Corporate Financial Theory 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 r Supply Real r Demand $ Qty

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 Banks Borrow Loan money to us

The Federal Reserve Dilemma Monetary Policy Fed Discount Rate Inflation Rate

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

Fed Funds vs. Mortgage 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 3 3 3 3 4 3

Fed Funds vs. Mortgage Rates 1991 2006 Source: federal reserve board

Fed Funds vs. Mortgage Rates 1991 2006 Source: federal reserve board

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 YTM 1 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 YTM 1 5.3 % 5 5.9 % 10 6.4 % 15 6.7 % 30 7.0 % AAA Corp Bond Term Structure

Term Structure of Interest Rates 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

Yield Curve The graph of the term Structure of Interest Rates is called the “Yield Curve” YTM (r) Year 1 5 10 20 30 The Dynamic Yield Curve – Web Link

US Treasury Strips (2012)

Term Structure Year YTM (r) 1 5 10 20 30 1981 1987 1976 Year 1 5 10 20 30 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

Term Structure Year YTM (r) 1 5 10 20 30 1981 1987 1976 Year 1 5 10 20 30 1987 is the normal Term Structure 1981 is abnormal & dangerous to the economy (because there is an incentive not to invest) EG. 1981 Spot Rate (nominal) = Real r + Inflation .15 = (-.05) + .20

Term Structure Year EG. 1981 Spot Rate (nominal) = Real r + Inflation YTM (r) 1981 1987 1976 Year 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

Valuing a Bond Cash Flows Sept 12 13 14 15 16 115 115 115 115 1115 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 12 13 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%)

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?

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?

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?

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?

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 Bond Price, % Interest Rates, %

Maturity and Prices Bond Price, % Interest Rates, %

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? Year CF PV@YTM % of Total PV % x Year

Debt & Risk Year CF PV@YTM % of Total PV % x Year 1 105 2 105 3 105 Example (Bond 1) Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? Year CF PV@YTM % of Total PV % x Year 1 105 2 105 3 105 4 105 5 1105

Debt & Risk Year CF PV@YTM % of Total PV % x Year 1 105 96.77 Example (Bond 1) Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? 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

Debt & Risk Year CF PV@YTM % of Total PV % x Year 1 105 96.77 .090 Example (Bond 1) Given a 5 year, 10.5%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? 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

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? 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

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? Year CF PV@YTM % of Total PV % x Year

Debt & Risk Year CF PV@YTM % of Total PV % x Year 1 90 2 90 3 90 4 90 Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? Year CF PV@YTM % of Total PV % x Year 1 90 2 90 3 90 4 90 5 1090

Debt & Risk Year CF PV@YTM % of Total PV % x Year 1 90 82.95 Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? 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

Debt & Risk Year CF PV@YTM % of Total PV % x Year 1 90 82.95 .081 Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? 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

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? 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

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 Example (Bond 3) Given a 5 year, 9.0%, $1000 bond, with a 8.75% YTM, what is this bond’s duration? 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

Debt & Risk Q: Given Bond 1 and its YTM of 8.5% 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:

Valuing Risky Bonds Example A: Bond Value Prob 1,050 .80 = 840.00 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:

Key to Bond Ratings 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)