33:390:400 Lecture Notes - Lecture 9: Debenture, Agency Cost

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Chapter 24: Convertible Bonds
Convertible Bond: Gives the bond holder the right to exchange it for a given # shares of stock at
any time up to and including the maturity date of the bond
Conversion Ratio: The number of shares received per bond
Conversion Price: (Face Value of the Bond ~ usually $1,000) / (Conversion Ratio)
Conversion Value: (Conversion Ratio) x (Stock issue price)
Conversion Premium: [ (Conversion Price / Actual C/S Price) 1 ] = x%
Ex: 11/01/06 - Company raises $1mm in 6.75% convertible subordinated debenture due in 2022.
- Stock price on issue date was $22.625
Face Value of bond: $1,000
Promised $33.75 interest every 6 months; 6.75% / 2 = 3.375%
6-month interest rate on straight A rated bonds was 4%
Conversion Ratio: 23.53 shares per bond
Conversion Price: ($1,000) / (23.53 shares per bond) = $42.50
Conversion Value: (23.53 shares per bond) x ($22.625) = $532.37
- This is what the bonds would be worth if immediately converted into C/S
Conversion Premium: [ ($42.50/$22.625) 1] = 87.8%
- The conversion price is 87.8% higher than the actual C/S price
The Value of Convertible Bonds
3 components to value a convertible: Straight bond value, Conversion value, option value
1. Straight Bond Value
- What the convertible bonds would sell for if they couldn’t be converted into C/S
- The PV of bond payments assuming the bond is never converted
Straight Bond Value = Discounting semiannual coupon payment and principal @ 4%
- To the 32nd b/c 16 years (2006 2022), so 32 semiannual payments
The straight bond value is a minimum value. The price of the convertible bonds could not go
lower than the straight bond value
- Straight Bond alue depends on firm value:
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2. Conversion Value
- What bonds would be worth today if they were immediately converted into C/S @ P0
- A convertible bond cannot sell for less than its conversion value
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Document Summary

Promised . 75 interest every 6 months; 6. 75% / 2 = 3. 375% 6-month interest rate on straight a rated bonds was 4% Convertible bond: gives the bond holder the right to exchange it for a given # shares of stock at any time up to and including the maturity date of the bond. Conversion ratio: the number of shares received per bond. Conversion price: (face value of the bond ~ usually ,000) / (conversion ratio) Conversion value: (conversion ratio) x (stock issue price) Conversion premium: [ (conversion price / actual c/s price) 1 ] = x% Ex: 11/01/06 - company raises mm in 6. 75% convertible subordinated debenture due in 2022. 3 components to value a convertible: straight bond value, conversion value, option value: straight bond value. Conversion price: (,000) / (23. 53 shares per bond) = . 50. Conversion value: (23. 53 shares per bond) x (. 625) = . 37. Conversion premium: [ (. 50/. 625) 1] = 87. 8%

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