FINE 3010-01 Financial Management

1. FINE 3010-01Financial Management Instructor: RogérioMazali Lecture 06: 10/03/2011

2. FINE 3010-01Instructor: RogérioMazali Fundamentals of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Alan J. Marcus McGraw Hill/Irwin Chapter 6: Valuing Bonds

3. Agenda • The Bond Market • Interest Rates and Bond Prices • How Bond Prices Vary with Interest Rates • Interest Rate Risk • Current Yield and Yield to Maturity • Bond Rates of Return • The Yield Curve • Nominal and Real Rates of Interest • Corporate Bonds and the Risk of Default • Variations in Corporate Bonds

4. Bonds • Definition of a Bond: • Security that obligates the issuer to make specific payments to the bondholder. • Who issues Bonds: • Governments (City, State/Province, and National) • Corporations • Bonds are a popular form of financing for U.S. companies

5. What characterizes a Bond • Face Value (Par Value or Principal Value): • Payment at the maturity of the bond. Usually $1,000 in the U.S. • Coupon: • Interest payment made tobondholders. Usually paid every six months in the U.S. It can be expressed in percentage of the face value (Coupon Rate). • Maturity: • Date of last payment

6. Example • T-Bond: the “13s of 2014” • Coupons: • Rate: 13% of Face Value yearly rate • Frequency of payment: semiannual • Maturity: Feb 2014 • Face Value: $1,000 $1,000 $65 $65 $65 $65 $65 $65 $65 Aug ‘10 Feb ‘11 Aug ‘11 Feb ‘12 Aug ‘12 Feb ‘13 Aug ‘13 Feb ‘14 Aug ‘14

7. The Bond Market

8. Pricing Bonds • The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return. • Bonds can be valued like “package of two investments”: • Present value of interest payments (coupons) • Present value of principal

9. Pricing Bonds F C C C C C … C … 0 1 2 3 4 T-1 T

10. Pricing Bonds • Coupons are an annuity. We can use annuity formula to find PV of coupons.

11. Pricing Bonds • General Formula for price of bonds:

12. Example • Pricing the “13s of 2014” • Coupons: • Rate: 13% of Face Value yearly rate • Frequency of payment: semiannual • Maturity: Feb 2014 • Face Value: $1,000 $1,000 $65 $65 $65 $65 $65 $65 $65 Aug ‘10 Feb ‘11 Aug ‘11 Feb ‘12 Aug ‘12 Feb ‘13 Aug ‘13 Feb ‘14 Aug ‘14

13. Example: Pricing the “13s of 2014” • Suppose you are buying these bonds on Aug 1, 2010. • Suppose discount rate is 3% (APR)

14. Example: Pricing the “13s of 2014”

15. Warning • The coupon rate IS NOT the discount rate used in the Present Value calculations. • The coupon rate merely tells us what cash flow the bond will produce. • Since the coupon rate is listed as a %, this misconception is quite common.

16. Determinants of required return • Time to maturity • Longer term bonds should have higher yields • Payment for investors’ patience • Risk of default • Risk is measured by bond ratings • Payment for investors’ risk aversion • Higher risk => higher return

17. Risk and Bond Rating • Moody’s investors Service or Standard & Poor’s could be hired by firms that need their debt rated • Debt Rating depends on: • Likelihood of Default • Protection afforded by the loan contract incase of default

18. Corporate Bonds and the Risk of Default

19. Types of Bonds 1 • Level Coupon Bond • Fixed-rate instrument in which the coupon is typically paid in two semiannual installments with only the last installment including the principal repayment. • Pure Discount Bond • Bonds that pay no interest but have a single payment at maturity. Sold at discount. The size of the discount depends on prevailing interest rate. • Deferred-Coupon Bond • Bonds that permit the issuer to avoid interest obligations for a certain period of time • Perpetuity Bonds • Bonds that last forever and only pay interest

20. Example 1: T-Bond • Value a treasury bond with the following • characteristics: • Face value: $1000 • Coupon rate : 5% • Frequency of payment: semi-annual • Time to maturity: 4 years (8 semesters) • Discount rate: 10% (annual/APR) • What is the sell price?

21. Example 2: Corporate Bond • Dupont issued a 30 year maturity bonds with a coupon rate of 7.95%. • Interest is paid semi-annually • These bonds currently have 28 years remaining to maturity and are rated AA. • The bonds have a par value of $1,000 • Newly issued AA bonds with maturities greater than 10 years are currently yielding 7.73% • What is the value of Dupont bond today?

22. Example 3: Pure Discount Bond • Puerto Rico Borrows Some Cash • In 2007, Puerto Rico needed to borrow about $2.6 billion for up to 47 years. It did so by selling IOUs (bonds), each of which simply promised to pay the holder $1,000 at the end of that time. The market interest rate at the time was 5.15%. How much would have been prepared to pay for one of these IOUs?

23. Deferred Coupon Bond • Main Feature: (Semi)-Annual Payments are deferred for a predetermined number of years F C C C … C … 0 1 2 3 4 T-1 T

24. Example: Deferred Coupon Bond • Annual Coupon: 8%, Deferred for 3 years, 23 years maturity. Discount Rate: 10% • Step 1: calculate the value at t=3 • Step 2: Discount Back to Time t=0

25. Example: Perpetuity Bonds • What is the price of a British Consol paying a £50 coupon if r=2.5%?

26. Pricing Summary • Pure Discount Bond • Level Coupon Bond • Deferred Coupon Bond (deferred for d periods) • Perpetuity Bond

27. Current Yield • Suppose you are considering the purchase of a 3-year bond with coupon rate of 10% • You pay $1,000 • You pay $1,136.16 Return = $100/$1,136.16 = 0.088 = 8.8% • This is known as current yield.

28. Yield to Maturity • In actual market situations, we know the following variables: • Coupon Rate • Face Value • Maturity • PRICE • The Yield-to-Maturity is that discount rate that makes the present value of the cash flows of the bond equal to the price, as follows:

29. Example: Yield to Maturity • Example: You buy a 3-year 5% annual coupon bond w/ $1,000 face value for $1,081.95. What is the Yield-to-Maturity? • Obs.: Yield to Maturity calculations can be cumbersome. There is no general closed-solution to the Yield to maturity problem

30. Yield to Maturity • Another interpretation for the YTM: the discount rate that is implied by the price system. • Therefore, the YTM is the discount rate that we will use to discount the payments coming from a Bond IF WE HOLD IT TO MATURITY

31. Bond Rate of Return • Rate of return: Total income per period per dollar invested • Do not confuse Yield to Maturity and Rate of Return!

32. Bond Rates of Return

33. The Yield Curve Yields on Treasury strips in Feb. 2008

34. The Yield Curve • Yields are usually increasing with maturity. • Two main reasons: • Higher interest-rate risk: Prices of long-term bonds fluctuate more than short-term bonds • Risk of default

35. Nominal and Real Rates of Interest • From previous class: • T-bonds coupons and face value are corroded by inflation • Starting in 1997, treasury started issuing Treasury Inflation Protected Securities (TIPS), with constant real value coupons, indexed by the CPI.

36. Nominal and Real Rates of Interest • Consider 3%-coupon 2-year TIPS: • Nominal cash flows depend on the inflation rate. Assume CPI change was: • from year 0 to year 1: 5%. • from year 1 to year 2: 4%. • Calculating the yield using real cash flows will give us the Real Yield to Maturity.

37. Variations in Corporate Bonds • Floating-Rate Bonds: • interest rate promised may change, coupons are tied to some measure of current market rates • Convertible Bonds • You can choose to exchange your bonds for the company’s shares • Exotic Bonds: • Catastrophe bonds (Travelers’) • Mortality bonds (AXA) • Etc.