1. Valuing Government Bonds
Principles of
Corporate Finance
Eighth Edition
Chapter 23
Valuing Government Bonds
Slides by
Matthew Will
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

2. Topics Covered Real and Nominal Rates of Interest
The Term Structure and YTM
How Interest Rate Changes Affect Bond Prices
Explaining the Term Structure

3. UK Bond Yields

4. 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

5. 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

6. Debt & Interest Rates Nominal r = Real r + expected inflation
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.

7. Present Value of a Loan
The Term Structure can be reflected in using various “r” terms for different time periods

8. Term Structure and Yields
The Return on US Treasury Bills and the Inflation rate ( )

9. Valuing a Bond

10. Valuing a Bond Cash Flows Sept 03 04 05 06 07 115 115 115 115 1115
Example
If today is October 2005, what is the value of the following bond? An IBM Bond pays $115 every Sept for 5 years. In Sept 2010 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
Cash Flows
Sept

11. Valuing a Bond Example continued
If today is October 2005, what is the value of the following bond? An IBM Bond pays $115 every Sept for 5 years. In Sept 2010 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)

12. Term Structure (Feb 2004)
Nov 2014
Feb 2004

13. Bond Prices and Yields
Price
Yield

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. Spot/Forward rates
Example
1000 = 1000
(1+R3)3 (1+f1)(1+f2)(1+f3)

19. Spot/Forward rates Forward Rate Computations
(1+ rn)n = (1+ r1)(1+f2)(1+f3)....(1+fn)

20. Spot/Forward rates Example What is the 3rd year forward rate?
2 year zero treasury YTM = 8.995
3 year zero treasury YTM = 9.660

21. Spot/Forward rates Example What is the 3rd year forward rate?
2 year zero treasury YTM = 8.995
3 year zero treasury YTM = 9.660
Answer
FV of YTM
2 yr 1000 x ( )2 =
3 yr 1000 x ( )3 =
IRR of (FV & PV= ) = 11%

22. Spot/Forward rates Example
Two years from now, you intend to begin a project that will last for 5 years. What discount rate should be used when evaluating the project?
2 year spot rate = 5%
7 year spot rate = 7.05%

23. Spot/Forward rates Coupons paying bonds to derive rates
Bond Value = C C2
(1+r) (1+r)2
Bond Value = C C2
(1+R1) (1+f1)(1+f2)
d1 = C d2 = C2
(1+R1) (1+f1)(1+f2)

24. Spot/Forward rates Example 8% 2 yr bond YTM = 9.43%
What is the forward rate?
Step 1
value bonds 8% = 975
10%= 1010
Step 2
975 = 80d d > solve for d1
1010 =100d d > insert d1 & solve for d2

25. Spot/Forward rates Example continued Step 3 solve algebraic equations
d1 = [975-(1080)d2] / 80
insert d1 & solve = d2 = .8350
insert d2 and solve for d1 = d1 = .9150
Step 4
Insert d1 & d2 and Solve for f1 & f2.
.9150 = 1/(1+f1) = 1 / (1.0929)(1+f2)
f1 = 9.29% f2 = 9.58%
PROOF

26. Term Structure Year Spot Rate - The actual interest rate today (t=0)
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

27. Term Structure What Determines the Shape of the TS?
1 - Unbiased Expectations Theory
2 - Liquidity Premium Theory
3 - Market Segmentation Hypothesis
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.

28. Yield To Maturity
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)

29. 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?

30. 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%

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