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CORPORATE FINANCIALTHEORY
Lecture 8
Corp Financial Theory
Topics Covered:* Capital Budgeting (investing)* Financing (borrowing)
Today:Revisit Financing Debt Financing, Risk & Interest Rates
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
Supply
Demand
$ Qty
r
Real r
Federal Reserve Policy
Conventional wisdom The Federal Reserve sets interest rates.
Whenever they raise or lower interest rates, the amount I pay on my credit card increases or decreases accordingly.
FALSE
The Federal Reserve and The Colts
Value of one Colts season ticket
Value of two Colts season tickets
Conclusions from Example
Too much cash = Inflation
Growth in cash = Growth in goods
Who controls Cash ? The Federal Reserve They DO NOT control interest rates They INFLUENCE inflation
Why do we care? Inflation determines YOUR Interest Rates
Federal Reserve Monetary Policy
Fed Rate
Loan money to us
Banks Borrow
The Federal Reserve Dilemma
Fed Discount Rate
Inflation Rate
Monetary Policy
The Fed & Interest Rates
Myth: The Federal Reserve Board controls the interest rates WE PAY
Fact: The Fed controls the rate BANKS PAY
Fact: The rate we pay is set by the Banks
Fact: Banks rates are determined by the Fed Rate AND INFLATION
Mortgage rate = Fed Rate + expected inflation
Interest Rates and Inflation
)1()1(1 realnominal irr
Fed Funds vs. Mortgage Rates
Rates
Fed Discount 30 Yr. Mortgage Inflation
Feb ‘06 5.75 % 6.24 % 2.50 %
Aug’08 2.25 % 6.67 % 5.83 %
July 2008 CPI = 9.60 %
Source: Bankrate.com 8/21/08 report, mortgage-x.com, & bls.gov July 2008 CPI report
Fed Funds vs. Mortgage Rates
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
Source: federal reserve board
1991 2006
Fed Funds vs. Mortgage Rates
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
Source: federal reserve board
1991 2006
The Fed & Interest Rates
Q: How does this link to mortgage rates?
A: Mortgage rates are the combination of inflation and the Fed Funds rate.
Nominal rate = Real rate + expected inflation
Mortgage rate = Fed Funds + expected inflation
Real rate is a theoretical number… KIND OF
Nominal rate is what we pay
Inflation is the real danger
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.
Term Structure of Interest Rates
Maturity YTM1 3.0 %5 3.5%10 3.8%15 4.2%30 4.5%
Listing of the hypothetical yields on U.S. Treasury Zero Coupon bonds= The Pure Term Structure
Term Structure of Interest Rates
Maturity YTM1 5.3 %5 5.9 %10 6.4 %15 6.7 %30 7.0 %
AAA Corp Bond Term Structure
• Expectations Theory• Term Structure and Capital
Budgeting• CF should be discounted using
term structure info• When rate incorporates all forward
rates, use spot rate that equals project term
• Take advantage of arbitrage
Term Structure of Interest Rates
Yield Curve
The graph of the term Structure of Interest Rates is called the “Yield Curve”
YTM (r)
Year1 5 10 20 30
The Dynamic Yield Curve – Web Link
US Treasury Strips (2012)
Term Structure
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
YTM (r)
Year
1981
1987
1976
1 5 10 20 30
Term Structure
1987 is the normal Term Structure 1981 is abnormal & dangerous to the economy (because
there is an incentive not to invest)
YTM (r)
Year
1981
1987
1976
1 5 10 20 30
EG. 1981
Spot Rate (nominal) = Real r + Inflation
.15 = (-.05) + .20
Term Structure
YTM (r)
Year
1981
1987
1976
1 5 10 20 30
EG. 1981
Spot Rate (nominal) = Real r + Inflation
.15 = (-.05) + .20
Forward Rate (nominal) = Real r + Inflation
.10 = .01 + .09
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.
Valuing a Bond
NN
r
C
r
C
r
CPV
)1(
000,1...
)1()1( 22
11
Valuing a Bond
Example If today is October 1, 2012, what is the value of the
following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2016 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
Cash Flows
Sept 1213 14 15 16
115 115 115 115 1115
Valuing a Bond
Example continued If today is October 1, 2012, what is the value of the following bond? An
IBM Bond pays $115 every September 30 for 5 years. In September 2016 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
84.161,1$
075.1
115,1
075.1
115
075.1
115
075.1
115
075.1
1155432
PV
Valuing a Bond
Example - Germany In July 2012 you purchase 100 Euros of bonds in Germany which pay a
5% coupon every year. If the bond matures in 2018 and the YTM is 3.8%, what is the value of the bond?
Euros 33.106
038.1
105
038.1
5
038.1
5
038.1
5
038.1
5
038.1
565432
PV
Valuing a Bond
Another Example - Japan In July 2012 you purchase 200 Yen of bonds in Japan which pay a 8%
coupon every year. If the bond matures in 2017 and the YTM is 4.5%, what is the value of the bond?
