1. BA350: Financial Management Stephen Gray Fuqua School of Business Office: 310 West Tel: 660-7786 E-mail: sg12@mail.duke.edu Web:

2. The Three Ideas in Finance l The Time Value of Money l Diversification and Risk l Arbitrage and Hedging

3. Topic 1: The Time Value of Money l A dollar in the future is worth less than a dollar now. l Should you take the $1000 cash back or the 4.9% APR financing on your new Ford? l Should you refinance your mortgage? l Should we convert our old warehouse into luxury apartments or a parking garage?

4. Topic 1: The Time Value of Money n Time Value of Money  Present values and future values  Valuation of stocks and bonds  Corporate investment decisions

5. Topic 2: Diversification and Risk l How should individuals invest their wealth? l Should you invest in stocks or bonds? l What ’ s a reasonable return for a particular investment? l What ’ s the relationship between risk and return?

6. Topic 2: Diversification and Risk n Diversification and Risk  Statistical review and utility theory  Portfolio theory  Relationship between risk and return: Capital Asset Pricing Model  Investment decisions under uncertainty

7. Topic 3: Arbitrage and Hedging l If two investments are guaranteed to produce the same set of cash flows, they must cost the same. l How can we hedge against common business risks? l How do option and futures contracts work? l When should a firm use derivatives?

8. Topic 3: Arbitrage and Hedging n Arbitrage and Hedging  Forwards  Futures  Options  Hedging in Practice –Foreign exchange rate risk –Interest rate risk –Stock market risk

9. Applications of the Three Ideas n Corporate Financial Policy »Investment decisions »Financing decisions »Dividend (payout) decisions l Mutual Fund Performance Evaluation l Real and Strategic Options

10. Goals of Course n Provide a solid foundation in the fundamental principles of finance. n Prepare students for subsequent courses in finance. n Introduce students to current issues and concerns regarding financial policy.

11. Course Material n Packet of course notes n Optional text:  R. Brealey and S. Myers, Principles of Corporate Finance (5th Ed.) n Current financial publications:  Wall Street Journal  Fortune  Business Week

12. Course Requirements and Grading n Assignments (10%) n Midterm exam (30%)  Covers first five classes  Closed book n Final Exam (60%)  December 13 (9-noon)  Closed book n Passing grade requires 50% on exams.

13. Help!!!!!!!!! n Classmates n Help sessions  Posted on web site and bulletin board n Review sessions  Fridays 4-5 pm n Tutors  Posted on web site and bulletin board n Me

14. Class 1 Present Value Mechanics and Bond Valuation

15. Future Values Suppose you have the opportunity to invest $1,000 in a savings account that promises to pay 7% interest per year. How much will you have in your savings account at the end of each of the next 2 years?

16. Future Value after One Year 0 1 $1,000 F 1 F 1 = P(1+i) F 1 = $1,000(1.07) F 1 = $1,070

17. Future Value after Two Years 0 1 2 $1,000 F 2 F 2 = F 1 (1+i) F 2 = [P(1+i)](1+i) = P(1+i) 2 F 2 = $1,000(1.07) 2 F 2 = $1,144.90

18. Future Value after n Years 0 n P F n F n = P(1+i) n

19. Manhattan Island In 1626, Peter Minuit purchased Manhattan Island for $24. Given today ’ s real estate values in New York, this appears to be a great deal for Minuit. But consider the current value of the $24 if it had been invested at an interest rate of 8% for the last 370 years (1996-1626 = 370). F 370 = $24(1.08) 370 F 370 = $55,847 Billion

20. Future Value of a Lump Sum l Example: A bank offers a rate of 10% per year, compounding quarterly. You invest $1000. How much is in your account after 1 year? l F n =P(1+i) n l F n =1000(1.025) 4 =1103.81

21. Present Value of a Lump Sum l Example: You need $100,000 in 18 years to pay for your newborn ’ s college education. How much must you invest today if you can earn 10% p.a.? l P=F n /(1+i) n l P=100,000/(1.1) 18 =17,985.87

22. Present Value of a Lump Sum l Example: If you invest $5,000 now, how long will it take you to triple your investment if you can earn 11% p.a.? l P=F n /(1+i) n l 5,000=15,000/(1.11) n l ln(5,000)=ln(15,000)-nln(1.11) l n=10.53 years.

23. Future Value of an Annuity l Example: If you work for 30 years and invest $500 per month into your retirement account, how much will you have at retirement if you can earn 12% p.a. compounding monthly? S i i R n n   11 b g Sm 360 1011 0 500747   .. $1. b g

24. Present Value of an Annuity l Example: You decide to fund a finance chair for the next 10 years. This requires $300,000 per year in salaries and add-ons. How much should you donate, if the school can earn 10% p.a?

25. Annuity Formulas l In all annuity formulas, it is assumed that the first payment in the stream occurs one period from now: 50

26. Mortgage Example l 30-year $100,000 fixed rate mortgage at 12% p.a. with monthly repayments. l The present value of the repayment scheme is the amount you borrowed:

27. Mortgage Example l The payout figure is the present value of all remaining repayments. After 120 repayments, this is:

28. Mortgage Example l If you make an extra repayment, this reduces the outstanding principal balance. Consider a payment of $50,000 after 10 years:

29. Definition of a Bond n A bond is a security that obligates the issuer to make specified interest and principal payments to the holder on specified dates.  Coupon rate  Face value (or par)  Maturity (or term) n Bonds are sometimes called fixed income securities.

30. Types of Bonds n Pure Discount or Zero-Coupon Bonds  Pay no coupons prior to maturity.  Pay the bond ’ s face value at maturity. n Coupon Bonds  Pay a stated coupon at periodic intervals prior to maturity.  Pay the bond ’ s face value at maturity. n Perpetual Bonds (Consuls)  No maturity date.  Pay a stated coupon at periodic intervals.

31. Types of Bonds n Self-Amortizing Bonds  Pay a regular fixed amount each payment period over the life of the bond.  Principal repaid over time rather than at maturity.

32. Bond Issuers n Federal Government and its Agencies n Local Municipalities n Corporations

33. U.S. Government Bonds n Treasury Bills  No coupons (zero coupon security)  Face value paid at maturity  Maturities up to one year n Treasury Notes  Coupons paid semiannually  Face value paid at maturity  Maturities from 2-10 years

34. U.S. Government Bonds n Treasury Bonds  Coupons paid semiannually  Face value paid at maturity  Maturities over 10 years  The 30-year bond is called the long bond. n Treasury Strips  Zero-coupon bond  Created by “ stripping ” the coupons and principal from Treasury bonds and notes.

35. Agencies Bonds n Mortgage-Backed Bonds  Bonds issued by U.S. Government agencies that are backed by a pool of home mortgages.  Self-amortizing bonds.  Maturities up to 20 years.

36. U.S. Government Bonds n No default risk. Considered to be riskfree. n Exempt from state and local taxes. n Sold regularly through a network of primary dealers. n Traded regularly in the over-the-counter market.

37. Municipal Bonds n Maturities from one month to 40 years. n Exempt from federal, state, and local taxes. n Generally two types:  Revenue bonds  General Obligation bonds n Riskier than U.S. Government bonds.

38. Corporate Bonds n Secured Bonds (Asset-Backed)  Secured by real property  Ownership of the property reverts to the bondholders upon default. n Debentures  General creditors  Have priority over stockholders, but are subordinate to secured debt.

39. Common Features of Corporate Bonds n Senior versus subordinated bonds n Convertible bonds n Callable bonds n Putable bonds n Sinking funds

40. Bond Ratings

41. Bond Valuation: General Formula 0 1 2 3 4... n C C C C C+F

42. Valuing Zero Coupon Bonds l What is the current market price of a U.S. Treasury strip that matures in exactly 5 years and has a face value of $1,000. The yield to maturity is r d =7.5%.

43. Finding the YTM on a Zero Coupon Bond l What is the yield to maturity on a U.S. Treasury strip that pays $1,000 in exactly 7 years and is currently selling for $591.11?

44. Valuing Coupon Bonds l What is the market price of a U.S. Treasury bond that has a coupon rate of 9%, a face value of $1,000 and matures exactly 10 years from today if the required yield to maturity is 10% compounded semiannually?

45. Valuing Coupon Bonds (cont.) n Semiannual coupon = $1,000(.09)/2 = $45 n Semiannual yield = 10%/2 = 5% n Payment periods = 10 years x 2 = 20

46. Valuing Coupon Bonds (cont.) l Suppose you purchase the U.S. Treasury bond described earlier and immediately thereafter interest rates fall so that the new yield to maturity on the bond is 8% compounded semiannually. What is the bond ’ s new market price?

47. Valuing Coupon Bonds (cont.) n New Semiannual yield = 8%/2 = 4% n What is the price of the bond if the yield to maturity is 9% compounded semiannually?

48. Relationship Between Bond Prices and Yields n Bond prices are inversely related to interest rates (or yields). n A bond sells at par only if its coupon rate equals the required yield. n A bond sells at a premium if its coupon is above the required yield. n A bond sells a a discount if its coupon is below the required yield.

49. Duration: A Measure of Interest Rate Sensitivity n The percentage change in the bond ’ s price for a small change in interest rates is given by: n The term within square brackets is called the bond ’ s duration. It can be interpreted as the weighted average maturity.

50. Duration Example What is the interest rate sensitivity of the following two bonds. Assume coupons are paid annually. Bond A Bond B Coupon rate 10% 0% Face value $1,000 $1,000 Maturity 5 years 10 years YTM 10% 10% Price $1,000 $385.54

51. Duration Example (cont.)

52. n Percentage change in bond price for a small increase in the interest rate: Pct. Change = - [1/(1.10)][4.17] = - 3.79% Bond A Pct. Change = - [1/(1.10)][10.00] = - 9.09% Bond B

53. Bond Prices and Yields Bond Price F c Yield Longer term bonds are more sensitive to changes in interest rates than shorter term bonds.

54. The Term Structure of Interest Rates n The term structure of interest rates is the relationship between time to maturity and yield to maturity: Yield Maturity 123 5.00 5.75 6.00

55. Spot and Forward Rates l A spot rate is a rate agreed upon today, for a loan that is to be made today. (e.g. r 1 =5% indicates that the current rate for a one-year loan is 5%). l A forward rate is a rate agreed upon today, for a loan that is to be made in the future. (e.g. 2 f 1 =6.50% indicates that we could contract today to borrow money at 6.5% for one year, starting two years from today).

56. Forward Rates l r 1 =5.00%, r 2 =5.75%, r 3 =6.00% l If we invest $100 for three years we earn 100(1.06) 3 l If we invest $100 for two years, and contract (today) at the one year rate, two years forward, we earn 100(1.0575) 2 (1+ 2 f 1 )

57. Forward Rates l Since both of these positions are riskless, they must yield the same returns l (1.06) 3 =(1.0575) 2 (1+ 2 f 1 ) l 2 f 1 =6.50% l More generally: (1+r n+t ) n+t =(1+r n ) n (1+ n f t )