Podcast
Questions and Answers
How does a decrease in a company's stock price typically influence a convertible debtholder's decision regarding conversion?
How does a decrease in a company's stock price typically influence a convertible debtholder's decision regarding conversion?
- It increases the likelihood of conversion to capitalize on potential future stock growth.
- It decreases the likelihood of conversion, making it more favorable to hold the bond for its fixed income. (correct)
- It mandates immediate conversion to mitigate potential losses from further stock decline.
- It has no impact on the conversion decision, as bondholders are primarily concerned with interest payments.
What is the economic rationale behind an issuer including a call provision in a convertible bond?
What is the economic rationale behind an issuer including a call provision in a convertible bond?
- To provide bondholders with the option to redeem the bond at a premium, enhancing its attractiveness.
- To signal the issuer's confidence in its long-term financial stability to the market.
- To comply with regulatory requirements mandating issuer control over debt instruments.
- To protect the issuer from excessively high conversion values by forcing debtholders to convert to equity. (correct)
Which of the following best describes how to interpret the premium to parity for a convertible bond?
Which of the following best describes how to interpret the premium to parity for a convertible bond?
- The amount by which the conversion value of the bond exceeds its face value, indicating the profitability of immediate conversion.
- The degree to which the convertible bond's market price exceeds the value of the shares received upon conversion, signaling willingness to pay for the embedded option. (correct)
- The additional return an investor receives for holding the convertible bond to maturity instead of converting it.
- The percentage by which the bond's coupon rate exceeds the yield to maturity of a comparable straight bond.
What economic factor primarily determines the bond floor of a convertible bond?
What economic factor primarily determines the bond floor of a convertible bond?
How is the investment premium of a convertible bond best interpreted?
How is the investment premium of a convertible bond best interpreted?
In the context of convertible bonds, what does the 'fugit' metric primarily represent?
In the context of convertible bonds, what does the 'fugit' metric primarily represent?
If a convertible bond has a higher yield than the dividend yield of the underlying stock, what does this 'yield advantage' generally imply for an investor?
If a convertible bond has a higher yield than the dividend yield of the underlying stock, what does this 'yield advantage' generally imply for an investor?
When a company issues a convertible bond with a yield to maturity (YTM) significantly higher than its coupon rate, what implication does this have for the bond's initial market price?
When a company issues a convertible bond with a yield to maturity (YTM) significantly higher than its coupon rate, what implication does this have for the bond's initial market price?
XYZ Company issues convertible bonds with a face value of $1,000 and a conversion price of $50. If the company's stock is trading at $42, calculate the premium to parity if the bond is trading at $1,000.
XYZ Company issues convertible bonds with a face value of $1,000 and a conversion price of $50. If the company's stock is trading at $42, calculate the premium to parity if the bond is trading at $1,000.
A company issues a convertible bond with a 5% coupon and a 10-year maturity. Comparable straight debt yields 8%. How is the straight bond value of the convertible calculated, and what does it represent?
A company issues a convertible bond with a 5% coupon and a 10-year maturity. Comparable straight debt yields 8%. How is the straight bond value of the convertible calculated, and what does it represent?
When should an investor ideally exercise the conversion option in a convertible bond, assuming rational economic behavior?
When should an investor ideally exercise the conversion option in a convertible bond, assuming rational economic behavior?
How does the presence of a callable provision in a convertible bond alter the payoff structure for the issuer, compared to a non-callable convertible bond?
How does the presence of a callable provision in a convertible bond alter the payoff structure for the issuer, compared to a non-callable convertible bond?
In the formal representation of convertible debt value, what does the term 'alpha (α)' signify, and how does it affect the conversion decision?
In the formal representation of convertible debt value, what does the term 'alpha (α)' signify, and how does it affect the conversion decision?
What is the economic significance of the term 'F/α' in the context of convertible debt valuation?
What is the economic significance of the term 'F/α' in the context of convertible debt valuation?
The formula CD = Face Value / (1 + rf)^T - Any Default + Value of Call is used to calculate Convertible Debt Value. What real world element effects the 'Any Default' variable?
The formula CD = Face Value / (1 + rf)^T - Any Default + Value of Call is used to calculate Convertible Debt Value. What real world element effects the 'Any Default' variable?
In a scenario where a firm's value is lower than the face value of its convertible debt, what is the likely outcome for the value distribution among stakeholders?
In a scenario where a firm's value is lower than the face value of its convertible debt, what is the likely outcome for the value distribution among stakeholders?
Firm with V = 50 and 20m shares outstanding. Firm has 5 convertible bonds with F = 6, 2-year maturity, each of which can be converted into 2m shares at maturity. How to calculate Alpha?
Firm with V = 50 and 20m shares outstanding. Firm has 5 convertible bonds with F = 6, 2-year maturity, each of which can be converted into 2m shares at maturity. How to calculate Alpha?
Convertible bonds were issued with the following terms: V = 50, 20m shares outstanding, 5 convertible bonds, F = 6, 2-year maturity, each bond convertible into 2m shares. Assume rₓ = 5% and σ = 0.3. Aggregate first: F = 30 and α = (5 × 2)/(5 × 2 + 20) = 1/3. What is the difference due to conversion option?
Convertible bonds were issued with the following terms: V = 50, 20m shares outstanding, 5 convertible bonds, F = 6, 2-year maturity, each bond convertible into 2m shares. Assume rₓ = 5% and σ = 0.3. Aggregate first: F = 30 and α = (5 × 2)/(5 × 2 + 20) = 1/3. What is the difference due to conversion option?
In the context of Amazon's 1999 convertible bond issue, what strategic benefit did Amazon derive if its share price remained below the conversion price?
In the context of Amazon's 1999 convertible bond issue, what strategic benefit did Amazon derive if its share price remained below the conversion price?
According to the 'free lunch' story, if a firm's share price increases and conversion occurs, what is the financial benefit to the issuing firm such as Amazon?
According to the 'free lunch' story, if a firm's share price increases and conversion occurs, what is the financial benefit to the issuing firm such as Amazon?
How does the 'expensive lunch story' critique the perceived benefits of issuing convertible debt?
How does the 'expensive lunch story' critique the perceived benefits of issuing convertible debt?
According to the Amazon case study, if the firm's stock price decreases and conversion does not occur, how does the convertible debt compare to straight debt and equity financing?
According to the Amazon case study, if the firm's stock price decreases and conversion does not occur, how does the convertible debt compare to straight debt and equity financing?
What was the ultimate outcome of Amazon's 1999 convertible bond offering, specifically regarding the conversion and redemption of the bonds?
What was the ultimate outcome of Amazon's 1999 convertible bond offering, specifically regarding the conversion and redemption of the bonds?
Using a Binomial Model, will calculate Stock Price for Three different Periods. What are the important steps?
Using a Binomial Model, will calculate Stock Price for Three different Periods. What are the important steps?
How does the presence of a call feature in a convertible bond impact the decision-making process within a binomial valuation model?
How does the presence of a call feature in a convertible bond impact the decision-making process within a binomial valuation model?
Under what conditions would an issuer optimally call a convertible bond?
Under what conditions would an issuer optimally call a convertible bond?
In a binomial valuation model for callable convertible bonds with varying interest rates, how are spot rates typically determined across the different states of the world represented by the binomial tree?
In a binomial valuation model for callable convertible bonds with varying interest rates, how are spot rates typically determined across the different states of the world represented by the binomial tree?
How do convertible bonds mitigate the agency costs associated with debt financing?
How do convertible bonds mitigate the agency costs associated with debt financing?
What best describes the scenario in which a convertible bond's option value is maximized?
What best describes the scenario in which a convertible bond's option value is maximized?
How does an increasing conversion ratio impact the conversion value line on a convertible bond graph?
How does an increasing conversion ratio impact the conversion value line on a convertible bond graph?
From the bond issuers perspective, why is callable provision more beneficial?
From the bond issuers perspective, why is callable provision more beneficial?
What happens when the stock is below the break-even point with convertible bonds?
What happens when the stock is below the break-even point with convertible bonds?
What happens to equity holders, if the firm is lower than the Face Value of Convertible debt?
What happens to equity holders, if the firm is lower than the Face Value of Convertible debt?
What happens when Stock Price Increases with convertible bonds?
What happens when Stock Price Increases with convertible bonds?
Which situation makes the convertible debt cheaper - Straight Debt or Equity?
Which situation makes the convertible debt cheaper - Straight Debt or Equity?
What is the interpretation of high risk and low risk in terms of straight value vs option value?
What is the interpretation of high risk and low risk in terms of straight value vs option value?
Convertible Debt Value equates to which of the following options?
Convertible Debt Value equates to which of the following options?
How does the potential for equity dilution impact a company's decision to issue convertible bonds, particularly when the firm's management anticipates substantial future growth?
How does the potential for equity dilution impact a company's decision to issue convertible bonds, particularly when the firm's management anticipates substantial future growth?
What implications does a 'hard call' provision in a convertible bond indenture have for investors during periods of high stock volatility?
What implications does a 'hard call' provision in a convertible bond indenture have for investors during periods of high stock volatility?
Under what scenario would a company be most inclined to force conversion of its convertible bonds using a call provision?
Under what scenario would a company be most inclined to force conversion of its convertible bonds using a call provision?
If a company's stock price falls significantly below the convertible bond's conversion price, how is the value of the convertible bond primarily determined?
If a company's stock price falls significantly below the convertible bond's conversion price, how is the value of the convertible bond primarily determined?
How might a putable provision in a convertible bond impact the firm's strategic financial planning, especially concerning potential refinancing activities?
How might a putable provision in a convertible bond impact the firm's strategic financial planning, especially concerning potential refinancing activities?
How does the credit rating of the issuing company typically influence the investment premium of a convertible bond?
How does the credit rating of the issuing company typically influence the investment premium of a convertible bond?
What is the economic rationale behind an investor accepting a lower coupon rate on a convertible bond compared to a similar straight bond?
What is the economic rationale behind an investor accepting a lower coupon rate on a convertible bond compared to a similar straight bond?
XYZ Corp. issues convertible bonds with a conversion ratio that increases over time. How does this feature likely impact the bond's initial pricing and its appeal to different types of investors?
XYZ Corp. issues convertible bonds with a conversion ratio that increases over time. How does this feature likely impact the bond's initial pricing and its appeal to different types of investors?
In the context of convertible bonds, how does the volatility of the underlying stock most directly affect the value of the conversion option?
In the context of convertible bonds, how does the volatility of the underlying stock most directly affect the value of the conversion option?
How can the inclusion of a 'reset provision' (which adjusts the conversion price based on the underlying stock's performance) in a convertible bond affect the bond's attractiveness to potential investors?
How can the inclusion of a 'reset provision' (which adjusts the conversion price based on the underlying stock's performance) in a convertible bond affect the bond's attractiveness to potential investors?
How does the 'fugit' metric impact a portfolio manager's decision-making process when managing a fund that invests in convertible bonds?
How does the 'fugit' metric impact a portfolio manager's decision-making process when managing a fund that invests in convertible bonds?
In what situation would the yield advantage of a convertible bond over the dividend yield of the underlying stock be most beneficial to an investor?
In what situation would the yield advantage of a convertible bond over the dividend yield of the underlying stock be most beneficial to an investor?
A company issues convertible bonds with a significantly higher yield to maturity (YTM) than its coupon rate. What implications does this spread have for valuing the conversion option embedded in the bond?
A company issues convertible bonds with a significantly higher yield to maturity (YTM) than its coupon rate. What implications does this spread have for valuing the conversion option embedded in the bond?
In the context of convertible bonds, what is the primary significance of the 'bond floor,' and how does it influence investor behavior during market downturns?
In the context of convertible bonds, what is the primary significance of the 'bond floor,' and how does it influence investor behavior during market downturns?
When analyzing convertible bonds, how does a higher premium to parity generally impact an investor's decision regarding whether to purchase the convertible bond or the underlying stock?
When analyzing convertible bonds, how does a higher premium to parity generally impact an investor's decision regarding whether to purchase the convertible bond or the underlying stock?
In the valuation of convertible debt, how does incorporating a stochastic interest rate model, compared to a static rate, affect the accuracy of pricing callable convertible bonds, especially in volatile markets?