Yen 73.230
045.1
216
045.1
16
045.1
16
045.1
16
045.1
165432
PV
Valuing a Bond
Example - USA In July 2012 you purchase a 3 year US Government bond. The bond has
an annual coupon rate of 4%, paid semi-annually. If investors demand a 2.48% return on 6 month investments, what is the price of the bond?
54.973$
0248.1
1020
0248.1
20
0248.1
20
0248.1
20
0248.1
20
0248.1
2065432
PV
Valuing a Bond
Example continued - USA Take the same 3 year US Government bond. The bond has an annual
coupon rate of 4%, paid semi-annually. If investors demand a 1.50% return on 6 month investments, what is the new price of the bond?
49.028,1$
015.1
1020
015.1
20
015.1
20
015.1
20
015.1
20
015.1
2065432
PV
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)
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 107.88, what is the YTM?
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 107.88, what is the YTM?
C0 C1 C2 C3 C4 C5
-1078.80 105 105 105 105 1105
Calculate IRR = 8.50%
Bond Prices and Yields
Interest Rates, %
Bon
d P
rice
, %
80.00
85.00
90.00
95.00
100.00
105.00
110.00
115.00
Maturity and Prices
0.00
50.00
100.00
150.00
200.00
250.00
0 1 2 3 4 5 6 7 8 9 10
3 yr 4% bond
30 yr 4% bond
Interest Rates, %
Bon
d P
rice
, %
Debt & Risk
If you have two bonds, both providing a YTM of 8.5%, do you care which one you would prefer to buy?
What additional information do you need to make your decision?
Why do you need this information?
Duration is the tool that tells us the difference in risk between two different bonds.
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
Example (Bond 1)Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 105
2 105
3 105
4 105
5 1105
Example (Bond 1)Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 105 96.77
2 105 89.19
3 105 82.21
4 105 75.77
5 1105 734.88
1078.82
Example (Bond 1)Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 105 96.77 .090
2 105 89.19 .083
3 105 82.21 .076
4 105 75.77 .070
5 1105 734.88 .681
1078.82 1.00
Example (Bond 1)Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 105 96.77 .090 0.090
2 105 89.19 .083 0.164
3 105 82.21 .076 0.227
4 105 75.77 .070 0.279
5 1105 734.88 .681 3.406
1078.82 1.00 4.166 Duration
Example (Bond 1)Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
Example (Bond 2)Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 90
2 90
3 90
4 90
5 1090
Example (Bond 2)Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 90 82.95
2 90 76.45
3 90 70.46
4 90 64.94
5 1090 724.90
1019.70
Example (Bond 2)Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 90 82.95 .081
2 90 76.45 .075
3 90 70.46 .069
4 90 64.94 .064
5 1090 724.90 .711
1019.70 1.00
Example (Bond 2)Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 90 82.95 .081 0.081
2 90 76.45 .075 0.150
3 90 70.46 .069 0.207
4 90 64.94 .064 0.256
5 1090 724.90 .711 3.555
1019.70 1.00 4.249 Duration
Example (Bond 2)Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is
this bond’s duration?
Debt & Risk
Using the two previous examples, which bond whould you buy and why?
Debt & Risk
Year CF PV@YTM % of Total PV % x Year
1 90 82.76 .082 0.082
2 90 76.10 .075 0.150
3 90 69.98 .069 0.207
4 90 64.35 .064 0.256
5 1090 716.61 .710 3.550
1009.80 1.00 4.245 Duration
Example (Bond 3)Given a 5 year, 9.0%, $1000 bond, with a 8.75% YTM, what
is this bond’s duration?
Debt & Risk
Q: Given Bond 1 and its YTM of 8.5% Given Bond 3 and its YTM of 8.75% Which bond should you buy and why?
A: It depends on your tolerance for risk.
Valuing Risky Bonds
The risk of default changes the price of a bond and the YTM.
Example
We have a 5% 1 year bond. The bond is priced at par of $1000. But, there is a 20% chance the company will go into bankruptcy and only pay $500. What is the bond’s value?
A:
%3.171895
1050
895$05.1
940
YTM
Value
Valuing Risky Bonds
Example
We have a 5% 1 year bond. The bond is priced at par of $1000. But, there is a 20% chance the company will go into bankruptcy and only pay $500. What is the bond’s value?
A: Bond Value Prob
1,050 .80 = 840.00
500 .20 = 100.00 .
940.00 = expected CF
Valuing Risky Bonds
Example – Continued
Conversely - If on top of default risk, investors require an additional 3 percent market risk premium, the price and YTM is as follows:
%64.20100.870
1050
37.870$08.1
940
YTM
Value
Key to Bond Ratings
Moody's S&P's & Fitch
Investment GradeAaa AAAAa AA A A
Baa BBBJunk Bonds
Ba BB B B
Caa CCCCa CC C C
The highest quality bonds are rated AAA. Investment
grade bonds have to be equivalent of Baa or
higher. Bonds that don’t make this cut are called “high-yield” or “junk”
bonds.
Key to Bond Ratings
Bond Terminology
Read Chapter 24 for terminology
Examples Collateralized Debt Obligations Asset Backed Securities Mortgage Backed Securities Loan Guarantees (Puttable bonds)