Question 1

A bond with a face value of $1,000 can be converted into 33 shares of stock.What is the conversion value if the stock is selling for $29.80 a share?

Accepted Answer

The conversion value is the current market value of the shares received by converting the bond.

33 shares of stock at $29.80 per share = 33 x $29.80 = $983.40

Thus, the conversion value is $983.40.

Question 2

A convertible bond is selling for $1,222.70.It has 10 years to maturity,a $1,000 face value,a coupon rate of 10 percent,and semiannual interest payments.Similar non-convertible bonds are priced to yield 4 percent per six months.The conversion ratio is 40.The stock currently sells for $30.13 a share.Calculate the convertible bond's option value.

Accepted Answer

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Question 3

The holders of Mikayla Corporation's bond with a face value of $1,000 can exchange that bond for 30 shares of stock.What is the conversion price if the stock is selling for $28.20 a share?

Accepted Answer

The conversion price is calculated by dividing the face value of the bond by the number of shares it can be converted into: $1,000 / 30 = $33.33.

Question 4

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?

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.

Question 5

A bond with a face value of $1,000 can be exchanged for 35 shares of stock with a current market price of $22 per share.What would the conversion ratio and conversion price be if the bond's issuer declared a stock split of 3-for-1?

Accepted Answer

Initially, the conversion ratio is 35/1000 = 0.035
After the 3-for-1 stock split, the number of shares received for each bond is 35*3 = 105
The new conversion ratio is 105/1000 = 0.105
The new conversion price is the market price divided by the new conversion ratio: $22/0.105 = $209.52 rounded to $9.52. Therefore, the correct answer is (B).

Question 6

Explain how a noncallable convertible bond's value is determined.

Accepted Answer

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Question 7

SBX bonds have a face value of $1,000 and can be exchanged for 20 shares of stock.Assume SBX declares a 3-for-1 stock split.What conversion price will be needed following the stock split for the conversion value and the straight bond value to be equal assuming the bond continually sells at par?

Accepted Answer

Before the stock split, the conversion rate is 20 shares per bond, so the conversion price is $50 ($1,000 / 20 shares). After the stock split, the conversion rate becomes 60 shares per bond (3-for-1 split multiplied by the original 20 shares per bond), so the new conversion price is $16.67 ($1,000 / 60 shares). To ensure that the conversion value and the straight bond value are equal after the split, the straight bond value must also be $1,000 / 60 shares, which is $16.67. Therefore, the conversion price needed for equality is $16.67. Choice A is correct.

Question 8

Aztec's convertible bonds each have a face value of $1,000 and a market value of $1,041.25.Each bond can be exchanged 25 shares of stock.The stock is selling for $41.54 a share.The straight bond value is $1,010.What is the option value per bond?

Accepted Answer

The option value per bond is calculated by subtracting the straight bond value from the market value of the convertible bond. Thus, $1,041.25 - $1,010 = $31.25.

Question 9

The holders of Mikayla Corporation's bonds with a face value of $1,000 each can exchange a bond for 20 shares of stock.The stock is selling for $49.40 a share.What is the conversion premium?

Accepted Answer

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Question 10

Assume a bond had a conversion price of $40 and a conversion ratio of 25.What would be the conversion ratio and conversion price if the bond issuer declared a stock split of 4-for-1?

Accepted Answer

If there is a 4-for-1 stock split, the number of shares increases by a factor of 4 and the stock price decreases by a factor of 4. Therefore, the new conversion price would be $40/4 = $10 and the new conversion ratio would be 25 x 4 = 100. Choice B matches these values.

Question 11

The holders of Xenron Corporation's bonds with a face value of $1,000 can exchange each of those bonds for 35 shares of stock.The stock is selling for $22 a share.What is the conversion price?

Accepted Answer

The conversion price is the price at which bondholders can convert their bonds into shares of stock.

To find the conversion price, we need to divide the face value of the bond by the number of shares of stock that can be exchanged for each bond.