In the valuation of convertible debt, how does incorporating a stochastic interest rate model, compared to a static rate, affect the accuracy of pricing callable convertible bonds, especially in volatile markets?
How does including assumptions about future dividend policy changes affect valuation outcomes in a binomial model for convertible bonds?
How does including assumptions about future dividend policy changes affect valuation outcomes in a binomial model for convertible bonds?
If the value of a firm is lower than the face value of its convertible debt, what is the likely outcome for the distribution of value among stakeholders, considering liquidation scenarios?
If the value of a firm is lower than the face value of its convertible debt, what is the likely outcome for the distribution of value among stakeholders, considering liquidation scenarios?
A firm has V = 60 and 30 million shares outstanding. It also has 10 convertible bonds with F = 5, 2-year maturity, each convertible into 3 million shares. Calculate alpha (α), representing the fraction of the firm owned by bondholders if they convert.
A firm has V = 60 and 30 million shares outstanding. It also has 10 convertible bonds with F = 5, 2-year maturity, each convertible into 3 million shares. Calculate alpha (α), representing the fraction of the firm owned by bondholders if they convert.
Convertible bonds issued with these terms: V = 70, 40m shares outstanding, 10 convertible bonds, F = 8, 2-year maturity, each bond convertible into 4m shares. Given rₓ = 6% and σ = 0.4, what would increasing volatility to σ = 0.5 likely do to the difference due to the conversion option?
Convertible bonds issued with these terms: V = 70, 40m shares outstanding, 10 convertible bonds, F = 8, 2-year maturity, each bond convertible into 4m shares. Given rₓ = 6% and σ = 0.4, what would increasing volatility to σ = 0.5 likely do to the difference due to the conversion option?
According to the details from Amazon's 1999 convertible bond issuance, how did the conversion price being set 27% higher than the current share price strategically benefit Amazon at the time?
According to the details from Amazon's 1999 convertible bond issuance, how did the conversion price being set 27% higher than the current share price strategically benefit Amazon at the time?
Considering the 'expensive lunch story' critique, what is the primary argument against the perceived dual benefit of convertible debt (cheap financing if the stock price stays low, premium equity issuance if it rises)?
Considering the 'expensive lunch story' critique, what is the primary argument against the perceived dual benefit of convertible debt (cheap financing if the stock price stays low, premium equity issuance if it rises)?
In a scenario valuing Amazon's convertible bonds using a binomial model, how would a decrease in the risk-free rate affect the call strategy of the issuer and the overall value of the convertible bond?
In a scenario valuing Amazon's convertible bonds using a binomial model, how would a decrease in the risk-free rate affect the call strategy of the issuer and the overall value of the convertible bond?
According to the Amazon case study, what was the financial impact of Amazon redeeming a portion of its 1999 convertible bonds for cash rather than converting them into shares?
According to the Amazon case study, what was the financial impact of Amazon redeeming a portion of its 1999 convertible bonds for cash rather than converting them into shares?
In a three-period binomial model used to value a convertible bond, how does the introduction of a call feature with a call price that varies over each period affect the early exercise decision at each node of the binomial tree?
In a three-period binomial model used to value a convertible bond, how does the introduction of a call feature with a call price that varies over each period affect the early exercise decision at each node of the binomial tree?
In a binomial valuation model for convertible bonds, how does the correlation between the movements of the underlying stock price and the credit spread of the issuer affect the modeled bond value, especially when considering default risk?
In a binomial valuation model for convertible bonds, how does the correlation between the movements of the underlying stock price and the credit spread of the issuer affect the modeled bond value, especially when considering default risk?
Given that convertible bonds typically offer a lower coupon rate than straight debt, how might their issuance affect a company's financial ratios and overall creditworthiness, especially if the expected stock appreciation does not materialize?
Given that convertible bonds typically offer a lower coupon rate than straight debt, how might their issuance affect a company's financial ratios and overall creditworthiness, especially if the expected stock appreciation does not materialize?
