### Discussion Issues and Derivations

1. An Intuitive Explanation of FCFE
Intuitively, the free cash flow to equity measures the cash left over for equity investors after all reinvestment needs are met (net capital expenditures and working capital needs) and after all debt commitments have been fulfilled (interest expenses and principal payments).
To arrive at the FCFE, therefore, we start with net income (which is after interest expenses), subtract out net capital expenditures and changes in working capital, and any principal payments that have to be made. This has to be set off against cash inflows that occur because of taking on new debt.
FCFE = Net Income - (Cap Ex - Depr + Chg in WC) - Principal Payment + New Debt Issued.
2. The FCFE when leverage is stable
To go from the general formula to one when leverage is stable, note that in stable leverage all principal payments will have to be covered with new debt issues (if you used equity, the leverage would decrease). In addition, note that the stable debt ratio has to be used to finance the firms reinvestment needs as well. Thus, the new debt issued is:
New Debt Issued = Principal Repayment + (D/(D+E)) (Cap Ex - Depr + Chg in WC)
Substituting back into the full form of the FCFE equation,
FCFE = Net Income - (Cap Ex - Depr + Chg in WC) - Principal Payment + New Debt Issued
FCFE = Net Income - (1 - D/(D+E)) (Cap Ex - Depr + Chg in WC)
This approach is useful when forecasting FCFE into future periods, because there are fewer inputs to estimate.
3. Inputs to FCFE Calculation
The inputs to the FCFE calculation vary depending upon whether we are looking back in time (estimating FCFE in past periods) or whether we are looking forward (estimating FCFE for future periods).
When estimating FCFE in past periods, we use the actual net income, capital expenditure, depreciation and change in non-cash working capital in each period. If the full form of FCFE is being estimated, the new debt issued and principal payments in each period are netted out to arrive at a net debt issued number each year. If the short form is used to estimate FCFE in the past, the net debt issued is divided by the total external financing over the period (net cap ex + Change in working capital) to arrive at a book debt ratio, which can then by plugged back to arrive at the FCFE.
When estimating FCFE into future periods, there is less structure, since all of the inputs have to be estimated. Once the net income, net capital expenditures and working capital changes have been estimated, the external financing requirement can be multiplied either by the book value debt ratio (if that is what the firm is targeting ) or the market value debt ratio. I prefer the market value debt ratio when forecasting into future periods, since it is much more consistent with my view of capital structure (target market valued debt ratios).
4. Estimating FCFE for a financial service firm
The standard definition of free cash flows to equity is straightforward to put into practice for most manufacturing firms, since the net capital expenditures, non-cash working capital needs and debt ratio can be estimated from the financial statements. In contrast, the estimation of free cash flows to equity is difficult for financial service firms, due to several reasons. First, estimating net capital expenditures and non-cash working capital for a bank or insurance company is difficult to do, since all of the assets and liabilites are in the form of financial claims. Second, it is difficult to define short-term debt for financial service firms, again due to the complexity of their balance sheets.
To estimate the FCFE for a bank, we began by by categorizing the income earned into three categories - net interest income from taking deposits and lending them out a higher interest rate, arbitrage income from buying financial claims (at a lower price) and selling financial claims (of equivalent risk) at a higher price and advisory and fee income from providing financial advice and services to firms. For each of these sources of income, we traced the equity investment that would be needed:
Type of Income Net Investment Needed
Net Interest Income Net Loans - Total Deposits
Arbitrage Income Investments in Financial Assets - Corresponding Financial Liabilities