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)