Dividend Discount, FCFE, FCFF, and Res ...
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A complete equity valuation using a disaggregated model follows six steps:
FCFF Calculation:
$$ \begin{align*}\text{NOPAT} & = [\text{Revenue} – \text{COGS} – \text{SG&A} – \text{D&A}] \times (1 – t) \\
\text{Net Investment} & = \Delta\text{Working Capital} + \Delta\text{Net Long-Term Assets} \\
\text{FCFF} & = \text{NOPAT} – \text{Net Investment} \end{align*} $$
FCFE Calculation:
$$ \text{FCFE} = \text{Net Income} – \Delta\text{Gross LT Assets} + \text{Depreciation} – \Delta\text{Working Capital} + \Delta\text{Debt} $$
Alternatively:
$$ \text{FCFE} = \Delta\text{Cash} + \text{Dividends} + \text{Stock Repurchases} – \text{Stock Issuance} $$
Constant Growth Model:
$$ \text{Firm Value}_{t+n} = \frac{\text{FCFF}_{t+n} \times (1 + g)}{\text{WACC} – g} $$
Where the sustainable growth rate (\(g\)) is:
$$ g = \left(1 – \frac{\text{FCFF}}{\text{NOPAT}}\right) \times \left(\frac{\text{NOPAT}}{\text{Book Value of Capital}}\right) $$
The first term represents the reinvestment rate, and the second term represents the return on capital.
Converting Terminal Value to a Multiple:
Converting a constant-growth terminal value into a multiple allows the analyst to:
For example, if the terminal value implies a P/E ratio significantly higher than industry peers, the analyst should re-examine the growth or WACC assumptions.
$$ \mathrm{IV}_t = \sum_{i=1}^{n} \frac{\mathrm{FCFF}_{t+i}}{(1+\mathrm{WACC})^i} + \frac{E(P_{t+n})}{(1+\mathrm{WACC})^n} – \text{MV} – \text{Debt} $$
A single forecast scenario rarely captures the full range of possible outcomes. Analysts should develop multiple scenarios and assign subjective probabilities to them.
Common Scenarios:
Probability-Weighted Valuation:
$$ \text{Expected Equity Value} = \sum_{i=1}^{n} P_i \times \text{Equity Value}_i $$
Where \(\sum P_i = 1.0\).
Interpretation:
Example: Complete Valuation of a Mature Company (Base Case)
Company Background:
Apex Manufacturing is a mature industrial company. The analyst has gathered historical financial statements and built a five-year forecast.
Step 1: Income Statement Forecast (USD millions)
$$
\begin{array}{l|r|r|r|r|r}
\textbf{Item} & \textbf{T+1} & \textbf{T+2} & \textbf{T+3} & \textbf{T+4} & \textbf{T+5} \\
\hline
\text{Revenue} & 210.0 & 222.6 & 238.2 & 254.9 & 270.2 \\ \hline
\text{COGS} & 98.7 & 104.6 & 108.8 & 112.9 & 116.3 \\ \hline
\text{SG&A} & 68.3 & 72.4 & 75.3 & 78.3 & 80.6 \\ \hline
\text{D&A} & 22.8 & 24.2 & 25.4 & 26.7 & 28.0 \\ \hline
\text{EBIT} & 20.2 & 21.4 & 28.7 & 37.0 & 45.3 \\ \hline
\text{Interest Expense} & 9.1 & 9.6 & 10.0 & 10.4 & 10.7 \\ \hline
\text{Interest Income} & 1.5 & 1.6 & 1.7 & 1.8 & 1.9 \\ \hline
\text{EBT} & 12.6 & 13.4 & 20.4 & 28.4 & 36.5 \\ \hline
\text{Taxes (30%)} & 3.8 & 4.0 & 6.1 & 8.5 & 11.0 \\ \hline
\text{Net Income} & 8.8 & 9.4 & 14.3 & 19.9 & 25.5 \\
\end{array}
$$
Step 2: Balance Sheet Forecast (USD millions)
$$
\begin{array}{l|r|r|r|r|r|r}
\textbf{Item} & \textbf{T} & \textbf{T+1} & \textbf{T+2} & \textbf{T+3} & \textbf{T+4} & \textbf{T+5} \\
\hline
\text{Cash} & 68.0 & 72.1 & 77.9 & 85.6 & 96.1 & 109.8 \\ \hline
\text{A/R} & 33.0 & 35.3 & 37.4 & 40.0 & 42.8 & 45.4 \\ \hline
\text{Inventory} & 37.0 & 39.6 & 42.0 & 44.9 & 48.0 & 52.9 \\ \hline
\text{Other CA} & 7.0 & 7.5 & 7.9 & 8.5 & 9.1 & 10.6 \\ \hline
\text{Total CA} & 145.0 & 154.5 & 165.2 & 179.0 & 196.0 & 218.7 \\ \hline
\text{Net PP&E} & 23.0 & 24.6 & 26.1 & 27.4 & 28.8 & 34.0 \\ \hline
\text{Intangibles} & 22.0 & 23.5 & 25.0 & 26.2 & 27.5 & 29.2 \\ \hline
\textbf{Total Asset} & \bf{190.0} & \bf{202.6} & \bf{216.3} & \bf{232.6} & \bf{252.3} & \bf{281.9} \\ \hline
\text{A/P} & 25.0 & 26.8 & 28.4 & 29.8 & 30.4 & 33.1 \\ \hline
\text{Other CL} & 4.0 & 4.3 & 4.5 & 4.8 & 5.0 & 5.3 \\ \hline
\text{Total CL} & 29.0 & 31.1 & 32.9 & 34.6 & 36.3 & 38.4 \\ \hline
\text{Total Debt} & 90.0 & 90.0 & 90.0 & 90.0 & 90.0 & 90.0 \\ \hline
\text{Other LT} & 14.0 & 15.0 & 15.9 & 16.7 & 17.5 & 18.6 \\ \hline
\text{Total Liabilities} & 133.0 & 136.1 & 138.8 & 141.3 & 143.8 & 147.0 \\ \hline
\text{Common Stock} & 5.0 & 5.0 & 5.0 & 5.0 & 5.0 & 5.0 \\ \hline
\text{Retained Earnings} & 52.0 & 61.5 & 72.5 & 86.3 & 104.4 & 129.9 \\ \hline
\textbf{Total Equity} & \bf{57.0} & \bf{65.8} & \bf{75.2} & \bf{89.5} & \bf{109.4} & \bf{134.9} \\ \hline
\textbf{Total Liabilities + Equity} & \bf{190.0} & \bf{202.6} & \bf{216.3} & \bf{232.6} & \bf{252.3} & \bf{281.9} \\
\end{array}
$$
Step 3: Calculate FCFF Forecast (USD millions)
$$
\begin{array}{l|r|r|r|r|r}
\textbf{Item} & \textbf{T+1} & \textbf{T+2} & \textbf{T+3} & \textbf{T+4} & \textbf{T+5} \\
\hline
\text{NOPAT} & 14.1 & 15.0 & 20.1 & 25.9 & 31.7 \\ \hline
\Delta\text{ Working Capital} & 3.3 & 3.1 & 4.4 & 4.8 & 6.9 \\ \hline
\Delta\text{ Net Long-Term Assets} & 3.1 & 3.0 & 2.5 & 2.7 & 6.9 \\ \hline
\text{Net Investment} & 6.4 & 6.1 & 6.9 & 7.5 & 13.8 \\ \hline
\text{FCFF} & 7.7 & 8.9 & 13.2 & 18.4 & 17.9 \\
\end{array}
$$
Step 4: Estimate Terminal Value
Year \(t+5\) FCFF = \(17.9\)
Year \(t+5\) NOPAT = \(31.7\)
Book Value of Capital (\(t+4\)) = Total Assets − Cash (\(t+4\)) = \(252.3 – 96.1 = 156.2\)
Reinvestment Rate = \(1 – (17.9 \div 31.7) = 1 – 0.565 = 0.435\)
Return on Capital = \(31.7 \div 156.2 = 0.203\)
Sustainable Growth (\(g\)) = \(0.435 \times 0.203 = 8.83\%\)
WACC = \(9.5\%\)
Terminal Value = \([17.9 \times (1.04)] \div (0.095 – 0.04) = 18.62 \div 0.055 = 338.5\)
Step 5: Calculate Present Value
$$
\begin{array}{c|c|c|c}
\textbf{Year} & \textbf{FCFF} & \textbf{PV Factor (9.5%)} & \textbf{PV} \\
\hline
\bf 1 & 7.7 & 0.913 & 7.03 \\ \hline
\bf 2 & 8.9 & 0.834 & 7.42 \\ \hline
\bf 3 & 13.2 & 0.762 & 10.06 \\ \hline
\bf 4 & 18.4 & 0.696 & 12.81 \\ \hline
\bf 5 & 17.9 + 338.5 & 0.635 & 226.31 \\
\hline
\textbf{PV of FCFF} & & & \textbf{263.63} \\
\end{array}
$$
Step 6: Calculate Equity Value
Firm Value = \(263.63\)
Debt (book value) = \(90.0\)
Equity Value = \(263.63 – 90.0 = 173.63\)
Step 7: Scenario Analysis
Apex Manufacturing: Optimistic Scenario
In the optimistic scenario, the analyst anticipates that Folium’s management will increase investment spending throughout the forecast period, accompanied by stronger revenue growth and an expansion in profit margins. The key assumptions are outlined below.
$$
\begin{array}{l|l|c|c|c|c|c}
\textbf{Forecasting Items} & \textbf{Notes} & \textbf{T+1} & \textbf{T+2} & \textbf{T+3} & \textbf{T+4} & \textbf{T+5} \\
\hline
\textbf{Revenue} & \text{Growth Rate} & 4.5\% & 6.0\% & 7.5\% & 9.0\% & 7.0\% \\ \hline
\textbf{Expenses} & \text{Growth Rate} & 7.0\% & 7.5\% & 5.0\% & 5.0\% & 4.5\% \\ \hline
\textbf{Tax Rate} & \text{Constant} & 30\% & 30\% & 30\% & 30\% & 30\% \\ \hline
\textbf{Assets} & \text{Growth Rate} & 7.0\% & 7.0\% & 8.0\% & 6.5\% & 6.0\% \\ \hline
\textbf{Liabilities} & \text{Growth Rate} & 8.0\% & 8.0\% & 7.0\% & 6.0\% & 6.0\% \\ \hline
\textbf{Cash} & & 100\% & 100\% & 100\% & 100\% & 100\% \\ \hline
\textbf{Debt} & & 0\% & 0\% & 0\% & 0\% & 0\% \\ \hline
\textbf{Equity} & \text{Zero dividends in forecast} & 0\% & 0\% & 0\% & 0\% & 0\% \\
\end{array}
$$
Pessimistic Scenario
In the pessimistic scenario, the analyst projects that Folium’s revenue growth will stagnate at relatively low levels compared to its historical performance. Profit margins are expected to continue their recent decline, while investment spending is assumed to decrease over time in order to preserve free cash flow. The underlying assumptions are outlined below.
$$
\begin{array}{l|l|c|c|c|c|c}
\textbf{Forecasting Items} & \textbf{Notes} & \textbf{T+1} & \textbf{T+2} & \textbf{T+3} & \textbf{T+4} & \textbf{T+5} \\
\hline
\textbf{Revenue} & \text{Growth Rate} & 6.0\% & 5.0\% & 4.0\% & 3.0\% & 3.0\% \\ \hline
\textbf{Expenses} & \text{Growth Rate} & 7.0\% & 6.5\% & 5.0\% & 4.0\% & 3.5\% \\ \hline
\textbf{Tax Rate} & \text{Constant} & 30\% & 30\% & 30\% & 30\% & 30\% \\ \hline
\textbf{Assets} & \text{Growth Rate} & 7.0\% & 6.0\% & 5.0\% & 4.0\% & 3.0\% \\ \hline
\textbf{Liabilities} & \text{Growth Rate} & 8.0\% & 6.0\% & 4.0\% & 4.0\% & 3.0\% \\ \hline
\textbf{Cash} & & 100\% & 100\% & 100\% & 100\% & 100\% \\ \hline
\textbf{Debt} & & 0\% & 0\% & 0\% & 0\% & 0\% \\ \hline
\textbf{Equity} & \text{Zero dividends in forecast} & 0\% & 0\% & 0\% & 0\% & 0\% \\
\end{array}
$$
Stable Scenario
After presenting the three valuation scenarios, a question arose regarding the possibility of a fourth. Specifically, concerns were raised that the analyst’s base case scenario reflected considerable optimism. In response, an alternative “stable scenario” was developed, in which expenses and assets are assumed to grow at the same pace as revenues. The details of this scenario are outlined below.
