Question

A convertible bond issued by firm BigRed has a conversion ratio of 20, coupon rate of 6.7% (interest paid annually), maturity of 8 years, yield to maturity of 6.0%, and par value of $1,000. The yield to maturity of a non-convertible bond issued by the same firm is 8.2%. BigRed's stock price is currently $39.71 and the stock pays an annual dividend of $1.61 per share. All rates are annualized assuming periodicity of 1 (i.e. annual compounding). What is the minimum value of BigRed's convertible bond? (If your solution is $4.44 then enter "4.44" as the answer. Precision is 0.01+/- 0.02.)

Answer 1

Minimum value of the bond is the value of bond if it is a straight bond or value of conversion.

Value of straight bond is the present value of the coupons and par value discounted at rate of Straight bond YTM

Value of conversion = Conversion Ratio * Price per share.

Straight Value of bond

We use financial calculator to find the present value

Coupon = 67

FV = 1000

N = 8

I/Y = 8.2%

Compute PV, we get = 914.45

Conversion Value of Bond

= Conversion Ratio * Price per share = 20 * 39.71 = 794.20

Hence minimum value of bond is higher of straight value of bond or conversion value of bond , which is 914.45