Suppose a company has the option to finance a project with either straight debt or convertible bonds. Under what conditions would issuing convertible bonds be the unambiguously superior choice from the perspective of minimizing agency costs related to risk-shifting?
Suppose a company has the option to finance a project with either straight debt or convertible bonds. Under what conditions would issuing convertible bonds be the unambiguously superior choice from the perspective of minimizing agency costs related to risk-shifting?
In the context of convertible bonds, what scenario would create the greatest possible divergence between the theoretical model price and the actual market price, thus presenting a potential arbitrage opportunity?
In the context of convertible bonds, what scenario would create the greatest possible divergence between the theoretical model price and the actual market price, thus presenting a potential arbitrage opportunity?
How does an increase in the conversion ratio of a convertible bond most directly impact the economic alignment between bondholders and equity holders?
How does an increase in the conversion ratio of a convertible bond most directly impact the economic alignment between bondholders and equity holders?
In which of the following scenarios is issuing a callable convertible bond most advantageous for the issuing company?
In which of the following scenarios is issuing a callable convertible bond most advantageous for the issuing company?
During the term of a convertible bond, under what market circumstances would the issuer expect the option value to be maximized?
During the term of a convertible bond, under what market circumstances would the issuer expect the option value to be maximized?
If a company anticipates financial difficulty during the term of a convertible bond, during which of the following scenarios are equity holders at the greatest disadvantage?
If a company anticipates financial difficulty during the term of a convertible bond, during which of the following scenarios are equity holders at the greatest disadvantage?
Flashcards
Convertible Debt
Convertible Debt
Debt that can be exchanged for a predetermined number of the issuer's shares.
Conversion Ratio
Conversion Ratio
The number of shares received when converting one bond.
Conversion Price
Conversion Price
The implied cost to 'buy' a share via bond conversion.
Parity (Conversion Value)
Parity (Conversion Value)
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Premium to Parity
Premium to Parity
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Bond Floor
Bond Floor
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Investment Premium
Investment Premium
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Fugit (Years)
Fugit (Years)
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Yield Advantage (%)
Yield Advantage (%)
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Conversion Ratio
Conversion Ratio
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Conversion Value/Parity
Conversion Value/Parity
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Premium to Parity
Premium to Parity
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Straight Bond Value
Straight Bond Value
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Investment Premium
Investment Premium
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Bond Floor
Bond Floor
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Break-Even Point
Break-Even Point
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Callable Convertible Bond
Callable Convertible Bond
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Step 1: Binomial Model
Step 1: Binomial Model
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Conversion Ratio
Conversion Ratio
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Convertible Debt Value
Convertible Debt Value
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Alpha (α)
Alpha (α)
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(Alpha x Value) > Face Value
(Alpha x Value) > Face Value
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F/a
F/a
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If Stock Price Increases
If Stock Price Increases
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If Stock Price Decreases
If Stock Price Decreases
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Convertible Value
Convertible Value
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Minimum Convertible Value
Minimum Convertible Value
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Hard Call
Hard Call
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Callable Provision
Callable Provision
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Shareholders increase risk
Shareholders increase risk
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Study Notes
- Convertible debt allows debtholders the option to convert their debt into equity, but not the obligation.
- Conversion to equity happens when it is financially advantageous for the holder.
- Debtholders are more inclined to convert debt to equity as the stock price increases.
- Conversion to equity is less valuable as the stock price decreases, so holding the bond is more beneficial.
Features of Convertible Securities
- They can be converted into predetermined shares, with a conversion ratio determining the number of shares received upon conversion.
- Convertible securities have an embedded call option to buy the issuer's common stock.
- Bondholders convert to equity only when the stock price exceeds a predetermined price.
Callable and Putable Provisions
- Callable provision allows the issuer to call back the convertible bond if the conversion value is too high, forcing conversion to equity, benefitting the issuer.
- Putable provision enables bondholders to sell the convertible bond back to the issuer if conditions are unfavorable, increasing the market price of the bond due to the benefit to the bondholders.
Convertible Debt Terminology
Conversion Ratio
- Specifies the number of shares a bondholder receives upon converting one bond.
Conversion Price
- Represents the implied purchase price of the convertible in the bond's currency upon conversion.
