Conversion Value

The value of convertible bonds depends on conversion value. Conversion value is what the bonds would be worth if they were immediately converted into the common stock at current prices. Typically, conversion value is computed by multiplying the number of shares of common stock that will be received when the bond is converted by the current price of the common stock.

6For a similar treatment see Richard Brealey and Stewart Myers, Principles of Corporate Finance, 2nd ed. (New York: McGraw-Hill, 1984), Chapter 23; and James C. Van Horne, Financial Markets and Flows, 2nd ed. (Englewood Cliffs, N.J.: Prentice Hall, 1987) Chapter 11.

7This formula assumes that coupons are paid annually.

Ross-Westerfield-Jaffe: I VI. Options, Futures, and I 24. Warrants and I I © The McGraw-Hill

Corporate Finance, Sixth Corporate Finance Convertibles Companies, 2002

Edition

Part VI Options, Futures, and Corporate Finance

■ FIGURE 24.2 Minimum Value of a Convertible Bond versus the Value of the Stock for a Given Interest Rate

Minimum convertible bond value (floor value)

jg Conversion

value

Convertible bond —/

floor ^2i\ue

/ 1

Straight bond

/ 1 / 1

j/\ = Conversion |

ratio

Straight bond value Straight bond value greater than less than conversion conversion value value

As shown, the minimum, or floor, value of a convertible bond is either its straight bond value or its conversion value, whichever is greater.

Straight bond value Straight bond value greater than less than conversion conversion value value

As shown, the minimum, or floor, value of a convertible bond is either its straight bond value or its conversion value, whichever is greater.

Stock price

On November 1, 1993, each Seagate convertible bond could have been converted into 23.53 shares of Seagate common stock. Seagate common was selling for $22.625. Thus, the conversion value was 23.53 X $22.625 = $532.37. A convertible cannot sell for less than its conversion value. Arbitrage prevents this from happening. If Seagate's convertible sold for less than $532.37, investors would have bought the bonds and converted them into common stock and sold the stock. The profit would have been the difference between the value of the stock sold and the bond's conversion value.

Thus, convertible bonds have two minimum values: the straight bond value and the conversion value. The conversion value is determined by the value of the firm's underlying common stock. This is illustrated in Figure 24.2. As the value of common stock rises and falls, the conversion price rises and falls with it. When the value of Seagate's common stock increased by $1, the conversion value of its convertible bonds increased by $23.53.

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