A convertible bond is convertible at $40 per share. The bond currently trades at $1,150. The parity price of the underlying stock is:
- A.$25.00That is the conversion RATIO (number of shares), not a stock price.
- B.$46.00Correct. 25-share ratio; $1,150 / 25 = $46 makes stock and bond values equivalent.
- C.$28.75This divides 1,150 by the $40 conversion price, mixing up price and ratio.
- D.$40.00That is the conversion price - parity only equals it when the bond trades exactly at par.
Why: Conversion ratio = $1,000 par / $40 = 25 shares. Parity stock price = bond market price / ratio = $1,150 / 25 = $46. Parity is the stock price at which conversion value equals the bond's market price. The clue: always derive the ratio from PAR, then divide the market price by it. Review: Equity and Debt Securities.
A convertible bond (1,000 par) is convertible at 40 dollars per share. The bond trades at 1,150 and the underlying stock trades at 44. Which action is more advantageous, and what is the parity relationship?
- A.Convert immediately, because the 44 stock price is above the 40 conversion price, guaranteeing a profitIncorrect. The bond already trades above parity, so converting surrenders value.
- B.Parity value is 1,760 (44 x 40), so the bond is deeply undervaluedIncorrect. Multiplying the stock price by the conversion price is not how parity is computed.
- C.Parity value is 1,000, equal to par, so converting and holding are equivalentIncorrect. Parity is 25 x 44 = 1,100, not 1,000.
- D.Parity value is 1,100, below the bond's 1,150 market price, so converting is disadvantageous and selling the bond captures more valueCorrect. With parity at 1,100 and the bond at 1,150, selling beats converting.
Why: The conversion ratio is par divided by the conversion price, 1,000 divided by 40, or 25 shares. Parity (the stock value of the bond) is 25 shares times 44, or 1,100. Because the bond trades at 1,150, above its 1,100 conversion value, converting would give the investor only 1,100 of stock, so selling the bond at 1,150 captures more value.