$$
\begin{array}{l|l|c|c|c|c|c}
\textbf{Forecasting Items} & \textbf{Notes} & \textbf{T+1} & \textbf{T+2} & \textbf{T+3} & \textbf{T+4} & \textbf{T+5} \\
\hline
\textbf{Revenue} & \text{Growth Rate} & 4.0\% & 5.0\% & 6.0\% & 6.0\% & 5.0\% \\ \hline
\textbf{Expenses} & \text{Growth Rate} & 4.0\% & 5.0\% & 6.0\% & 6.0\% & 5.0\% \\ \hline
\textbf{Tax Rate} & \text{Constant} & 30\% & 30\% & 30\% & 30\% & 30\% \\ \hline
\textbf{Assets} & \text{Growth Rate} & 4.0\% & 5.0\% & 6.0\% & 6.0\% & 5.0\% \\ \hline
\textbf{Liabilities} & \text{Growth Rate} & 4.0\% & 5.0\% & 6.0\% & 6.0\% & 5.0\% \\ \hline
\textbf{Cash} & & 100\% & 100\% & 100\% & 100\% & 100\% \\ \hline
\textbf{Debt} & & 0\% & 0\% & 0\% & 0\% & 0\% \\ \hline
\textbf{Equity} & \text{Zero dividends in forecast} & 0\% & 0\% & 0\% & 0\% & 0\% \\
\end{array}
$$
$$
\begin{array}{l|c|c|c|c}
\textbf{Scenario} & \textbf{Base} & \textbf{Optimistic} & \textbf{Pessimistic} & \textbf{Stable} \\
\hline
\textbf{Firm Value (in USD millions)} & 263.63 & 276.93 & 76.00 & 172.75 \\ \hline
\textbf{Equity Value (in USD millions)} & 173.63 & 186.93 & -14.00 & 82.75 \\ \hline
\textbf{Revenue CAGR (5 years)} & 6.20\% & 6.79\% & 4.19\% & 5.20\% \\ \hline
\textbf{EBIT margin } (t+5) & 16.77\% & 13.74\% & 5.19\% & 9.60\% \\ \hline
\textbf{FCFF } (t+5) & 17.90 & 20.49 & 5.98 & 12.47 \\
\end{array}
$$
Interpretation: Assuming equal (\(25\%\)) probability weights across the four scenarios, the probability-weighted equity value is approximately:
\(0.25 \times 173.63 + 0.25 \times 186.93 + 0.25 \times -14.00 + 0.25 \times 82.75 = \$107.3\text{ million}\)
If the company’s current market capitalization is close to \(\$107.3\text{ million}\), the stock is fairly valued relative to the analyst’s probability-weighted scenarios. If the market price is significantly above \(\$107.3\text{ million}\), the stock is overvalued; if significantly below, undervalued.
An analyst estimates a terminal value using a constant growth model and then converts this estimate into a multiple of earnings. Which of the following best describes an advantage of converting the terminal value estimate into a multiple?
Solution:
The correct answer is B.
Converting a constant-growth terminal value to a multiple allows the analyst to compare it with peer-group multiples or the company’s historical multiples. If the terminal value implies a P/E multiple far above comparable companies, the analyst must re-examine the assumptions underlying the constant growth model.
A is incorrect. Converting a terminal value into a multiple does not automatically ensure proper peer group definition. The analyst must still exercise judgment in selecting an appropriate peer group.
C is incorrect. The terminal value is initially calculated using the constant growth model, not a multiple. The conversion into a multiple is a subsequent step used for validation, not a replacement methodology.
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