A bond with a face value of $5,000 can be exchanged for 70 shares of stock.The bond has a coupon rate of 6.5 percent which equals the market rate of interest.Assume the option premium is $50.What is the market value of the bond if the stock is selling for $68.90 a share and the bond matures in exactly one year?
A)$4,744.84
B)$4,873.00
C)$5,000.00
D)$4,940.00
E)$5,050.00

Question

Quizplus · Accepted Answer

The market value of the bond can be calculated by considering the conversion value and the bond's value as a regular bond. The conversion value is the current value of the shares it can be converted into, which is 70 shares * $68.90/share = $4,823. The bond's value as a regular bond can be calculated by adding the present value of its coupon payments and the present value of its face value. Since the coupon rate equals the market rate, the bond's value as a regular bond is its face value, $5,000. However, since the bond can be converted into stock worth more than its face value, the bond's value is the conversion value plus the option premium: $4,823 + $50 = $4,873. But, given the choices and the correct calculation method, it seems there might have been a mistake in my explanation regarding the final value. The correct approach to find the market value of the convertible bond involves considering the higher of the bond's value as a regular bond or its conversion value, plus any option premium. Since the bond's regular value equals its face value ($5,000) because the coupon rate matches the market rate, and the conversion value is $4,823 (not including the premium), the correct market value should include the premium when the conversion value is considered. However, the correct answer should reflect the bond's highest value, which is its face value or the conversion value plus the premium if that exceeds the face value. Given the provided options and the correct calculation method, the answer provided initially seems incorrect because it didn't properly account for the comparison between the bond's face value and the conversion value plus premium. The correct market value should be the higher of the bond's face value or the conversion value plus the option premium, which, based on the calculation provided, would actually be the face value of $5,000 plus the option premium of $50, totaling $5,050, aligning with option E. My initial explanation mistakenly overlooked the correct application of these values in determining the final market value.

A Bond with a Face Value of $5,000 Can Be