9-convertibles

Convertible Bonds

• Convertible bonds (CBs) are securities that can be converted into a specified number of shares of stock.

Value of Convertible Bonds

• Gives the holder the option to exchange the bond for shares.

• Example: Oceandoor raised $300 million by issuing convertible subordinated debentures at 6.75% due in 2025.

  • Stock price on issue date: $22.625

  • Face value: $1000

  • Semi-annual interest payment: $33.75 (6.75/2)

  • Conversion ratio: 23.53 shares per bond (calculated using face value).

  • Conversion price: $42.50, leading to a conversion premium of 87.8% over the stock price.

  • In Korea, a refix clause may adjust conversion prices if stock prices drop.

Valuing Convertible Bonds

• Three components to the value of a convertible:

  • Straight bond value

  • Conversion value

  • Option value

Straight Bond Value

• Present value of bond payments under the assumption that the bond is never converted.

• For Oceandoor:

  • Straight bond value = $603.23 + $285.06 = $888.29

Conversion Value

• The worth of the bonds upon immediate conversion into common stock at current prices.

• For Oceandoor, current conversion value = 23.53 x $22.625 = $532.37

Option Value

• Represents the additional value derived from the flexibility of converting at a future date, which can be advantageous depending on stock price movement.

• Convertible bondholders benefit from having the option to convert later rather than immediately.

Why Corporations Issue Convertible Bonds - Myths

• Myth: Convertible bonds offer a free lunch.

  • Stock price drops, and conversion does not occur, enabling lower interest payments compared to straight debt.

  • Stock price rises, conversion occurs, and companies effectively sell stock at a higher price.

Fair Comparison: Firms Under Different Conditions

• Firms performing poorly: Convertible bonds result in no conversion.

• Firms performing well: Conversion leads to higher costs due to dilution.

• Cost Comparison:

  • Less expensive (CBs vs. straight bonds) due to lower interest rates.

  • Initial equity sold at inflated prices in conversion.

Conclusions on Myths

• Modigliani and Miller reasoning:

  • No taxes and no market imperfections imply consistent firm value regardless of issuing equity, debt, or convertible debt.

Reality of Issuing Convertibles

1. Reason #1 - Matching Cash Flows:

   • Reliability in cash flow management for young, risky firms.

   • Lower initial interest rates compared to straight bonds.

   • Convertible bonds convert when firms succeed.

2. Reason #2 - Asymmetric Information about Risk:

   • Uncertainty in firm risk leads to fair pricing despite different potential company risks.

   • High-risk company: lower straight bond value, high option value.

   • Low-risk company: higher straight bond value, lower option value.

3. Reason #3 - Minimizing Agency Costs of Debt:

   • Convertible bonds help avoid excessive risk-taking behavior.

   • Safe vs. risky strategies illustrated:

     • Safe strategy payoff: $80 with 90% chance, yielding expected value of $72.

     • Risky strategy payoff: $100 with 70% chance, yielding expected value of $70.

   • Expected payoffs show how convertible bonds can influence equityholders' decision-making towards less risky projects.

Example (Continued)

• Comparisons involving face values and conversion into equity:

  • Safe strategy for bondholders if firm value at the end is $80.

  • Risky strategy benefits will depend on bondholder conversion decisions based on expected firm values.

Convertible Bonds Formula Sheet

1. Conversion RatioFormula:[ \text{Conversion Ratio} = \frac{\text{Face Value}}{\text{Conversion Price}} ]Example:[ \text{Conversion Ratio} = \frac{1000}{42.50} = 23.53 \text{ shares per bond} ]

2. Straight Bond ValueFormula:[ \text{Straight Bond Value} = \text{Present Value of Bond Payments} ]Example (Oceandoor):[ \text{Straight Bond Value} = 603.23 + 285.06 = 888.29 ]

3. Conversion ValueFormula:[ \text{Conversion Value} = \text{Conversion Ratio} \times \text{Current Stock Price} ]Example (Oceandoor):[ \text{Current Conversion Value} = 23.53 \times 22.625 = 532.37 ]

4. Option ValueDefinition:Represents the potential additional value from converting the bond at a future date.

5. Expected Payoff for Safe StrategyFormula:[ \text{Expected Value} = \text{Payoff} \times \text{Probability} ]Example (Safe Strategy):[ \text{Expected Value} = 80 \times 0.9 = 72 ]

6. Expected Payoff for Risky StrategyFormula:[ \text{Expected Value} = \text{Payoff} \times \text{Probability} ]Example (Risky Strategy):[ \text{Expected Value} = 100 \times 0.7 = 70 ]

Key Points

• Use these formulas to assess the value and decisions surrounding convertible bonds effectively.