Dealing with Warrants, Convertibles and other Equity Securities in Valuation
Basic Proposition: When the value of all equity in a firm is estimated, it is generally divided by the number of shares outstanding to arrive at the value of equity per share. This is appropriate if there are no other claims on equity. When such claims exist, they have to be subtracted out before dividing by the number of shares outstanding.
Steps Involved:
Step 1: Value the firm, using discounted cash flow or other valuation models.
Step 2: Subtract out the value of the outstanding debt to arrive at the value of equity. Alternatively, skip step 1 and estimate the of equity directly.
Step 3: Subtract out the market value (or estimated market value) of other equity claims:
Value of Warrants = Market Price per Warrant * Number of Warrants : Alternatively estimate the value using OPM
Value of Conversion Option = Market Value of Convertible Bonds - Value of Straight Debt Portion of Convertible Bonds
Step 4: Divide the remaining value of equity by the number of shares outstanding to get value per share.
An Example: Valuing Sterling Software
Step 1: Value the firm
Approach used: Three Stage FCFE Model
Inputs used
High Growth | Transition Phase | Stable Phase | |
Length | 5 years | 3 years | Forever |
Growth Rate | 20% | Linear drop | 6% |
Cap Ex/Depreciation | 2.00 | 2.00 | 1.00 |
Working Capital | 15% of Revenues | 15% of Revenues | 15% of Revenues |
Beta | 1.50 | Linear drop | 1.10 |
Debt Ratio | Current (See below) | Current | Current |
Current Debt Ratio Calculation
Convertible Debt has market value of $ 175 million; face value of $ 115 million; coupon rate of 5.75%; expires in 8 years;
Bond Rating is A-; Interest rate on comparable debt = 8.50%;
Coupon on Convertible Debt = .0575 * 115 million = $ 6.6125 million
Value of Straight Debt Portion of Convertible Debt = $ 6.6125 (PV of Annuity,7.5%,8 years) + $ 115 million/1.075^{8} = $ 103.21 million
Value of Conversion Option in Debt = Market Value of Convertible Debt - Straight Debt Portion = $ 175 - $ 103 = $ 72 million :Equity
Value of Warrants = Number of warrants * Warrant Price = 1.8 million warrants * $ 30 = $ 54 million
Total Market Value of Equity = ($ 56 * 25.50 million shares) + $ 72 + $ 54 = $ 1554 million
Value of Debt = $ 103 million
Debt Ratio = $ 103/($103 + $ 1554) = 6.22%
Value of Equity
Value of Equity from Three-Stage FCFE Model = $2,036 million
- Value of Equity in Convertible Debt = $ 72 million
- Value of Equity in Warrants = $ 54 million
Value of Equity in Common Stock = $ 1,910 million
/ Number of Shares outstanding = 25.50 million shares
Value per Share = $ 74.90