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There are three forms of income approach:

This method values an asset based on estimates of future cash flows for several years until cash flows are expected to stabilize. Then, a terminal value—discounted by an appropriate discount rate reflective of the risks associated with these cash flows—is calculated. The terminal value estimation involves capitalizing the final estimated cash flow using a sustainable long-term growth rate or using pricing multiples that should also assume sustainable cash flows.

$$ \begin{align*} \text{Value of the firm} & = \text{Present value of expected future cash flows} \\ & + \text{Present value of terminal value} \end{align*} $$

The following information relates to ABC Ltd.

$$\small{\begin{array}{l|c}\text{Net profit margin} & \text{15%} \\ \hline\text{Sales in Year 0} & \$8\text{m} \\ \hline\text{Fixed capital investment in Year 0} & \$3\text{m} \\ \hline \text{Depreciation in Year 0}& \$4\text{m} \\ \hline\text{Working capital investment as a percentage of sales} & 5.5\% \\ \hline\text{Tax rate }& 30\% \\ \hline \text{Interest expense on the par value of debt of \$5m in Year 0} & 10\% \\ \hline\text{WACC during the high growth phase} & 15\% \\ \hline\text{WACC during the mature phase} & 12\% \\ \hline\text{Growth rate for the next two years} & 8\% \\ \hline\text{Long-term constant growth rate} & 3\% \end{array}}$$

The value of the firm is *closest* to:

$$\small{\begin{array}{l|c|c|c}\textbf{Year} & \textbf{0} & \textbf{1} & \textbf{2} \\ \hline\text{Sales} & 8.00 & 8.64 & 9.33 \\ \hline \text{Net income} & 1.20 & 1.30 & 1.40 \\ \hline \text{Add Depreciation} & 4.00 & 4.32 & 4.67 \\ \hline \text{Add After tax interest expense} & 0.35 & 0.38 & 0.41 \\ \hline\text{Less Fixed capital investment} & 3 & 3.24 & 3.50 \\ \hline \text{Less Working capital investment} & 0.44 & 0.48 & 0.51 \\ \hline\textbf{FCFF} & \bf{2.11} & \bf{2.28} & \bf{2.46} \end{array}}$$

Then using the constant growth model,

$$\begin{align*}\text{Terminal value}_{\text{T}} &= \text{FCFF}_{\text{T}}\times\frac{(1+\text{g})}{(\text{WACC}-\text{g})}\\ \text{Terminal value}_5&=2.46×\frac{1.03}{(0.12-0.03)}\\&=$28.15\\ \\ \text{Value of the firm}&=\frac{2.28}{1.15}+\frac{(2.46+28.15)}{1.15^2} \\&=$25.13\end{align*}$$

This method estimates the value of a private company based on the value of a growing perpetuity. This is similar to the single-stage free cash flow model. This is appropriate for private companies where no projections are available, and an expectation of stable future operations exists. For companies whose growth rate is expected to significantly change in the future, the free cash flow method is more appropriate.

The formula for the capitalized cash flow is:

$$\text{V}_{\text{f}}=\frac{\text{FCFF}_1}{(\text{WACC}-\text{g}_{\text{f}})}$$

Where:

\(\text{V}_{\text{f}}=\) Value of the firm.

\(\text{FCFF}_{1}= \) Free cash flow to the firm for the next twelve months.

\(\text{WACC}=\) Weighted average cost of capital.

\(\text{g}_{\text{f}}=\) Sustainable growth rate of FCFF .

The denominator of the above equation, \((\text{WACC}-\text{g}_{\text{f}})\), is known as the capitalization rate.

The value of equity can be computed by deducting the market value of debt.

$$\text{V}_{\text{e}}=\text{V}_{\text{f}}-\text{Market Value of debt}$$

The capitalized cash flow method can also be used to value equity directly.

$$\text{V}_{\text{e}}=\frac{\text{FCFE}_{1}}{(\text{r}-\text{g})}$$

Where:

\(\text{r} =\) Required return on equity.

