If a $1000 per share value of convertible bond is issued for $1000, and is convertible into 20 shares of issuer’s common stock that pays no dividend…

The convertible bond's value in the "equity-equivalent region" is primarily driven by its conversion value, not its value as a debt instrument. The conversion value is the market price of the common stock multiplied by the conversion ratio. In this case, the conversion ratio is 20 shares. Therefore, for every $1 increase in the price of a single share of common stock, the total conversion value of the bond increases by $20 (20 shares × $1/share). As the bond's price tracks its conversion value in this region, the bond's value will also increase by $20.

A. $25: This would be the correct increase if the bond were convertible into 25 shares, not 20.

B. $50: This represents the conversion price ($1000 face value / 20 shares), not the incremental change in value.

D. $10: This would be the correct increase if the bond were convertible into 10 shares, not 20.

1. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education. In Chapter 24-3, "The Value of a Convertible Bond," the text explains that when the stock price is high (placing the bond in the equity-equivalent region), the convertible's value is determined by its conversion value (stock price multiplied by the number of shares into which it can be converted).

2. Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). John Wiley & Sons. In Chapter 29, "The Value of Flexibility," the valuation of convertible bonds is discussed. When a convertible is deep in-the-money, it behaves like the underlying equity, and its value changes in direct proportion to the stock price multiplied by the conversion ratio.

3. Pratt, S. P., & Grabowski, R. J. (2014). Cost of Capital: Applications and Examples (5th ed.). John Wiley & Sons. While not a direct quote, the principles in Chapter 17, "Valuing Complex-Capital-Structure Securities," support that the value of a convertible security, when its conversion feature is valuable, is directly linked to the value of the underlying equity shares. The change in value is a function of the conversion ratio.