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The Valuation and Characteristics of Bonds

The Valuation and Characteristics of Bonds. Chapter 6. Bonds. A bond issue represents borrowing from many lenders at one time under a single agreement While one person may not be willing to lend a single company $10 million, 10,000 investors may be willing to lend the firm $1,000 each.

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The Valuation and Characteristics of Bonds

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  1. The Valuation and Characteristics of Bonds Chapter 6

  2. Bonds • A bond issue represents borrowing from many lenders at one time under a single agreement • While one person may not be willing to lend a single company $10 million, 10,000 investors may be willing to lend the firm $1,000 each

  3. Bond Terminology and Practice • A bond’s term (or maturity) is the time from the present until the principal is to be returned • Bond’s mature on the last day of their term • A bond’s face value (or par) represents the amount the firm intends to borrow (the principal) at the coupon rate of interest • Bonds typically pay interest (coupon rate) every six months • Bonds are not amortized (meaning the principal is repaid all at once when the bond matures rather than being repaid in increments throughout the bond’s life)

  4. Determining the Price of a Bond • Intrinsic Value is the present value of cash flows • With a bond, predicting the future cash flows is somewhat ‘easy,’ because the promised cash flows are specified. • Interest • Principal • Maturity (in years) In practice most bonds pay interest semi-annually.

  5. 0 1 2 n k CF1 CF2 CFn Financial asset values: Value (=PV) Value = Present Value of the cash flows

  6. Valuation of Financial Assets: Bonds - long term debt instruments • Principal Amount, Face Value, Maturity Value, Par Value:The amount of money the firm borrows and promises to repay at some future date, often at maturity. • Coupon Payment:The specified number of dollars of interest paid each period, generally each six months, on a bond. Key Terms

  7. Key Terms • Coupon Interest Rate:The stated annual rate of interest paid on a bond. (Before 1980s, physical coupons attached to bonds.) • Maturity Date:A specified date on which the par value of a bond must be repaid. • Original Maturity:The number of years to maturity at the time the bond is issued. • Call Provision:Gives the issuer right to pay off bonds prior to maturity.

  8. Q: A bond has 10 years to maturity, a par value of $1,000, and a coupon rate of 10%. What cash flows are expected from the bond? A: 0 1 5 10 a year for 10 years $100 $100 Example $1,000 $1,100 ? Determining the Price of a Bond Price = present value; PV is the unknown

  9. INPUTS 10 10 100 1,000 N I/YR PV PMT FV -1,000 OUTPUT

  10. What would happen if expected inflation rose by 3%, causing kd = 13%? INPUTS 10 13 100 1,000 N I/YR PV PMT FV -837.21 OUTPUT When kd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.

  11. What would happen if inflation fell, and kd declined to 7%? INPUTS 10 7 100 1,000 N I/YR PV PMT FV -1,210.71 OUTPUT Price rises above par, and bond sells at a premium, if Coupon >kd.

  12. Determining the Price of a Bond—Example Q: The Emory Corporation issued an 8%, 25-year bond 15 years ago. At the time of issue it sold for its par (face) value of $1,000. Comparable bonds are yielding 10% today. What must Emory’s bond sell for in today’s market to yield 10% (YTM) to the buyer? Assume the bond pays interest semiannually. Also calculate the bond’s current yield. Example

  13. N PV FV PMT Bond Example This can be calculated via a financial calculator: 20 Example -875.39 Answer 1000 40 I/Y 5

  14. Changes in Bond Prices When Interest Rates Change • If the market rate associated with a bond, kd, equals the coupon rate of interest, the bond will sell at its par value. • If interest rates in the economy fall after the bonds are issued, kd is below the coupon rate, and the present value will increase (bond price increases is above par) • If interest rates in the economy rise after the bonds are issued, kd is above the coupon rate, and the present value will decrease (bond price decreases and is below par)

  15. Changes in Bond Values Discount Bond A bond that sells below its par value, which occurs whenever the going rate of interest rises above the coupon rate Premium Bond A bond that sells above its par value, which occurs whenever the going rate of interest falls below the coupon rate

  16. INPUTS INPUTS 15 16 150 1000 N I/YR PV PMT FV ? 15 14 150 1000 N I/YR PV PMT FV ? OUTPUT OUTPUT 15% coupon, 15year, $1,000 bonds valued at 14, 15, and 16% required rate of return Financial calculator solution:

  17. Changes in Bond Values Over Time Current yieldis the annual interest payment on a bond divided by its current market value Current yield Capital gains yield

  18. Changes in Bond Values Over Time The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt

  19. Expected time path of value of a 15% Coupon, 15 year, 1000 par value bond when interest rates are 10%, 15%, and 20%

  20. Bond Value Kd < Coupon Rate Kd = Coupon Rate Kd > Coupon Rate Years Expected Changes in Bond Values Over Time Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20%

  21. At maturity, the value of any bond must equal its par value. • The value of a premium bond would decrease to $1,000. • The value of a discount bond would increase to $1,000. • A par bond stays at $1,000 if kd remains constant.