\(\text{g}=\) Sustainable growth rate of FCFE.

Suppose a company’s free cash flow to the firm was $30 million in the previous period and is expected to grow by 3.5% annually. The WACC is estimated to be 12%. Given the market value of its debt is $60 million, the value of the firm and equity can be calculated as:

$$\begin{align*}\text{Value of the firm}&=\frac{\text{FCFE}_{1}}{(\text{WACC}-\text{g})}\\ &=\frac{30(1.035)}{0.12-0.035}\\&=365.29\ \text{million}\\ \\\text{Value of equity}&=365.29\ \text{m}-\text{60 m}\\&=\text{305.29 m}\end{align*}$$

This method estimates the value of all the intangible assets of the business by capitalizing future earnings in excess of the estimated return requirements associated with working capital and fixed assets.

$$ \begin{align*} \text{Residual income (RI)} & = \text{Normalized earnings} – \text{Return on working capital} \\ & – \text{Return on fixed assets} \end{align*} $$

And

Value of intangible assets: \(\text{V}_{\text{intangible}}=\frac{\text{RI}_{0}(1+\text{g})}{(\text{r}_{\text{intangible}}-\text{g})}\)

Value of the firm: \(\text{V}_{\text{firm}}=\text{V}_{\text{intangible}}+\text{Working capital}+\text{Fixed assets}\)

Consider the following information:

$$\small{\begin{array}{l|r}\text{Working capital }& 45,000 \\ \hline \text{Fixed assets} & 180,000 \\ \hline\text{Normalized earnings (year just ended)} & 21,150 \\ \hline \text{The required return for working capital} & 3\% \\ \hline \text{The required return for fixed assets} & 8\% \\ \hline \text{The growth rate of residual income} & 2.5\% \\ \hline \text{Discount rate for intangible assets} & 18\% \end{array}}$$

The value of the firm is *closest* to:

$$\begin{align*}\text{Return on working capital}&= 3\% \times$45,000\\&= $1,350\\ \\ \text{Return on fixed assets}&= 8\% \times$180,000 \\&= $14,400\\ \\ \text{Residual Income}&= $21,150－ $1,350 －$14,400\\&= $5,400\end{align*}$$

Value of intangible assets: $$\begin{align*}\text{V}_{\text{intangible}}&=\frac{\text{RI}_{0}(1+\text{g})}{(\text{r}_{\text{intangible}}-\text{g})}\\ \\ \text{Value of intangible assets}&=\frac{$5400\times1.025}{0.18-0.025}\\&=$35,710\end{align*}$$

Value of the firm: $$\begin{align*}\text{V}_{\text{firm}}&=\text{V}_{\text{intangible}}+\text{Working capital}+\text{Fixed assets}\\&=$35,710+$45,000+$180,000 \\&= $260,710

\end{align*}$$

## Question

For a company with the following information:

- Working capital = $23,000
- Fixed assets = $85,000
- Normalized earnings for the previous period = $90,000
- The required rate of return for working capital assets and fixed assets is 6% and 11%, respectively.
- Residual income is expected to grow at 6%, and the discount rate of intangible assets is 10%.
The value of the firm is closest to:

- $2,208,655.
- $2,802,655.
- $2,028,655.
## Solution

The correct answer is A.$$\begin{align*}\text{Working capital required return}&=$23,000\times0.06=$1,380\\ \text{Fixed assets required return}&=$85,000 \times 0.11=$9,350\\ \text{Residual income} &= $90,000-$1,380-$9,350 \\ & =$79,270\\ \text{Value of intangible assets}&= \frac{$79,270 \times 1.06}{0.10-0.06}\\ & =$2,100,655\\ \text{Value of the firm}&=$2,100,655+$23,000+$85,000 \\ & =$2,208,655\end{align*}$$

Reading 27: Private Company Valuation

*LOS 27 (e) Calculate the value of a private company using free cash flow, capitalized cash flow, and/or excess earnings methods.*