 Valuing Debt Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 23 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Topics Covered  The Classical Theory of Interest  The Term Structure and YTM  Duration and Volatility  Explaining the Term Structure  Allowing for the Risk of Default

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Interest Rates Classical Theory of Interest Rates (Economics)  developed by Irving Fisher

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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 & present

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk Example (Bond 1) Calculate the duration of our 10.5% 8.5% YTM of Total PV% x Year

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk Example (Bond 1) Calculate the duration of our 10.5% 8.5% YTM of Total PV% x Year

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk Example (Bond 1) Calculate the duration of our 10.5% 8.5% YTM of Total PV% x Year

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk of Total PV% x Year Example (Bond 1) Calculate the duration of our 10.5% 8.5% YTM

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk of Total PV% x Year Duration Example (Bond 1) Calculate the duration of our 10.5% 8.5% YTM

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration? of Total PV% x Year

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk 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?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk 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?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk 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?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Debt & Risk of Total PV% x Year Duration Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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 inother theories take advantage of the arbitrage.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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).

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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? C0C1C2C3C4C Calculate IRR = 8.5%

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Default, Premiums & Ratings The risk of default changes the price of a bond and the YTM. Book Example We have a 9% 1 year bond. The built in price is $1000. But, there is a 20% chance the company will go into bankruptcy and not be able to pay. What is the bond’s value? A:

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Default, Premiums & Ratings Book Example We have a 9% 1 year bond. The built in price is $1000. But, there is a 20% chance the company will go into bankruptcy and not be able to pay. What is the bond’s value? A: Bond ValueProb = = =expected CF

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Default, Premiums & Ratings Conversely - If on top of default risk, investors require an additional 2 percent market risk premium, the price and YTM is as follows: