1. Valuing Debt Chapter 24

2. 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

3. Valuing a Bond

4. 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 0304050607 1151151151151115

5. 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%)

6. Bond Prices and Yields Yield Price

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

8. 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

9. 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

10. 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.

11. Debt & Risk YearCFPV@YTM% of Total PV% x Year 168.7565.54.0600.060 268.75 62.48.0580.115 368.75 59.56.0550.165 468.75 56.78.0520.209 5 68.75841.39.7753.875 1085.741.00 Duration 4.424 Example (Bond 1) Calculate the duration of our 6 7/8 % bond @ 4.9 % YTM

12. Debt & Risk YearCFPV@YTM% of Total PV% x Year 1 9082.95.0810.081 2 9076.45.0750.150 3 9070.46.0690.207 4 9064.94.0640.256 5 1090724.90.7113.555 1019.701.00 Duration= 4.249 Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration?

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

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

15. Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995 3 year zero treasury YTM = 9.660 Spot/Forward rates

16.  Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995 3 year zero treasury YTM = 9.660 Answer FV of principal @ YTM 2 yr1000 x (1.08995) 2 = 1187.99 3 yr1000 x (1.09660) 3 = 1318.70 IRR of (FV1318.70 & PV=1187.99) = 11% Spot/Forward rates

17. 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

18. 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 )

19. 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% = 975 10%= 1010 Step 2 975 = 80d1 + 1080 d2 -------> solve for d1 1010 =100d1 + 1100d2 -------> insert d1 & solve for d2 Spot/Forward rates

20. 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 2..9150 = 1/(1+f 1 ).8350 = 1 / (1.0929)(1+f 2 ) f 1 = 9.29% f 2 = 9.58% PROOF Spot/Forward rates

21. 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 & Normal 1976 1 5 10 20 30

22. 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.

23. 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)

24. 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?

25. 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? C0C1C2C3C4C5 -1078.801051051051051105 Calculate IRR = 8.5%

26. 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:

27. 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 1090.80= 872.00 0.20= 0. 872.00=expected CF

28. 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: