Chapter 13: Business Valuation
1. Valuation Master Formula Bank
1. Free Cash Flow to Firm (FCFF) & Enterprise Value:
$$\text{FCFF} = \text{EBIT}(1 - T) + \text{Depreciation} - \text{Capex} - \Delta\text{Working Capital}$$ $$\text{Enterprise Value (EV)} = \sum_{t=1}^n \frac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \frac{\text{Terminal Value}_n}{(1 + \text{WACC})^n}$$ $$\text{Terminal Value}_n = \frac{\text{FCFF}_{n+1}}{\text{WACC}_{\text{stable}} - g_{\text{stable}}}$$ $$\text{Equity Value} = \text{Enterprise Value} - \text{Debt} + \text{Cash & Liquid Investments}$$
$$\text{FCFF} = \text{EBIT}(1 - T) + \text{Depreciation} - \text{Capex} - \Delta\text{Working Capital}$$ $$\text{Enterprise Value (EV)} = \sum_{t=1}^n \frac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \frac{\text{Terminal Value}_n}{(1 + \text{WACC})^n}$$ $$\text{Terminal Value}_n = \frac{\text{FCFF}_{n+1}}{\text{WACC}_{\text{stable}} - g_{\text{stable}}}$$ $$\text{Equity Value} = \text{Enterprise Value} - \text{Debt} + \text{Cash & Liquid Investments}$$
2. Hamada Equation (Beta Re-leveraging):
$$\beta_L = \beta_U \left[ 1 + (1 - T)\frac{D}{E} \right]$$
$$\beta_L = \beta_U \left[ 1 + (1 - T)\frac{D}{E} \right]$$
3. Economic Value Added (EVA):
$$\mathbf{\text{EVA} = \text{NOPAT} - (\text{WACC} \times \text{Invested Capital})}$$ $$\text{NOPAT} = \text{EBIT}(1 - T) = \text{PAT} + \text{Interest}(1 - T)$$ $$\text{EVA Dividend per share} = \frac{\text{Total EVA}}{\text{Number of Shares}}$$
$$\mathbf{\text{EVA} = \text{NOPAT} - (\text{WACC} \times \text{Invested Capital})}$$ $$\text{NOPAT} = \text{EBIT}(1 - T) = \text{PAT} + \text{Interest}(1 - T)$$ $$\text{EVA Dividend per share} = \frac{\text{Total EVA}}{\text{Number of Shares}}$$
4. Market Value Added (MVA):
$$\text{MVA} = \text{Market Value of Equity} - \text{Book Value of Equity}$$
$$\text{MVA} = \text{Market Value of Equity} - \text{Book Value of Equity}$$
5. Profit Earning Capacity Value (PECV):
$$\text{PECV per share} = \frac{\text{Future Maintainable PAT} / \text{Capitalization Rate}}{\text{Number of Equity Shares}}$$
$$\text{PECV per share} = \frac{\text{Future Maintainable PAT} / \text{Capitalization Rate}}{\text{Number of Equity Shares}}$$
6. Regulatory Fair Value per Share:
$$\text{Fair Value per share} = \frac{\text{Net Asset Value (NAV) per share} + \text{PECV per share}}{2}$$
$$\text{Fair Value per share} = \frac{\text{Net Asset Value (NAV) per share} + \text{PECV per share}}{2}$$
2. FCFF vs FCFE Quick Comparison
| Metric | FCFF Model (Firm Level) | FCFE Model (Equity Level) |
|---|---|---|
| Starting Point | $\text{EBIT}(1 - T)$ (NOPAT) | $\text{PAT} - \text{Preference Dividends}$ |
| Debt Adjustment | Zero (Debt flows included in overall capital) | $+\text{New Debt Issued} - \text{Debt Repaid}$ |
| Discount Rate | WACC (Weighted Cost of Debt & Equity) | $k_e$ (Cost of Equity via CAPM) |
| Direct Output | Enterprise Value (Firm Value) | Equity Value |
| To get Equity Value | Subtract Debt and add Cash from EV | Obtained directly from model |
3. EVA Adjustments & Decision Matrix
| Item | Impact on NOPAT | Impact on Invested Capital |
|---|---|---|
| Unrecorded Patents / Intangibles | No change (already in earnings) | Add market value of patent to capital |
| R&D Expenses | Add back current year R&D, subtract amortisation | Add unamortised R&D asset to capital |
| Bad Debts Provisions | Add back non-cash provision to EBIT | Add back provision to Current Assets / Capital |
| Non-Operating Assets | Deduct non-operating income | Deduct non-operating asset from capital |
4. Chop-Shop (Break-Up Value) 4-Step Protocol
- Segment Sales Capitalization: $\sum (\text{Segment Sales} \times \text{Industry } P/S \text{ multiple})$.
- Segment Assets Capitalization: $\sum (\text{Segment Assets} \times \text{Industry } P/\text{Asset} \text{ multiple})$.
- Segment Income Capitalization: $\sum (\text{Segment Operating Income} \times \text{Industry } P/E \text{ multiple})$.
- Synthesize & Average: Take simple average of the three totals $\implies$ Compare with current aggregate market price. If $\text{Chop-Shop Value} > \text{Market Price}$, conglomerate discount exists.
5. Swap Ratio Guidelines in Mergers
| Valuation Method | Swap Ratio Formula |
|---|---|
| Book Value / NAV Basis | $$\text{Swap Ratio} = \frac{\text{NAV per share of Target Company}}{\text{NAV per share of Acquirer Company}}$$ |
| Earnings / PECV Basis | $$\text{Swap Ratio} = \frac{\text{PECV per share of Target Company}}{\text{PECV per share of Acquirer Company}}$$ |
| Market Price Basis | $$\text{Swap Ratio} = \frac{\text{Market Price per share of Target}}{\text{Market Price per share of Acquirer}}$$ |
6. ICAI Exam Traps & Pitfalls
⚠️ Pitfall 1: Stable Phase Reinvestment Assumption
In 2-stage DCF problems (like TYK PR-7 & PR-8), notice that during stable growth, Capital Expenditure equals Depreciation (Net capex = 0). Do not subtract the high-growth capex percentage in the terminal year!
In 2-stage DCF problems (like TYK PR-7 & PR-8), notice that during stable growth, Capital Expenditure equals Depreciation (Net capex = 0). Do not subtract the high-growth capex percentage in the terminal year!
⚠️ Pitfall 2: Discounting the Terminal Value
Remember that $TV_n = \frac{\text{FCFF}_{n+1}}{\text{WACC} - g}$ gives the value at Year $n$. You must multiply $TV_n$ by $\text{PVIF}_{\text{WACC}, n}$ to bring it back to Year 0.
Remember that $TV_n = \frac{\text{FCFF}_{n+1}}{\text{WACC} - g}$ gives the value at Year $n$. You must multiply $TV_n$ by $\text{PVIF}_{\text{WACC}, n}$ to bring it back to Year 0.
⚠️ Pitfall 3: NOPAT Tax Rate on Interest
$\text{NOPAT} = \text{EBIT}(1 - T)$. If starting from PAT, add back post-tax interest: $\text{PAT} + \text{Interest}(1 - T)$, NOT pre-tax interest!
$\text{NOPAT} = \text{EBIT}(1 - T)$. If starting from PAT, add back post-tax interest: $\text{PAT} + \text{Interest}(1 - T)$, NOT pre-tax interest!