2.2 Analytics of convertibles and structured convertibles Conversion premium and break-even calculations Decomposition of convertible value into different components bond plus warrant plus default risk put plus stock plus yield advantage Interest rate sensitivities - duration Lattice tree calculations: incorporation of default risk, call and conversion rights Structured convertibles Mandatory convertibles (performance based conversion premium, parallel debts Exchangeables convertible stock notes Debt exchangeable for common stock
1 2.2 Analytics of convertibles and structured convertibles • Conversion premium and break-even calculations • Decomposition of convertible value into different components - bond plus warrant plus default risk - put plus stock plus yield advantage • Interest rate sensitivities – duration • Lattice tree calculations: incorporation of default risk, call and conversion rights • Structured convertibles - Mandatory convertibles (performance based conversion premium, parallel debts) - Exchangeables - convertible stock notes - Debt exchangeable for common stock
Premium for conversion right An investor who purchases a convertible bond rather than the underlying stock typically pays a premium over the current market price of the stock Why would someone be willing to pay a premium to buy this stock? The market conversion premium per share is related to the price of a call option limit the downside risk of the convertible bond
2 Premium for conversion right • An investor who purchases a convertible bond rather than the underlying stock typically pays a premium over the current market price of the stock. • Why would someone be willing to pay a premium to buy this stock? The market conversion premium per share is related to the price of a call option – limit the downside risk of the convertible bond
Analytics of convertible bonds stock price $30.00 per share stock dividend $0. 50 per share convertible market price $1000 coupon rate 7.00 maturity 20 years conversion price $36.37 Stock dividend yield= annual dividend rate current stock price =$0.50/$30.00=1.67%
3 Analytics of convertible bonds stock price $30.00 per share stock dividend $0.50 per share convertible market price $1,000 coupon rate 7.00% maturity 20 years conversion price $36.37 Stock dividend yield = annual dividend rate / current stock price = $0.50 / $30.00 = 1.67%
Conversion ratio number of shares for which one bond may be exchanged par/ conversion price =$1,000/$3637=27.50 shares Conversion value equity value or stock value of the convertible stock price x conversion ratio =$30.00x27.50=$82500
4 Conversion ratio = number of shares for which one bond may be exchanged = par / conversion price = $1,000 / $36.37 = 27.50 shares Conversion value = equity value or stock value of the convertible = stock price x conversion ratio = $30.00 x 27.50 = $825.00
Conversion premium (convertible price-conversion value) conversion value ($13000-$825)/$825.00=21.21% Dollar premium convertible price-conversion value(expressed in points) ($12000-$825)/$1,000×100% 17.50 points
5 Conversion premium = (convertible price – conversion value) / conversion value = ($1,000 – $825) / $825.00 = 21.21% Dollar premium = convertible price – conversion value (expressed in points) = ($1,000 – $825) / $1,000 x 100% = 17.50 points
Break even calculations Break even(years) conversion premium /(convertible yield - stock yield =2121/(7.00-1.67)=3.98( years) Number of years necessary for the stock investor to recover the conversion premium from the convertibles higher income relative to an instrument of an equivalent amount in the stock After 3.98 years, the convertible has made up, in income alone, the amount of the conversion premium
6 Break even calculations Break even (years) = conversion premium / (convertible yield – stock yield) = 21.21 / (7.00 – 1.67) = 3.98 (years) Number of years necessary for the stock investor to recover the conversion premium from the convertible’s higher income relative to an instrument of an equivalent amount in the stock. After 3.98 years, the convertible has made up, in income alone, the amount of the conversion premium
Break-even calculations (contd) Dollar maintenance market price-conversion value coupon market price stock price stock dividend The time it takes for the convertible yield advantage to pay for its premium compared to an equivalent dollar amount purchased of the underlying stock May use conversion ratio instead of market rice/ stock pr price
7 Break-even calculations (cont’d) Dollar maintenance The time it takes for the convertible yield advantage to pay for its premium compared to an equivalent dollar amount purchased of the underlying stock. • May use conversion ratio instead of market price/ stock price. market price – conversion value coupon - stock dividend market price stock price =
Weaknesses of break-even analysis It ignores the main advantage of convertible protection on downside risk on the underlying equity It ignores the margin of safety offered by the convertible with the payment of principal at maturity
8 Weaknesses of break-even analysis • It ignores the main advantage of convertible: protection on downside risk on the underlying equity. • It ignores the margin of safety offered by the convertible with the payment of principal at maturity
Stripping different components of convertible bonds A convertible bond consists of 3 components bond component -interest rate risk equity component-equity risk credit quality component credit risk coupon payment periodic Default risk Fixed income Financial payment protection Investor e principal- Institution ayment provider upon default holding ig a convertible bond
9 Stripping different components of convertible bonds A convertible bond consists of 3 components • bond component – interest rate risk • equity component – equity risk • credit quality component - credit risk holding a convertible bond Fixed income investor Financial institution Default risk protection provider coupon payment principal periodic payment payment contingent upon default
Contingent claims approach Wide spread use of the option pricing theory for pricing convertibles The underlying state variable is issuer's frim value process. The firm value is not the total value of assets owned by the firm. It is the takeover value when the firm is sold Overall assessment of the price impact of different features in a convertible
10 Contingent claims approach Wide spread use of the option pricing theory for pricing convertibles. The underlying state variable is issuer’s frim value process. The firm value is not the total value of assets owned by the firm. It is the takeover value when the firm is sold. Overall assessment of the price impact of different features in a convertible