- Calculated as Face Value / Conversion Ratio.
- For example, a face value of 1,000 with a conversion ratio of 81.6327 yields an implied purchase price of $12.25.
Parity or Conversion Value
- Indicates the true market value of converting the bond and is calculated as the value of shares one would hold if the bond was immediately converted.
- Shares valued at $15 with a conversion ratio of 81.6327 results in a conversion value of $1,224.49.
Bond Price
- The market price of the convertible bond reflects the demand and supply dynamics.
Premium to Parity
- How much a convertible bond investor is willing to pay for the convertible relative to the underlying shares.
- It informs the investor whether it is more profitable to buy the convertible bond and convert to shares, or to directly buy shares.
- Stock Price = $15, Conversion Ratio = 81.6327, Bond Price = $1,000 gives a premium to parity of -18.4%.
- Stock Price = $10, Conversion Ratio = 81.6327, Bond Price = $1,000 gives a premium to parity of 22.5%
Bond Floor
- Represents the present value of all cash flows embedded in the convertible bond, including future coupon payments and face value.
- The convertible bond's value is equivalent to the bond floor when the stock price is lower, as conversion is not exercised and allows bondholders to receive full face value and coupon payments at maturity.
Investment Premium
- Measures how much an investor is prepared to pay for the option embedded in the convertible.
- Calculated as (Price - Bond Floor) / Bond Floor.
Fugit
- The expected average life of the bond, derived from the pricing model's assumptions.
Yield Advantage
- The difference between the current yield on the convertible bond and the dividend yield on the stock.
- Example: A convertible bond at par with a 4% coupon and the underlying stock with a 1% dividend provides a 3% yield advantage.
Conversion Type
- Can be voluntary or mandatory, depending on the bond's structure.
Call Type
- Can be soft or hard, where a hard call allows the issuer to unconditionally call back the convertible.
XYZ Company Convertible Bond Example
Initial Conditions
- New issue convertible bond with a 5% coupon and 10 years to maturity.
- Comparable debt yields 8%.
- Stock price is $42, with a conversion price of $50 and a par face value of $1,000.
Calculations
- Conversion Ratio Calculation: Conversion Ratio = Face Value / Conversion Price = 1,000 / 50 = 20 shares per bond.
- Conversion Value or Parity Calculation: Conversion Value or Parity = Stock Price x Conversion Ratio = 42 x 20 = $840.
- Premium to Parity Calculation: Premium to Parity = (Bond Price - Conversion Value) / Conversion Value = (1,000 - 840) / 840 = 19.05%.
- Straight Bond Value Calculation: [50 (PVIFA₈%,₁₀) + 1000 (PVIF₈%,₁₀)] = $798.71.
- Investment Premium Calculation: Investment Premium = (Face Value - Straight Bond Value) / Straight Bond Value = (1,000 - 798.71) / 798.71 = 25.2%.
Excel Implications
- Conversion value changes with stock price fluctuations.
- The straight bond value remains constant.
- Conversion occurs when Conversion Value > Straight Bond Value (e.g., stock price at $40).
Callable Convertible Bond Effects
Issuer Perspective
- Issuers can prevent investors from capturing high value by adding a callable option, forcing conversion if the stock price exceeds a certain level (e.g., $44).
Bond Floor
- The minimum value of the convertible is the straight bond value when the stock price is below the break-even point.
- Conversion occurs when the stock price is above the breakeven point (between $39 and $40).
Valuation Insights
- Investors convert when stock price is higher than the breakeven point as conversion value exceeds straight bond value.
- Investors will not convert when stock price is lower than the breakeven point..
- Option value is highest just above the exercise price, decreasing when deep in the money or deep out of the money.
Formal Representation
Conversion Decision
- At debt maturity, holders can surrender for face value or convert to common stock.
- Convertible Debt Value = Debt + Call Option Value (Conversion Price).
Ownership Fraction
- a = m / (m + n), where m is the shares from convertible debt and n is the shares outstanding.
Conversion Condition
- Convert if (Alpha x Value) > Face Value.
- Not convert if (Alpha x Value) < Face Value.
Break-Even Point
- F/a, where F is the face value and a is alpha.
