# Convertible Bond

A convertible bond is a bond that gives the bond-holder an option to convert the bond to a specified number of shares of the company’s common stock at a pre-determined conversion date. Convertible bonds give early stage companies access to funding at lower rates while also reduce risk for the bond-holders.

The number of common stocks to which a bond can be converted is called the bond’s conversion ratio. For example, if a $1,000 par value bond can be converted to 20 shares of common stock, the conversion ratio is 20. The par value of convertible bond per share of common stock is called the conversion price, i.e.$50 (=$1,000/20). ## Advantages Convertible bonds are useful for both early stage high-risk companies and investors interested in lending to them. The investors demand high yield on straight bonds on start-ups and other small companies due to high risk. Due to the conversion feature, the risk for investors is reduced and so does the yield which the companies must pay. If the company is successful, its stock price rises which makes the conversion option valuable and the bond-holders share the upside. If the company doesn’t do well but is solvent, convertible debt bond-holders have the assurance of interest income. However, if the company defaults, convertible debt-holders are worse off than the straight debt-holders because they receive any money only after straight debt-holders are paid off. If the market price of the common stock rises, the convertible bonds behaves like equity and if the market price is significantly lower than the par value of the bond, the bond behaves like a straight-bond i.e. as bond without any conversion feature. The product of conversion ratio and current market price of a share of common stock is called the conversion value. The excess of current market price over the higher of conversion value or the straight-bond value is called the conversion premium. ## Formula $$Conversion\ Ratio\ (CR)=\frac{Number\ of\ Shares\ of\ Common\ Stock}{Number\ of\ Bonds}$$ $$Conversion\ Price\ (CP)=\frac{Bond\ Par\ Value}{Conversion\ Ratio}\$$ $$Conversion\ Value\ (CV)\ =CR\times Current\ Common\ Share\ Price$$ $$Conversion\ Premium=BP\ -\ MAX(CV,BV)$$ Where CV stands for conversion value and BV stands for bond value without the conversion feature, it equals the bond value as if it was a straight bond. ## Example A technology company issued$100 million in convertible bonds on 1 January 2011 with a maturity date of 31 December 2025. The last date of conversion is 31 December 2020. The bonds have $1,000 par value and coupon rate of 6% compounded semiannually. 3 bonds can be converted to 50 shares of common stock. The current market interest rate is 5%. It is 1 January 2018 and the bonds currently trade at$1,325 when the current share price of the stock is $75.50 per share. Find out the bond’s conversion ratio, conversion price, conversion value and conversion premium. $$Conversion\ ratio\ =\ \frac{50}{3}=\ 16.67$$ $$Conversion\ price\ =\frac{\ 1,000}{16.67}=60$$ $$Conversion\ Value=16.67\times75.50=1,258.58$$ The price of the bond as if it is a plain-vanilla bond can be worked out using Excel PRICE function which equals$1,065.28.

The conversion value ($1,258.58) is higher than the straight-bond value ($1,065.28), so conversion premium equals $66.42 Conversion premium =$1,325 – $1,258.58 =$66.42

The conversion premium reflects the potential of further stock price increase which before the conversion date.