$1,000 face value / 35 shares of stock = $28.57 conversion price

Therefore, the correct answer is B) $28.57.

Question 12

Diamond Drill has 150,000 shares of stock outstanding at a market price of $46 a share.The holder of a $1,000 face value bond can exchange the bond at any time for 25 shares of stock.What is the conversion price?

Accepted Answer

The conversion price is calculated by dividing the face value of the bond by the number of shares for which it can be exchanged. Thus, $1,000 / 25 shares = $40 per share.

Question 13

Cooper Industries has 400,000 shares of stock outstanding with a market price of $32 a share.The firm also has 10,000 bonds outstanding with a face value of $1,000 and a conversion price of $40.The bonds mature tomorrow.You currently own 25,000 shares of this stock and no bonds.What percent ownership in the firm should you expect to have after tomorrow?

Accepted Answer

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Question 14

Looper Industries bonds have a face value of $1,000 and can be exchanged for 30 shares of stock.The stock is selling for $35 a share.Looper has an outstanding call option on the bonds at $1,040.If the bonds are called,the holders must either convert or surrender their bonds.What should be the current market value of one of these bonds if the option premium per bond is $15? Assume the bond coupon rate equals the market rate of interest at time of call.

Accepted Answer

The current market value of the bond should be the greater of the conversion value or the call price plus the option premium. The conversion value is 30 shares * $35/share = $1,050. The call price is $1,040, and adding the option premium of $15 gives $1,055. Since $1,050 (conversion value) is less than $1,055 (call price plus option premium), the correct value is $1,055. However, there's a slight mistake in my calculation: the correct approach should compare the conversion value directly to the call price without adding the option premium to the call price. The correct market value is the higher of the conversion value ($1,050) or the call price ($1,040), which is $1,050, plus the option premium of $15, totaling $1,065.

Question 15

A convertible bond is valued at $1,062,has a conversion ratio of 25,and an option premium of $3.What is the conversion value if the straight bond value is equal to the bond's par value?

Accepted Answer

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Question 16

A convertible bond is selling for $967,matures in 15 years,has a $1,000 face value,pays interest semiannually,and has a coupon rate of 8 percent.Similar non-convertible bonds are priced to yield 4.25 percent per six months.The conversion ratio is 20.The stock currently sells for $47.50 a share.Calculate the convertible bond's option value.

Accepted Answer

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Question 17

Assume Jamestown Markets has 500 shares of stock and 100 bonds outstanding.The bonds have a face value of $1,000,are convertible into 5 shares of newly issued common stock,and mature today.What is the value of this firm to its shareholders if the total value of the firm is $184,500? What if the value is $225,000?

Accepted Answer

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Question 18

A convertible bond matures in 15 years,pays annual coupons,and has a coupon rate of 8 percent.The face value is $1,000 and the conversion ratio is 40.The stock currently sells for $22.80 a share.Similar nonconvertible bonds are priced to yield 9 percent.What is the minimal value of the convertible bond?

Accepted Answer

First, calculate the annual coupon payment: 0.08 x $1,000 = $80.
Then, calculate the conversion price: $1,000/40 = $25.
Next, we need to determine whether it is more valuable to hold the convertible bond or a similar nonconvertible bond. To do this, we need to calculate the yield to maturity of the convertible bond. We can use trial and error to approximate the YTM. For example, if we assume a YTM of 8%, the bond would be worth:
($80/1.08) + ($80/1.08^2) + ... + ($80/1.08^15) + $1,000/1.08^15 = $919.39
Since similar nonconvertible bonds are priced to yield 9%, the convertible bond would be more valuable if its YTM were less than 9%. If we repeat our calculation using a YTM of 7%, we get a value of $955.28, which is still less than the minimum value of a similar nonconvertible bond ($1,000). Therefore, the minimal value of the convertible bond is $919.39.

Question 19

Identify five factors that help determine the value of a warrant above its lower limit.

Accepted Answer

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Question 20

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?

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.

Quiz 24: Warrants and Convertibles