Given the following information concerning a convertible bond: Principal: $1,000

Question

Given the following information concerning a convertible bond:

Principal: $1,000

Coupon: 5%

Maturity: 15 years

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)?

Explanation / Answer

a) Current yield = Coupon/market price of bond = 50/1040 = 4.81%

b) Value of the bond based on current on current market price of stock = 32*27 = 864

c) value of the common stock based on the market price of the bond = 1040/27 = 38.51

d) Premium paid = 38.51 - 32 = 6.518

e)

  K = N          
BOND PRICE= [(Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1

                    K = 15   
BOND PRICE= [(5*1000/100)/(1 + 7/100)^k]     +   1000/(1 + 7/100)^10
                   k=1

= 817.84

Please ask remaining parts seperately

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