Chapter 24: The Many Different Kinds of Debt (Convertible Bonds) Problem Sets (8, 23, 24, 25)
Problem 8:
(See Ch24, p.644)
Maple Aircraft has issued a convertible subordinated debenture due 2020. The conversion price is $47 and the debenture is callable at 102.75% of face value. The market price of the convertible is 91% of face value, and the price of the common is $41.50. Assume that the value of the bond in the absence of a conversion feature is about 65% of face value. a) What is the conversion ratio of the debenture? b) If the conversion ratio were 50, what would be the conversion price? c) What is the conversion value?
Problem 8: Cont. d) At what stock price is the conversion value equal to the bond value? e) Can the market price of the convertible be less than the conversion value? f) How much is the convertible holder paying for the option to buy one share of common stock? g) By how much does the common have to rise by 2020 to justify conversion? h) When should Maple call the debenture?
Problem 8: Cont. a) What is the conversion ratio of the debenture? Conversion ratio = face value of the bond to conversion price = 1,000/47 = 21.28 b) If the conversion ratio were 50, what would be the conversion price? Conversion price = face value of the bond to conversion ratio = 1,000/50 = $20 c) What is the conversion value? Conversion value = conversion ratio x market share price = 21.28 X 41.50 = $883.12
Problem 8: Cont. d) At what stock price is the conversion value equal to the bond value? Stock price = bond value to conversion ratio = 650/21.28 = $30.55 e) Can the market price of the convertible be less than the conversion value? No (not if the investor is free to convert immediately) f) How much is the convertible holder paying for the option to buy one share of common stock? Value of the conversion option per share = the difference between the price of the convertible bond and the price of the straight bond to conversion ratio = (910 – 650)/21.28 = $12.22
Problem 8: Cont. g) By how much does the common have to rise by 2020 to justify conversion? (Conversion price to the price of the common) - 1 = (47/41.50) - 1 = .1325, or 13.25% The conversion value = (or >) the face value 21.28 shares x (41.50 x 1.1325) = 1000 h) When should Maple call the debenture? When the price reaches 102.75% of face value.
Problem 23:
(See Ch24, p.646)
Piglet Pies has issued a zero-coupon 10-year bond that can be converted into 10 Piglet shares. Comparable straight bonds are yielding 8%. Piglet stock is priced at $50 a share. a)
b) c)
Suppose that you had to make a now-or-never decision on whether to convert or to stay with the bond. Which would you do? If the convertible bond is priced at $550, how much are investors paying for the option to buy Piglet shares? If after one year the value of the conversion option is unchanged, what is the value of the convertible bond?
Problem 23: Cont. a) Suppose that you had to make a now-or-never decision on whether to convert or to stay with the bond. Which would you do? If the fair rate of return on a 10-year zero-coupon non convertible bond is 8%, then the price would be: $1,000 /1.0810 = $463.19 The conversion value is: 10 $50 = $500 You would convert. By converting, you would gain: $500 – $463.19 = $36.81 That is, you could convert, sell the ten shares for $500, and then buy a comparable straight bond for $463.19. Otherwise, if you do not convert, and the bond is no longer convertible in the future,
Problem 23: Cont. b) If the convertible bond is priced at $550, how much are investors paying for the option to buy Piglet shares? The value of the conversion option = the price of a convertible bond – the price of an equivalent straight bond = $550 – $463.19 = $86.81 investors are paying for the option to buy ten shares. c) If after one year the value of the conversion option is unchanged, what is the value of the convertible bond? In one year, bond value = $1000/1.089 = $500.25 (i.e., the value of a comparable non-convertible bond)
Then the value of the convertible bond is: $500.25 +
Problem 24:
(See Ch24, p.646)
Iota Microsystems’ 10% convertible is about to mature. The conversion ratio is 27. Assume a face value of $1000.
a) What is the conversion price? b) The stock price is $47. What is the conversion value? c) Should you convert?
Problem 24: Cont. a) What is the conversion price? Conversion price = face value of the bond to conversion ratio = $1,000/27 = $37.04 b) The stock price is $47. What is the conversion value? Conversion value = conversion ratio x market share price = 27 $47 = $1,269 c) Should you convert? Yes, you should convert because the value of the shares ($1,269) is greater than the maturity value of the bond.
Problem 25:
(See Ch24, p.646)
In 1996 Marriott International made an issue of unusual bonds called Liquid Yield Option Notes, or LYONS. The bond matures in 2011, has a zero coupon, and was issued at $532.15. It could be converted into 8.76 shares. Beginning in 1999 the bonds could be called by Marriott. The call price was $603.71 in 1999 and increased by 4.3% a year thereafter. Holders had an option to put the bond back to Marriott in 1999 at $603.71 and in 2006 at $810.36. At the time of issue the price of the common stock was about $50.50.
Problem 25: Cont. a) What was the yield to maturity on the bond? b) Assuming that comparable nonconvertible bonds yielded 10%, how much were investors paying for the conversion option? c) What was the conversion value of the bonds at the time of issue? d) What was the initial conversion price of the bonds? e) What was the conversion price in 2005? Why did it change? f) If the price of the bond in 2006 was less than $810.36, would you have put the bond back to Marriott? g) At what price could Marriott have called the bonds in 2006? If the price of the bond in 2006 was more than this, should Marriott have called them?
Problem 25: Cont. a) What was the yield to maturity on the bond? The yield to maturity on the bond is computed as follows: $532.15 = $1,000/(1 + r) 15 $1,000 = $532.15 (1 + r)15 1,000/532.15 = (1 + r) 15 1.8792 = (1 + r)15 1.8792(1/15) = (1 + r) 1.0430 = (1 + r) r = 0.0430 = 4.30% b) Assuming that comparable nonconvertible bonds yielded 10%, how much were investors paying for the conversion option? The value of the non-convertible bond would be: $1,000/(1.10)15 = $239.39 The conversion option = $532.15 $239.39 = $292.76
Problem 25: Cont. c) What was the conversion value of the bonds at the time of issue? Conversion value of the bonds at time of issue was: 8.76 × $50.5 = $442.38 d) What was the initial conversion price of the bonds? The initial conversion price was: $532.15/8.76 = $60.75 e) What was the conversion price in 2005? Why did it change? Call price in 2005 = $603.71 1.04306 = $777.20 Therefore, the conversion price = $777.20/8.76 = $88.72 The increase in the conversion price reflects the accreted value of the bond since it has a zero coupon.
Problem 25: Cont. f) If the price of the bond in 2006 was less than $810.36, would you have put the bond back to Marriott? If investors act rationally, they should put the bond back to Marriott as soon as the market price falls to the put exercise price. g) At what price could Marriott have called the bonds in 2006? If the price of the bond in 2006 was more than this, should Marriott have called them? Call price in 2006= $603.71 1.04307 = $810.62 Marriott should call the bonds if the price is greater than $810.62.
