Investment Valuation: Equity, Enterprise Value & Options
This paper works through a series of investment valuation problems spanning several core finance topics. It covers the calculation of equity value per share using EBITDA-based perpetuity models, the impact of equity options using both the straight subtraction method and the treasury stock approach, and enterprise value derivation using WACC and EBIT-based formulas. Additional problems address consolidated EBIT statements, minority equity stakes, firm valuation incorporating subsidiary assets, closed-end fund discount analysis, and the iterative effect of option pricing on per-share equity value. Together, these problems illustrate fundamental techniques used in corporate finance and equity valuation.
- Equity Value Per Share and the Effect of Options: Calculating equity per share with option adjustments
- Treasury Stock Approach to Option Valuation: Treasury stock method for option-adjusted share price
- Enterprise Value and EBIT Back-Calculation: Deriving EBIT from known enterprise value and WACC
- Consolidated Statements and Minority Equity Stakes: EBIT consolidation and minority stake valuation
- Firm Valuation with Subsidiary Assets: Valuing a firm with operating and subsidiary components
- Closed-End Fund Discount Analysis: Discount rate analysis for closed-end fund liquidation
- Iterative Option Pricing and Per-Share Equity Value: Iterative Black-Scholes option and share price feedback
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What makes this paper effective
- Each problem follows a clearly staged numerical sequence, making the logic of each valuation method easy to trace step by step.
- The paper covers a broad range of valuation contexts — from basic equity-per-share calculations to more advanced topics like minority stake discounts and iterative option pricing — demonstrating breadth of technique.
- Intermediate results are explicitly labeled and carried forward, which models good quantitative problem-solving discipline.
Key academic technique demonstrated
The paper demonstrates the application of perpetuity-based valuation models (using EBITDA, EBIT, and free cash flow) alongside the Black-Scholes framework for option pricing. Particularly notable is the treatment of equity options under two distinct methods — straight subtraction and the treasury stock approach — and the iterative feedback loop explored in Problem 8, where a revised share price changes the option value, which in turn changes the share price again.
Structure breakdown
The paper is organized as a numbered problem set. Problems 1–3 address per-share equity valuation and option adjustments. Problem 4 back-calculates EBIT from a known enterprise value using WACC. Problem 5 handles consolidated financials and minority stakes. Problem 6 values a firm with both operating and subsidiary assets. Problem 7 applies discounted cash flow logic to a closed-end fund. Problem 8 introduces the iterative complexity of option pricing, showing how per-share value and option value are mutually dependent.
Equity Value Per Share and the Effect of Options
The value of ABV's equity per share is calculated in several steps. First, the value of the operating assets is found by taking EBITDA, adjusting for the tax rate, the reinvestment rate, and the perpetual growth rate, then dividing by the cost of capital less the growth rate. This yields the present value of operating assets under a standard perpetuity-based valuation framework.
To this operating asset value, cash is added and debt is subtracted to arrive at the total value of equity. That figure is then divided by the number of shares outstanding (200 million) to produce a base equity value per share.
If equity options exist on the shares, those options must be subtracted from the share value. In this case, the value of the options is 50 × $5 = $250 million. Subtracting this from the equity value gives:
$799.90 − $250.00 = $549.90 million
Dividing by the number of shares outstanding:
$599.90 / 200 = $3.00 per share
Treasury Stock Approach to Option Valuation
With the treasury stock method, the first step is to calculate the exercise proceeds from the options:
6 × 50 = $300 million
The treasury stock value per share is then calculated as follows:
= (Value of Equity + Exercise Proceeds) / (Number of Shares + Number of Options)
= ($799.90 + $300) / (200 + 50) = $4.40 per share
Enterprise Value and EBIT Back-Calculation
To back-calculate EBIT from a known enterprise value, the enterprise value is first established. The market value of equity is $25 billion and the market value of debt is $5 billion, giving a total market value of $30 billion. Subtracting cash of $3 billion yields an enterprise value of $27 billion.
The weighted average cost of capital (WACC) is calculated as:
WACC = 12.5% × (25/30) + 5% × (5/30) = 11.25%
Using the enterprise value formula:
Enterprise Value = EBIT(1 − t)(1 − Reinvestment Rate)(1 + g) / (r − g)
27,000 = EBIT(1 − 0.30)(1 − 0.06/0.15)(1.1125/0.06)
Solving for EBIT: EBIT = $3,184 million
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