# Calculating FCFF and FCFE

Consider the following information regarding ABC Ltd:

$$\textbf{Income Statement (in \ million)}$$

$$\small{\begin{array}{l|r|r} & \textbf{2020} & \textbf{2019} \\ \hline\text{Sales} & 294 & 212 \\ \hline\text{COGS} & 132 & 106 \\ \hline\text{Gross profit} & 162 & 106 \\ \hline\text{SG&A} & 12 & 9 \\ \hline\text{Depreciation} & 28 & 24 \\ \hline\text{EBIT} & 122 & 73 \\ \hline\text{Interest Expense} & 9 & 7 \\ \hline\text{Pre-tax earnings} & 113 & 66 \\ \hline\text{Taxes} & 28.25 & 17 \\ \hline\textbf{Net income} & \bf{84.75} & \bf{50}\\ \end{array}}$$

$$\textbf{Balance Sheet (in \ million)}$$

$$\small{\begin{array}{l|r|r} & \textbf{2020} & \textbf{2019} \\ \hline\text{Gross PPE} & 678 & 529 \\ \hline\text{Accumulated depreciation} & 122 & 94 \\ \hline\text{Net PPE} & 556 & 435 \\ \hline\text{Inventory} & 25 & 21 \\ \hline\text{Accounts receivable} & 4 & 7 \\ \hline\text{Cash} & 11 & 9 \\ \hline\text{Total current assets} & 40 & 37 \\ \hline\textbf{Total assets} & \bf{596} & \bf{472} \\ \hline\text{Common stock} & 141 & 141 \\ \hline\text{Retained earnings} & 236 & 157 \\ \hline\text{Total equity} & 377 & 298 \\ \hline \text{Long-term debt} & 172 & 136 \\ \hline\text{Short-term debt} & 29 & 24 \\ \hline\text{Accounts payable} & 18 & 14 \\ \hline\text{Total current liabilities} & 47 & 38 \\ \hline\text{Total liabilities} & 219 & 174 \\ \hline\textbf{Total equity and liabilities} & \bf{596}& \bf{472}\\ \end{array}}$$

We can estimate FCFF and FCFE for 2020 starting with:

• Net income.
• EBIT.
• EBITDA.
• CFO.

### Starting from Net Income

#### Calculating FCFF

\begin{align*}\text{FCFF}&=\text{NI}+\text{NNC}+\text{Int} (1-\text{Tax rate})-\text{FCInv}-\text{WCInv}\\ \\\text{FCInv} &= \text{Gross PPE}_{2020}– \text{Gross PPE}_{2019}\\&=\678-\529=\149\\ \\ \text{WCInv}&=(\text{Accounts receivables}_{2020}+\text{Inventory}_{2020}-\text{Accounts payable}_{2020})\\&-(\text{Accounts receivables}_{2019}+\text{Inventory}_{2019}-\text{Accounts payable}_{2019})\\&=(4+25-18)-(7+21-14)=-3\end{align*}

Therefore,

$$\text{FCFF} = 84.75 + 28 + 9(1-0.25)-149-(-3) = -26.50$$

#### Calculating FCFE

\begin{align*}\text{FCFE}&= \text{NI} + \text{NCC} – \text{FCInv} – \text{WCInv} + \text{Net borrowing}\\ \text{Net borrowing}&= \text{Short and long}-\text{term increase in debt over the year}\\&=(172+29)-(136+24)=41\end{align*}

Therefore,

$$\text{FCFE} = 84.75+28-149-(-3)+41 = 7.75$$

### Starting from EBIT

#### Calculating FCFF

\begin{align*}\text{FCFF}&=\text{EBIT} (1–\text{Tax rate})+\text{Dep}–\text{FCInv}–\text{WCInv}\\&=122(1-0.25) +28-149-(-3) = -26.50\end{align*}

#### Calculating FCFE

\begin{align*}\text{FCFE} &= \text{EBIT} (1-\text{Tax rate}) – \text{Int} (1-\text{Tax rate}) +\text{Dep} -\text{WCInv} + \text{Net borrowing}\\& = 122 (1-0.25) – 9 (1-0.25) + 28 – 149 -(-3)+41 = 7.75\end{align*}

### Starting from EBITDA

#### Calculating FCFF

\begin{align*}\text{FCFF}&=\text{EBITDA} (1 – \text{t}) +\text{Dep}(\text{t})– \text{FCInv} – \text{WCInv}\\&= (162-12)(1-0.25)+28(0.25)-149-(-3) =-26.50\end{align*}

#### Calculating FCFE

\begin{align*}\text{FCFE}& = \text{EBITDA}(1-\text{t}) – \text{Int}(1-\text{t}) + \text{Dep}(\text{t})-\text{FCInv}-\text{WCInv} \\&+ \text{Net borrowing}\\& = (162-12)(1-0.25)-9(0.75)+28(0.25)-149-(-3)+41 = 7.75\end{align*}

### Starting from CFO

#### Calculating FCFF

\begin{align*}\text{CFO}& = \text{Net income} +\text{Depreciation} – \text{WCInv}\\&= 84.75+28–3=115.75\end{align*}

Therefore,

$$\text{FCFF}=115.75+9 (1–0.25) –149=-26.50$$

#### Calculating FCFE

$$\text{FCFE} = 115.75 – 149 + 41 = 7.75$$

## Question

Blue Ltd.’s capital constitutes a debt of $200,000 and equity of$300,000. It recently announced a net income of $275,000. The company managers have invested$90,000 in fixed capital and $60,000 in working capital. The company’s only non-cash expense for the period was$40,000. If the company’s average after-tax interest on debt is 8%, the free cash flow to the firm (FCFF) is closest to:

1. $90,000. 2.$181,000.
3. \$145,000.

#### Solution

\begin{align*}\text{FCFF}&=\text{Net income}+\text{Net non-cash charges}+\text{Interest expense} (1-\text{Tax rate})\\&-\text{Fixed capital investments}-\text{Working capital investments}\\&=\275,000+\40,000+(8\%×\200,000)-\90,000-\60,000\\&=\181,000\end{align*}

Reading 24: Free Cash Flow Valuation

LOS 24 (d) Calculate FCFF and FCFE.

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