Characteristics, Uses and Taxation of Investments - Convertible Bond Mathematics



  1. Analysis and valuation of convertible bonds could fill volumes and actually do [Much has been written about convertible securities. Two volumes, in particular, explore both the basics and the arcana of these instruments. They come from the portfolio managers at Calamos Investments, an investment management firm with a focus on convertible bonds. Calamos, John P. CONVERTIBLE SECURITIES The Latest Instruments, Portfolio Strategies, and Valuation Analysis Revised Edition McGraw-Hill ,1998 and Calamos, Nick P. Convertible Arbitrage: Insights and Techniques for Successful Hedging John Wiley & Sons, Inc. 2003]. For the purpose of the Certified Financial Planner ™ examination, a working knowledge of the basic traits, the mathematics of conversion and their suitability in a client portfolio is sufficient. Evaluation considers several factors, to wit:
    1. Price appreciation required of the underlying common stock of the issuer for conversion to be attractive. The conversion premium ration measures this.
    2. The growth prospects of the underlying common stock.
    3. The bond's downside potential should the underlying common stock's price be so low as to render the conversion privilege worthless.
    4. The yield sacrifice required to purchase the convertible.
    5. The income advantage to acquiring the convertible bond rather than the quantity of shares of the underlying common stock that would be obtained upon conversion.
    6. The quality of the bond and the underlying stock, both of which are, in turn, a function of the quality of the issuer.
    7. The breakeven time which is the number of years over which the premium paid to acquire the convertible will be recovered through what the bondholder expects to be the favorable income differential offered by the convertible bond relative to the underlying common stock.
  2. Formulae: better than committing them to memory alone is an understanding of how and where they figure in the analytical and valuation process. Therefore, a detailed example is provided to bring these concepts together and reinforce them.

    Information on the Globotron Meganet (GMN) 5 ¾ % Convertible Bond Due in 9+ Years and Common Stock
Convertible Bond
Coupon rate 5 ¾ %
Current market price $106.5
Conversion Ratio 25.320 shares of ADC/$1,000 par value
Non-callable for three years
Rating A3/A
Maturity Date 9+ Years

Call Price Schedule
In Year 4 103.59
In Year 5 102.88
In Year 6 102.16
In Year 7 101.44
In Year 8 100.72
In Year 9 100.00
In Year 10 100.00

ADC Common Stock
Expected volatility 17%
Current dividend yield 2.727%
Dividend Per Share $0.90
Stock price $33

Conversion Ratio: the number of shares of common stock that the investor receives from exercising the call option. The ratio may be valid for all or a portion of the bond's life and the ratio itself may change. It is adjusted proportionately for stock splits and stock dividends. ADC Conversion ratio: 25.32 shares

(Stated) Conversion Price: par value/conversion ratio. ADC's conversion price: $1,000/25.32 shares = $39.49

Conversion (parity) Value: conversion value = market price of common stock x conversion ratio. This formula determines the value of the security if immediately converted. Callable and Foreign Bonds and Promissory Notes
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