Calculating a Justified Price Multiple
A justified price multiple estimates the fair value of a price multiple... Read More
In earlier sections, we discussed adjusting valuation parameters for private companies, including income normalization and required rate of return changes. After determining the firm's value, control, and marketability, premiums or discounts may be applied based on the evaluator's perspective and objectives. Now, we focus on conducting a private company valuation using the income approach and these adjustments.
Estimate top-down FCFF from company information
$$ \begin{align*} \text{FCFF} & = \text{EBIT}(1-\text{Tax Rate})+\text{Depreciation}(\text{Tax Rate}) \\ & -\Delta \text{LT Assets}-\Delta \text{Working Capital} \end{align*} $$
Solve for enterprise value (EV) using the DCF model.
$$ EV_t=\sum_{i=1}^n \frac {\text{FCFF}_{t+i}}{(1+\text{WACC})^i }+\frac { \frac {\text{FCFF}_{t+n+1}}{(\text{WACC}-g)}}{(1+\text{WACC})^n } $$
We will illustrate this using an example.
Example 1 Vickers Prinsloo.
Claudia Jean owns 100% of the shares in SereniTea LTD and is also the CEO. SereniTea LTD produces a line of Chinese herbal green tea. Vickers Prinsloo, a private equity analyst, has been tasked with the purchase evaluation of SereniTea LTD on behalf of a client. The following are notes that Prinsloo made during his evaluation.
Prinsloo uses the following income statement to calculate the operating income.
$$ \textbf{Exhibit 1: SereniTea Income Statement} \\
\begin{array}{l|r}
& \$‘000 \\ \hline
\text{Sales revenue} & 25,000 \\ \hline
\text{Purchases} & 15,000 \\ \hline
\text{Gross profit} & 10,000 \\ \hline
\text{Operating expenses} & 2,000 \\ \hline
\text{EBITDA} & 8,000 \\ \hline
\text{Depreciation and amortization} & 500 \\ \hline
\text{EBIT} & 7,500 \\ \hline
\text{Tax }(20\%) & 1,500 \\ \hline
\text{Operating income after tax} & 6,000
\end{array} $$
He goes further and calculates the discount rates for SereniTea LTD, and the results are summarized below.
$$ \textbf{Exhibit 2: SereniTea Discount Rates} \\
\begin{array}{l|l|r}
\text{Calculated variable} & \text{Approach} & \text{Result} \\ \hline
\text{Required return on equity} & \text{Build-up approach} & 10.2\% \\ \hline
\text{Required return on equity} & \text{CAPM} & 7.4\% \\ \hline
\text{Required return on equity} & \text{Expanded CAPM} & 11.3\% \\ \hline
\text{WACC} & {\text{Using the firm’s actual debt ratio}} & 10.2\% \\ \hline
\text{WACC} & {\text{Using the firm’s optimal ratio}} & 9.6\%
\end{array} $$
To estimate the valuation of SereniTea using the income approach, Prinsloo uses the following steps:
Step 1: Estimate WACC
Since the build-up approach gave a required return on equity of 10.2%, and the expanded CAPM resulted in 11.3%. Prinsloo uses the average of the two,10.75%, as part of the WACC calculation. He arrives at a differing WACC estimate of 9.9% for the debt ratios.
Step 2: Develop a base-year estimate FCFF
Using information from the income statement, the FCFF will be:
$$ \begin{align*} FCFF & =EBIT(1-\text{Tax rate})+\text{Depreciation}(\text{Tax rate}) \\ &-\Delta \text{LT Assets}-\Delta \text{Working capital} \\
FCFF & =7,500,000 \times (1-0.2)+500,000 \times 0.2-980,000-450,000 \\
FCFF & =\$5,570,000 \end{align*} $$
Step 3: Estimate EV using an FCFF forecast an expected terminal value
Prinsloo creates a five-year forecast of revenue based on expected industry trends. A downside case of 3% FCFF growth for the next five years, a 5% base case, and an optimistic case of 7%. An expected perpetual growth rate of 2% is used to calculate the terminal value. All results are summarized below:
$$ \textbf{Exhibit 3: SereniTea FCFF and Terminal Value Forecasts } \bf{($)} \\
\begin{array}{c|c|c|c}
\textbf{Year} & \bf{\text{Downside }(3\%)} & \bf{\text{Base }(5\%)} & \bf{\text{Optimistic} (7\%)} \\ \hline
\text{Base year} & 5,570,000 & 5,570,000 & 5,570,000 \\ \hline
1 & 5,737,100 & 5,848,500 & 5,959,900 \\ \hline
2 & 5,909,213 & 6,140,925 & 6,377,093 \\ \hline
3 & 6,086,489 & 6,447,971 & 6,823,590 \\ \hline
4 & 6,269,084 & 6,770,370 & 7,301,134 \\ \hline
5 & 6,457,157 & 7,108,888 & 7,812,213 \\ \hline
\text{Terminal value} & 84,188,244 & 94,485,224 & 105,810,988
\end{array} $$
Year 5 FCFF for the base case is calculated as follows:
$$ \text{FCFF}(\text{Base})_5=FCFF_0 (1+0.05)^5=\$7,108,888 $$
The terminal value of the base case is calculated as follows:
$$ \text{Terminal Value (Base)}=\text{FCFF}(\text{Base})_5 \times \frac {(1+0.05)}{(0.099-0.02)} $$
$$ \text{Terminal Value (Base)}=\frac { \$7,64,332.4}{0.079}=94,485,224 $$
The Equity and enterprise value of the firm are shown below.
$$ \textbf{Exhibit 4: Equity and Enterprise Value Estimates }\bf{($)} \\
\begin{array}{c|c|c|c}
\textbf{Case} & \textbf{Downside} & \textbf{Base} & \textbf{Optimistic} \\ \hline
\textbf{Equity value} & 75,535,864.17 & 83,274,310.88 & 91,721,191.84 \\ \hline
\textbf{EV} & 78,095,864.17 & 85,834,310.88 & 94,281,191.84
\end{array} $$
SereniTea had an outstanding debt of $2,560,000. We deduct the debt from the enterprise value estimate to get the equity value.
Step 4: Apply appropriate discounts/premiums to complete the valuation
After calculating the equity value, Prinsloo concludes that he needs to account for SereniTea LTD's privately held company status by discounting the estimates for lack of marketability. After a thorough analysis, he concludes that a 10% DLOM will be appropriate for SereniTea LTD. The table below shows the estimated value range for SereniTea after discounting for lack of marketability.
$$ \textbf{Exhibit 5: SereniTea Non-Marketable Equity Value Estimates }\bf{($)} \\
\begin{array}{c|c|c|c}
& \textbf{Downside} & \textbf{Base} & \textbf{Optimistic} \\ \hline
\text{Equity value less DLOM} & 67,982,277.76 & 74,946,879.79 & 82,549,072.66 \end{array} $$
Reading 27: Private Company Valuation
LOS 27 (h) Calculate the value of a private company income-based methods