  22. What’s “yield to maturity”? • YTM is the rate of return earned on a bond held to maturity. Also called “promised yield”.

  23. 0 1 9 10 kd=? 90 90 90 What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 1,000 -877 Find kd that “works”!

  24. INPUTS 10 -887 90 1,000 N I/YR PV PMT FV 10.91 OUTPUT Find kd

  25. INPUTS 10 -1,134.2 90 1,000 N I/YR PV PMT FV 7.08 OUTPUT Find YTM if price is $1,134.20. Sells at a premium. Because coupon = 9% > kd = 7.08%, bond’s value > par.

  26. INPUTS 2n kd/2 OK INT/2 OK N I/YR PV PMT FV OUTPUT Semi-annual Bonds 1. Multiply years by 2 to get periods = 2n. 2. Divide nominal rate by 2 to get periodic rate = kd / 2. 3. Divide annual interest by 2 to get PMT = INT / 2.

  27. Find the value of 10-year, 10% coupon, semi-annual bond if kd = 13%. 2(10) 13/2 100/2 20 6.5 50 1,000 N I/YR PV PMT FV -834.72 INPUTS OUTPUT

  28. Definitions: Current yield = Annual coupon pmt Current price Cap gains yld = Change in price Beginning price Exp total = YTM = Exp + Exp cap return Curr yld gains yld • Ads up to YTM each year, but components may not always be the same every year.

  29. Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%. Current yield = $90 $887 = 0.1015 = 10.15%

  30. YTM = Current yld + Capital gains yld. Cap gains yld = YTM - Current yld. = 10.91% - 10.15% = 0.76% We have ‘backed out’ what the expected capital gain yield must be. Could also find value in Years 1 and 2, get difference, and divide by value in Year 1. Same answer.

  31. What’s interest rate (or price) risk? Does a 1-yr or 10-yr 10% bond have more risk? Interest rate risk: Rising kd causes bond’s price to fall.

  32. Call Provisions • If interest rates have dropped substantially since a bond was originally issued, a firm may wish to ‘refinance,’ or retire their old high interest bond issue • However, the issuing corporation would have to get all the bondholders to agree to this • From the bondholder’s viewpoint, this could be a bad idea—they would be giving up high coupon bonds and would have to reinvest their cash in a market with lower interest rates • To ensure that the corporation can refinance their bonds should they wish to do so, the corporation makes the bonds ‘callable’

  33. Call Provisions • Call provisions allow bond issuers to retire bonds before maturity by paying a premium (penalty) to bondholders • Many corporations offer a deferred call period (meaning the bond won’t be called for at least x years after the initial issuing date) • Known as the call-protected period

  34. Call Provisions • The Effect of A Call Provision on Price • When valuing a bond that is probably going to be called when the call-protected period is over • Cannot use the traditional bond valuation procedure • Cash flows will not be received through maturity because bond will probably be called

  35. A 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1,135.90 with an 8% yield to maturity. It can be called after 5 years at $1,050. What’s the bond’s nominal yield to call (YTC)?

  36. INPUTS 10 -1,135.9 50 1,050 N I/YR PV PMT FV 3.765 x 2 = 7.53% OUTPUT A 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1,135.90 with an 8% yield to maturity. It can be called after 5 years at $1,050. What’s the bond’s nominal yield to call (YTC)?

  37. In general, if a bond sells at a premium, then (1) coupon > kd, so (2) a call is likely. • So, expect to earn: • YTC on premium bonds. • YTM on par & discount bonds.

  38. Convertible Bonds • Unsecured bonds that are exchangeable for a fixed number of shares of the company’s stock at the bondholder's discretion • Allows bondholders to participate in a stock’s price appreciation should the firm be successful • Conversion ratio represents the number of shares of stock that will be received for each bond • Conversion price is the implied stock price if bond is converted into a certain number of shares • Usually set 15-30% higher than the stock’s market value at the time the bond is issued • Can usually be issued at lower coupon rates

  39. Effect on Earnings Per Share—Diluted EPS • Upon conversion convertible bonds cause dilution in EPS • EPS drops due to the increase in the number of shares of stock • Thus convertible bonds have the potential to dilute EPS • Therefore convertible bonds will impact the calculation of Diluted EPS according to FASB 128

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