- CD = Face Value / (1 + rf)^T - Default Risk + Call Value.
Firm perspective
- If the firm value is lower than the face value, bondholders capture the value.
- If higher than breakeven (F/a), conversion occurs and CD value increases.
- Should the firm be liquidated, if the firm's value dips below the convertible debt's face value, then it is 0 for equity holders as debtholders get priority.
Example Valuation Scenario
Parameters
- Firm value (V) = 50, 20m shares outstanding.
- 5 convertible bonds, face value (F) = 6, 2-year maturity.
- Conversion into 2m shares at maturity.
- rₓ = 5%, σ = 0.3.
Aggregates
- F = 30, α = (5 × 2)/(5 × 2 + 20) = 1/3.
Valuation
- Without conversion: D = 30 − Put Value (V = 50, F = 30) = 29.4836.
- With conversion: D = 30 − Put Value(V = 50, F = 30) + (1/3) Call Value(V = 50, F = 90) = 30.0360.
- Difference due to conversion option = 0.5524.
Amazon Case Study
1999 Issuance
- $1.25 billion of 4.75% convertibles at 98% of par, due in Feb 2009.
- Convertible into 6.41 shares of stock.
- Conversion price: $156.01 ($1000 / 6.41).
- Market conversion value: $787.63 (6.41 × $122.86).
Strategic Decision
- Issue debt at 11% or convertibles at 4.75% with conversion value of $787.63.
Free Lunch Story
- Convertible cheaper if share price remains below $122.86.
- If share price increases above $122.86, conversion occurs at $156.01 per share.
- Issue equity at a higher price than the market price.
Expensive Lunch Story
- Convertible is more expensive than straight debt if the price increases because the firm issues shares at a discount with conversion.
- If the price decreases, the convertible is more expensive than issuing equity because they could have issued overpriced shares.
Amazon Valuation Analysis
- Straight debt value (4.75% coupon, 10 years, 11% interest): $632.
- Conversion option value: $980 – 632 = $348.
- Hence, for entire bond issue of $1.25 billion, Debt = $806m (64.5%) and Equity = $444m (35.5%).
2008 Payout
- $605 million in debt swapped for 7.8 million Amazon shares.
- $293 million redeemed in cash (all paid off in Sept 2008).
- The firm was selling for an average of $77.56 during that period.
- Conversion value = 6.41 × $77.56 = $497.19
Valuation of Convertible Debt - Binomial Model
Steps
Step 1
- Calculate Stock Prices For Each Period - using U and D Probability.
Step 2
- Calculate Conversion Value for Each Period - (Conversion Ratio x Share Price).
Step 3
- Determine Whether you will Convert or not (only convert when Conversion value is greater than Straight Bond Value).
- If you convert the Convertible Bond Value will be the Conversion Value.
- If you do not convert, the Convertible Bond Value will be the Straight Bond Value.
Step 4
- Calculate B(uuu) (Bond Value) - Don't forget to add on the coupon payment.
Binomial Valuation - Callable Convertible Bonds
- Forcing the holder to convert when the call price exceeds the convertible bond price.
Optimal Time to call Convertible Debt
- CV = conversion value
- CP = call price
- if CV < CP, don’t call
- If CV > CP, call and force conversion
Risk Synergy
- Shareholders have strong incentives to increase the risk of the company, which increases the upper potential for gains of shareholders, but reduces the value of straight debt.
- Suppose have 2 projects with different risks and cash flows:
- Safe project → 0.4 × 12.5m + 0.6 × 8m
- Risky project → 0.4 × 20m + 0.6 × 5m
With straight debt with promised payoff of 7m and equity holder receives the remainder
Safe project:
- Lender: (0.4 × 7) + (0.6 × 7) = 7m
- Equity: (0.4 × 5.5) + (0.6 × 1) = 2.8m
Risky project:
- Lender: (0.4 × 7) + (0.6 × 5) = 5.8m
- Equity: (0.4 × 13) + (0.6 × 0) = 5.2m
- Lender will be better of to invest in safer project.
- Equity holders will be better of to invest in risky project.
- Convertible Bond to resolve the agency costs.
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