A convertible bond is selling for $800,matures in 10 years,has a face value of $1,000,and a coupon rate of 10 percent.Similar nonconvertible bonds are priced to yield 14 percent.The conversion price is $32.The stock currently sells for $31.30 a share.What is the conversion premium?

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Quizplus · Accepted Answer

The conversion premium is calculated as the difference between the bond price and the value of the shares it can be converted into, divided by the value of the shares it can be converted into, all multiplied by 100 to get a percentage. The bond can be converted into $1,000 / $32 = 31.25 shares. The value of these shares at the current stock price is 31.25 shares * $31.30/share = $977.81. The conversion premium is then ($800 - $977.81) / $977.81 * 100 = -18.14%. However, since none of the options match this calculation, it seems there was a mistake in the calculation process. The correct approach to find the conversion premium is to compare the investment needed to acquire the bond to the investment needed to acquire the equivalent number of shares directly. The conversion premium formula is [(Bond Price - (Conversion Ratio * Stock Price)) / (Conversion Ratio * Stock Price)] * 100. The conversion ratio is the face value of the bond divided by the conversion price, which is $1,000 / $32 = 31.25. The stock value for these shares is 31.25 * $31.30 = $977.81. The conversion premium is then [(800 - 977.81) / 977.81] * 100, which does not directly match any of the provided choices, indicating a need to reevaluate the explanation or the choices given. Correctly, the bond price itself should not be subtracted from the stock value but rather compared in terms of additional cost over the direct stock purchase value. The correct calculation for the premium actually involves assessing the extra cost of buying the bond over buying the stock directly, which was not accurately captured in the initial explanation. Given the discrepancy and the provided options, a reevaluation or clarification of the correct process to calculate the conversion premium in this context is necessary, focusing on the premium over the current stock value for the shares the bond can be converted into.

A Convertible Bond Is Selling for $800,matures in 10 Years,has