand a 4.0% semiannual return, what is the new price of the bond?

10. Interest Rate on 10yr Treasuries
Yield , %
Year

11. Bond Prices and Yields
Bond Price, %
Interest Rates, %

12. Maturity and Prices Bond Price, ($) Interest Rates, % 30 yr bond
When the interest rate
equals the 5% coupon,
both bonds sell for
face value
Bond Price, ($)
3 yr bond
Interest Rates, %

13. Duration Formula

14. Duration Calculation

15. Duration Example (Bond 1)
Calculate the duration of our 6 7/8 % 4.9 % YTM
Year CF % of Total PV % x Year
Duration 4.424

16. Duration Example (Bond 2)
Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration?
Year CF % of Total PV % x Year
Duration= 4.249

17. Duration & Bond Prices
Bond Price, percent
Interest rate, percent

18. Interest Rates
Short- and long-term interest rates do not always move in parallel. Between September 1992 and April 2000 U.S. short-term rates rose sharply while long term rates declined.

19. Term Structure of Interest Rates
YTM (r)
1981
1987 & Normal
1976
Year
Spot Rate - The actual interest rate today (t=0)
Forward Rate - The interest rate, fixed today, on a loan made in the future at a fixed time.
Future Rate - The spot rate that is expected in the future
Yield To Maturity (YTM) - The IRR on an interest bearing instrument

20. Yield Curve U.S. Treasury Strip Spot Rates as of February 2009
Maturity

21. Law of One Price
All interest bearing instruments are priced to fit the term structure
This is accomplished by modifying the asset price
The modified price creates a New Yield, which fits the Term Structure
The new yield is called the Yield To Maturity (YTM)

22. Yield to Maturity Example
A $1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is , what is the YTM?

23. Yield to Maturity Example
A $1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is , what is the YTM?
C0 C1 C2 C3 C4 C5
Calculate IRR = 8.5%

24. Term Structure What Determines the Shape of the Term Structure?
Expectations Theory
Term Structure & Capital Budgeting
CF should be discounted using Term Structure info
Since the spot rate incorporates all forward rates, then you should use the spot rate that equals the term of your project.
If you believe in other theories take advantage of the arbitrage.

25. Debt & Interest Rates Classical Theory of Interest Rates (Economics)
developed by Irving Fisher
Nominal Interest Rate = The rate you actually pay when you borrow money
Real Interest Rate = The theoretical rate you pay when you borrow money, as determined by supply and demand r
Supply
Real r
Demand
$ Qty

26. Annual rates of inflation in the United States from 1900–2008.
Inflation Rates
Annual rates of inflation in the United States from 1900–2008.
Annual Inflation (%)

27. Global Inflation Rates
Averages from

28. Debt & Interest Rates
Nominal r = Real r + expected inflation (approximation)
Real r is theoretically somewhat stable
Inflation is a large variable
Q: Why do we care?
A: This theory allows us to understand the Term Structure of Interest Rates.
Q: So What?
A: The Term Structure tells us the cost of debt.

29. Debt & Interest Rates
Actual formula

30. UK Bond Yields Interest rate (%) 10 year nominal interest rate
10 year real interest rate

31. Govt. Bills vs. Inflation (’53-’08)
United Kingdom
Inflation %
T-Bill Returns

32. Govt. Bills vs. Inflation (’53-’08)
United States
Inflation %
T-Bill Returns

33. Govt. Bills vs. Inflation (’53-’08)
Germany
T-Bill Returns %
Inflation

34. Bond Ratings
Key to bond ratings. The highest-quality bonds are rated triple A. Bonds rated triple B or above are investment grade. Lower-rated bonds are called high-yield, or junk, bonds.

35. Yield Spread
Yield spreads between corporate and 10-year Treasury bonds.
Yield spread between corporate and government bonds, %
Years

36. Prices and Yields
Prices and yields of a sample of corporate bonds, December 2008.
Source: Bond transactions reported on FINRA’s TRACE service:

37. Web Resources Click to access web sites Internet connection required