Convertible Bond and Convertible Preferred Stock

1) Given the following information concerning a convertible bond:
Principal $1000
Coupon 5%
Maturity 15 yrs
Call Price $1,050
Conversion price $37 (i.e., 27 shares)
Market price of the common stock $32
Market price of the bond $1,040

a) What is the current yield of this bond?
b) What is the value of the bond based on the market price of the common stock?
c) What is the value of the common stock based on the market price of the bond?
d) What is the premium in terms of stock that the investor pays when he/she purchases the convertible bond instead of stock?
e) Nonconvertible bonds are selling with a yield to maturity of 7 %. If this bond lacked the conversion feature, what would the approximate price of the bond be?
f) What is the premium in terms of debt that the investor pays when he or she purchase convertible bond instead of a nonconvertible bond?
g) If the price of the common stock should double, would the price of the convertible bond double? Briefly explain your answer
h) If the price of the common stock should decline by 50%, would the price of the convertible bond decline by the same percentage" Briefly explain your answer.
i) What is the probability that the corporation will call the bond?
j) Why are investors willing to pay the premiums mentioned in parts (d) and (f)?

2) The following information concerns a convertible bond:
Coupon 6% ($60 per $1,000 bond)
Exercise price $25
Maturity 20 yrs
Call price $1,040
Price of the common stock $30
a) If this bond were nonconvertible, what would be its approximate value if comparable interest rates were 12%?
b) Into how many shares can the bond be converted?
c) What is the value of the bond in terms of stock?
d) What is the current minimum price that the bond will command?
e) IF the current minimum price of the bond is $976, what should you do?
f) Is there any reason to anticipate that the firm will call the bond?
g) What do investors receive if they do not convert the bond when it is called?
h) If the bond were called, would it be advantageous to convert?
i) IF the interest rates rise, would that affect the bond's current yield?
j) If the stock price were $10, would your answer to part (i0 be different?

3) Given the following information concerning Continental Group $2.00 convertible preferred stock :
One share of preferred is convertible into 0.50 shares of common stock
Price of common stock: $34
Price of convertible preferred stock: $25
a) What is the value of the preferred stock in terms of common stock?
b) What is the premium over the preferred stock's value as common stock?
c) IF the preferred stock is perpetual and comparable preferred stock offers a dividend yield of 10%, what would be the minimum price of this stock if it were not convertible?
d) IF the price of the common stock rose to $60, what would be the minimum increase in the value of the preferred stock that you would expect?
4) Two bonds have the following terms:
Bond A Bond B
Principal $1,000 Principal $1,000
Coupon 8% Coupon 7.6%
Maturity 10 yrs Maturity 10 yrs

Bond B has an additional feature: It may be redeemed at par after 5 yrs, (i.e., it has a put feature) Both bonds were initially sold for their face amounts (1.e., $1,000)
a) If interest rates fall to 7 %, what will be the price of each bond?
b) If interest rates rise to 9 %, what will be the decline in the price of each bond from its initial price?
c) Given your answers to questions (a) and (b), what is the trade-off implied by the put option in bond B?
d) Bond B requires the investor to forgo $4 a yr (i.e., $40 if the bond is in existence for 10 yrs) If interest rates are 8 %, what is the present value of this forgone interest? If the bond had lacked the put feature but had a coupon of 7.6 % and a term to maturity of 10 yrs, it would sell for $973.16 when interest rates were 8 %. What, then, is the implied cost of the put option?
5) Two firms have common stock and convertible bonds outstanding. Information concerning these securities is as follows:

Common Stock Firm A Firm B
Price of common stock $46 $30
Cash dividend none $1
Convertible bond
Principal $1,000 $1,000
Conversion price $50 $33 1/3
(20 shares) (30 shares)
Maturity 10 yrs 10 yrs
Coupon 7.5% 7.5%
Market price $1,100 $1,100

a) What is the value of each bond in terms of stock?
b) What is the premium paid over each bond's value as stock?
c) What is each bond's income advantage over the stock into which the bond may be converted?
d) How long will it take for the income advantages to offset premium determined in part (b)?
e) If after 4 yrs firm A's stock sells for $65 and the firm calls the bond, what is the holding period return and the annual rate of return earned on an investment in the stock or in the bond?