Valuing Debt Chapter 24

Topics Covered  The Classical Theory of Interest  Duration and Volatility  The Term Structure and YTM  Explaining the Term Structure  Allowing for the Risk of Default

Valuing a Bond

Example  If today is October 2002, what is the value of the following bond? An IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%) Cash Flows Sept

Valuing a Bond Example continued  If today is October 2002, what is the value of the following bond? An IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)

Bond Prices and Yields Yield Price

Debt & Interest Rates Classical Theory of Interest Rates (Economics)  developed by Irving Fisher

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

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

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.

Debt & Risk of Total PV% x Year Duration Example (Bond 1) Calculate the duration of our 6 7/8 % 4.9 % YTM

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?

example 1000=1000 (1+R 3 ) 3 (1+f 1 )(1+f 2 )(1+f 3 ) Spot/Forward rates

Forward Rate Computations (1+ r n ) n = (1+ r 1 )(1+f 2 )(1+f 3 )....(1+f n ) Spot/Forward rates

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

 Example What is the 3rd year forward rate? 2 year zero treasury YTM = year zero treasury YTM = Answer FV of YTM 2 yr1000 x ( ) 2 = yr1000 x ( ) 3 = IRR of (FV & PV= ) = 11% 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% Spot/Forward rates

coupons paying bonds to derive rates Spot/Forward rates Bond Value = C 1 + C 2 (1+r)(1+r) 2 Bond Value = C 1 + C 2 (1+R 1 )(1+f 1 )(1+f 2 ) d1 = C 1 d2 = C 2 (1+R 1 )(1+f 1 )(1+f 2 )

example 8% 2 yr bond YTM = 9.43% 10% 2 yr bond YTM = 9.43% What is the forward rate? Step 1 value bonds 8% = %= 1010 Step = 80d d > solve for d =100d d > insert d1 & solve for d2 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 f 1 & f = 1/(1+f 1 ).8350 = 1 / (1.0929)(1+f 2 ) f 1 = 9.29% f 2 = 9.58% PROOF Spot/Forward rates

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 & Normal

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.

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 , 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 , what is the YTM? C0C1C2C3C4C Calculate IRR = 8.5%

Default, Premiums & Ratings The risk of default changes the price of a bond and the YTM. 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:

Default, Premiums & Ratings 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

Default, Premiums & Ratings Conversly - If on top of default risk, investors require an additional 2 percent market risk premium, the price and YTM is as follows: