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# Chapter 7

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1. Chapter 7 Bonds and Their Valuation

2. Chapter 7 Topic Overview • Bond Characteristics • Annual and Semi-Annual Bond Valuation • Reading Bond Quotes • Finding Returns on Bonds • Bond Risk and Other Important Bond Valuation Relationships

3. Bond Characteristics • Par (or Face) Value (M) = stated face value that is the amount the issuer must repay, usually \$1,000 • Coupon Interest Rate • Coupon (INT) = Coupon Rate x Face Value • Maturity Date = when the face value is repaid. • A legal contract called the bond indenture specifies these values. • This makes a bond’s cash flows look like this:

4. INT INTINT+M 0 1 2 . . . n Bond Valuation • Discount the bond’s cash flows at the investor’s required rate of return. • the coupon payment (INT) stream (an annuity). • the par (M) value payment (a lump sum). • V = INT (PVA r, n) + M /(1+r)n

5. Bond Valuation Example #1 • Duff’s Beer has \$1,000 par value bonds outstanding that make annual coupon payments. These bonds have a 7.5% annual coupon rate and 15 years left to maturity. Bonds with similar risk have a required return of 9%, and Moe Szyslak thinks this required return is reasonable. • What’s the most that Moe is willing to pay for a Duff’s Beer bond?

6. 1000 ? 75 75 75 . . . 75 0 1 2 3 . . . 15 r = 9%

7. Let’s Play with Example #1 • Homer Simpson is interested in buying a Duff Beer bond but demands an 7.5 percent required return. • What is the most Homer would pay for this bond?

8. 1000 ? 75 75 75 . . . 75 0 1 2 3 . . . 15 r = 7.5%

9. Let’s Play with Example #1 some more. • Barney (belch!) Gumble is interested in buying a Duff Beer bond and demands on a 6 percent required return. • What is the most Barney (belch!) would pay for this bond?

10. 1000 ? 75 75 75 . . . 75 0 1 2 3 . . . 15 r = 6%

11. Lesson from Example 1: Bond Prices and Interest Rates have an inverse relationship!

12. r > Coupon Interest Rate r = Coupon Interest Rate P0 < par value P0 = par value DISCOUNT PAR = = r < Coupon Interest Rate P0> par value PREMIUM = Another Example 1 Lesson: Bond Premiums and Discounts • What happens to bond values if required return is not equal to the coupon rate? • The bond's price will differ from its par value

13. Bonds with Semiannual Coupons • Double the number of years, and divide required return and annual coupon by 2. Vd = INT/2(PVAr/2,2n) + M /(1+r/2)2n

14. Semiannual Example • Kwickee-Mart has an \$1000 par value bond with an annual coupon rate of 6% that pays coupons semiannually with 20 years left to maturity. What is the most you would be willing to pay for this bond if your required return is 7% APR? • Semiannual coupon = 6%/2(\$1000) = \$30 • 20x2 = 40 remaining coupons

15. 1000 30 30 30 . . . 30 0 1 2 3 . . . 40

16. Bond Yields • Current Yield - Annual coupon payments divided by bond price. • Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price. Also known as the market’s required rate of return. • Yield To Maturity = total expected return = current yield + expected capital gains yield (change in price)

17. Yield Definitions

18. Bond Yields Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.

19. Yield to Maturity Example • Burns Power \$1000 face value bond with a 5% coupon rate paid annually with 10 years left to maturity sells for \$890. • What is this bond’s yield to maturity?

20. 1000 -890 50 50 50 . . . 50 0 1 2 3 . . . 10 What is bond’s YTM? What is the bond’s current yield?

22. Verifying the T-bond’s YTM (Ask Yld) • Par Value = \$1000, semi-annual coupons • Ask Price = 136.969%(\$1000) = \$1,369.69 • INT/2 = 8.5%(\$1000)/2 = \$42.50 • N = 2020-2007 = 13, 2N = 26

23. Causes of Bond Price Changes Since a bond’s cash flows are fixed: • Changes in interest rates, and • Passage of time. cause changes in a bond’s price.

24. Bond Value Changes Over Time • Returning to the Duff’s Beer original example #1, where r = 9%, N = 15, C (PMT) = \$75, par (FV) = \$1000, & PV = \$879.09. • What is bond value one year later when N = 14 and r is still = 9%?

25. Bond values over time • At maturity, the value of any bond must equal its par value. • If rd remains constant: • The value of a premium bond would decrease over time, until it reached \$1,000. • The value of a discount bond would increase over time, until it reached \$1,000. • A value of a par bond stays at \$1,000.

26. Changes in Bond Value over Time • What would happen to the value of these three bonds is bond if its required rate of return remained at 10%: VB 1,184 1,000 816 13% coupon rate 10% coupon rate. 7% coupon rate Years to Maturity 10 5 0

27. What about this? • What if Barney buys Duff Bond at \$1145.68 with n =15 and sells at r = 7% with n = 14. What is his return?

28. Interest Rate Risk • Measures Bond Price Sensitivity to changes in interest rates. • In general, long-term bonds have more interest rate risk than short-term bonds. • Also, for bonds with same time to maturity, lower coupon bonds have more interest rate risk than higher coupon bonds.

29. Interest Rate Risk Example • Recall from our earlier example (#1), the 15-year, 7.5% annual coupon bond has the following values at kd = 6%, 7.5%, & 9%. Let’s compare with a 2-yr, 7.5% annual coupon bond. • 15-year bond2-year bond r=6%: PV = \$1,145.68 PV = \$1,027.50 r=7.5%: PV = \$1,000 PV = \$1,000 r=9%: PV = \$879.09 PV = \$973.61

30. Interest Rate Risk: Bond Price Sensitivity Graph

31. Reinvestment rate risk • Reinvestment rate risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won \$500,000 playing the lottery. You intend to invest the money and live off the interest.

32. Reinvestment rate risk example • You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. • If you choose the 1-year bond strategy: • After Year 1, you receive \$50,000 in income and have \$500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to \$15,000. • If you choose the 10-year bond strategy: • You can lock in a 10% interest rate, and \$50,000 annual income.

33. Conclusions about interest rate and reinvestment rate risk • CONCLUSION: Nothing is riskless!

34. Default Risk • Credit risk • Default premium • Investment grade • Speculative grade (Junk bonds)

35. Default Risk

36. Callable Bonds & the effect of a call provision • Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor). • Borrowers are willing to pay more, and lenders require more, for callable bonds. • Most bonds have a deferred call and a declining call premium.

37. A 10-year, 10% semiannual coupon bond selling for \$1,135.90 can be called in 4 years for \$1,050, what is its yield to call (YTC)? • The bond’s yield to maturity can be determined to be 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV. 8 - 1135.90 50 1050 INPUTS N I/YR PV PMT FV OUTPUT 3.568

38. Yield to call • 3.568% represents the periodic semiannual yield to call. • YTCNOM = rNOM = 3.568% x 2 = 7.137% is the rate that a broker would quote. • The effective yield to call can be calculated • YTCEFF = (1.03568)2 – 1 = 7.26%

39. If you bought these callable bonds, would you be more likely to earn the YTM or YTC? • The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%. • Could replace bonds paying \$100 per year with bonds paying only \$71.37 per year. • Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%.

40. When is a call more likely to occur? • In general, if a bond sells at a premium, then (1) coupon rate > rd, so (2) a call is more likely. • So, expect to earn: • YTC on premium bonds. • YTM on par & discount bonds.

41. Sinking Fund • Provision to pay off a loan over its life rather than all at maturity. • Similar to amortization on a term loan. • Reduces risk to investor, shortens average maturity. • But not good for investors if rates decline after issuance.

42. How are sinking funds executed? • Call x% of the issue at par, for sinking fund purposes. • Likely to be used if rd is below the coupon rate and the bond sells at a premium. • Buy bonds in the open market. • Likely to be used if rd is above the coupon rate and the bond sells at a discount.

43. Other types (features) of bonds • Convertible bond – may be exchanged for common stock of the firm, at the holder’s option. • Warrant – long-term option to buy a stated number of shares of common stock at a specified price. • Putable bond – allows holder to sell the bond back to the company prior to maturity. • Income bond – pays interest only when interest is earned by the firm. • Indexed bond – interest rate paid is based upon the rate of inflation.