Estimating a Company’s Value using the Free Cash Flow Model

The following two examples will do a good job at putting in application the theoretical models we have learned previously

Example: Simple Two-Step FCF Models

$$\small{\begin{array}{l|r}\text{Current sales per share} & 9 \\ \hline\text{Sales growth for the first three years} & 15.0\% \\ \hline\text{Sales growth for year four and thereafter} & 4.0\% \\ \hline\text{Net income margin} & 7.5\% \\ \hline\text{FCInv/Sales growth} & 30.0\% \\ \hline\text{WCInv/Sales growth} & 18.8\% \\  \hline\text{Debt financing of FCInv and WCInv growth} & 22.5\% \\ \hline\text{Required rate of return} & 7.5\%\\ \end{array}}$$

The equity value of the firm is closest to:

Solution

$$\small{\begin{array}{l|c|c|c|c|c}& \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} &\textbf{5} \\ \hline\text{Percentage sales growth} & 15\% & 15\% & 15\% & 4\% & 4\% \\ \hline\text{Sales per share} & 10.350 & 11.903 & 13.688 & 14.235 & 14.805 \\ \hline\text{EPS} & 1.150 & 1.323 & 1.521 & 1.582 & 1.645 \\ \hline\text{FCInv per share} & 0.405 & 0.466 & 0.536 & 0.164 & 0.171 \\ \hline\text{WCInv per share} & 0.253 & 0.291 & 0.335 & 0.103 & 0.107 \\ \hline\text{Debt financing per share} & 0.148 & 0.170 & 0.196 & 0.060 & 0.062 \\ \hline\textbf{FCFE per share} & \bf{0.266} & \bf{0.306} & \bf{0.352} & \bf{0.861} & \bf{0.895} \\ \hline\text{Growth in FCFE} & & 15.0\% & 15.0\% & 144.5\% & 4.0\\ \end{array}}$$

FCFE for the first year is calculated as:

$$\begin{align*}\text{FCFE}& = (\text{Sales} × \text{Net income margin})-∆\text{FCInv}-∆\text{WCInv}\\&+∆\text{Debt financing}\\ \\&=(9×1.15×7.5\%)-(9×15\%×30\%)-(9×15\%×18.8\%)\\&+(9×15\%×48.8\%×22.5\%)= 0.266\\ \\
\text{Equity value}&= ∑_{\text{t}=1}^{\text{n}}\frac{\text{FCFE}_{\text{t}}}{(1+\text{r})^{\text{t}}} +\frac{\text{FCFE}_{\text{n}+1}}{(\text{r}-\text{g})}\frac{1}{(1+\text{r})^{\text{n}}}\\&=\frac{0.266}{1.075}+\frac{0.306}{1.075^2} +\frac{0.352}{1.075^3} +\frac{0.861}{(0.075-0.04)}\bigg(\frac{1}{1.075^3}\bigg)\\&=20.60\end{align*}$$

Example: Three Stage FCF Model

Consider the following information:

$$\small{\begin{array}{l|r}\text{Current FCFF}\ (\text{in \$ million}) & 175 \\ \hline\text{Outstanding shares}\ (\text{in million}) & 525 \\ \hline{\text{Long-term debt value}\\ (\text{in \$ million})} & 700 \\ \hline\text{FCFF growth for years 1 to 3} & 45\% \\ \hline\text{FCFF growth for year 4} & 36\% \\ \hline\text{FCFF growth for year 5} & 18\% \\ \hline{\text{FCFF growth for year 6}\\ \text{and thereafter}} & 7.5\% \\ \hline\text{WACC} & 15\%\\ \end{array}}$$

Calculate:

• Firm value
• Equity value
• Equity value per share

Solution

All figures in $ million except equity value per share.

$$\small{\begin{array}{l|c|c|c|c|c|c}& \textbf{1} & \textbf{2} &\textbf{3} & \textbf{4} & \textbf{5} & \textbf{6} \\ \hline\text{FCFF growth rate} & 45\% & 45\% & 45\% & 36\% & 18\% & 8\% \\ \hline\text{FCFF} & 253.8 & 367.9 & 533.5 & 725.6 & 856.2 & 920.4 \\ \hline\text{PV of FCFF} & 220.65 & 278.21 & 350.79 & 414.85 & 425.67 &{}\\ \end{array}}$$

$$\begin{align*}\text{Terminal value}&= \frac{\text{FCFF}_{\text{n}-1}}{(\text{WACC}-\text{g})}\frac{1}{(1+\text{WACC}^{\text{n}})}\\&=\frac{920.4}{(0.15-0.075)}\frac{1}{(1+0.15)^{5}}=\$6,101.35\\ \\ \text{Firm value}&=\sum_{\text{t}-1}^{\text{n}}\frac{\text{FCFE}_{t}}{(1+\text{WACC})^{\text{t}}}+\frac{\text{FCFF}_{\text{n}+1}}{(\text{WACC}-\text{g})}\frac{1}{(1+\text{WACC})^{\text{n}}}\\& =220.65 + 278.21 + 350.79 + 414.85 + 425.67 + 6,101.35 \\&=\$7,791.52\\ \\ \text{Equity value}&=\text{Firm value}-\text{Debt value}\\&=7,791.52-700=\$7,091.52\\ \\ \text{Equity value per share}&=\frac{$7,091.52}{525 \text{ shares}}=\$13.51 \text{ per share}\end{align*}$$

Question

A company’s current FCFF is $600,000. It is currently experiencing a growth rate of 8% that is expected to last for three years, after which its growth rate will decline to 4% and remain at that rate indefinitely. If its WACC is 9%, the value of the firm is closest to:

1. $13,907,095.
2. $950,230.
3. $18,750,300.

Solution

The correct answer is A.

$$\begin{align*}\text{Firm value}&=\sum_{\text{t}-1}^{\text{n}}\frac{\text{FCFE}_{t}}{(1+\text{WACC})^{\text{t}}}+\frac{\text{FCFF}_{\text{n}+1}}{(\text{WACC}-\text{g})}\frac{1}{(1+\text{WACC})^{\text{n}}}\\ \\&=\frac{648,000}{(1+9\%)^1} + \frac{699,840}{(1+9\%)^2}+\frac{755,827}{(1+9\%)^3} \\& +\frac{755,827(1+4\%)}{(9\%-4\%)}\frac{1}{(1+9\%)^3}\\ \\&=13,907,095\end{align*}$$

Reading 24: Free Cash Flow Valuation

LOS 24 (j) Estimate a company’s value using the appropriate free cash flow model(s).