A and B walk through the Free Cash Flow to Equity model, a discounted cash flow method that calculates cash available to shareholders after operating costs, taxes, interest, and capital investments. The tutorial covers the step-by-step calculation from revenue to after-tax income, adjustments for depreciation and working capital changes, and terminal value using the perpetuity-with-growth formula. An R code example shows how a year-5 FCFE of $100 with a 3% growth rate and 15% cost of equity yields a terminal value of roughly $858.
Chapters
Now we turn to discussing the free cash flow to equity model in more detail. The first DCF approach you will learn is the Free Cash flow to equity or FCFE model. FCFE is cash flow after you have paid off all your suppliers, employees, lenders and taxes, as well as after deducting amounts you need for additional capital investments and working capital. In this course, for simplicity, we will assume new borrowings offset debt repayments. So free cash flows are cash flows you can take away from the firm and give to the shareholders without affecting the operations and growth prospects of the firm.
The first step in an FCFV calculation is to calculate the after tax income of the company. We first start with the firm's revenues or sales and subtract the cost of goods sold. The difference is called the gross profit. We then subtract operating expenses from the gross profit to arrive at operating income. This is sometimes called earnings before interest taxes or ebit.
Then we subtract interest from EBIT to get to pre tax income. Then we subtract taxes from pre tax income to get to after tax income. After tax income is calculated using accrual accounting. This means that there were some components of after tax income that are non cash items. A common non cash item is depreciation and amortization.
What is depreciation? When you buy a tangible asset, say a machine.
As the machine gets older, a portion of its value erodes. This erosion in value is is what.
Depreciation attempts to capture. Amortization is a similar concept, but it generally applies to intangible assets. Depreciation and amortization reduces taxable income, which is why we need to include it to calculate after tax income. But the cash used to acquire the asset that is being depreciated or amortized has already been spent in the past. So we add it back.
Another adjustment is the additional capital investments the firm needs to fund the growth in its projections. If the firm had to buy a new machine next year, for example, we have to spend cash in year one to buy that machine. That would be a drain on our year one cash and should be subtracted to get to our free cash flow. The last common adjustment is the increase in non cash working capital. For valuation purposes, working capital is equal to non cash current assets like accounts receivable in inventory, less non interest bearing current liabilities like accounts payable. Increasing working capital means that you need to invest more cash. The projections are only for a finite period of time of between five to 10 years typically.
But firms are assumed to have indefinite lives. So the value of the firm should account for for the cash flows the firm receives beyond the five or ten year projection period. The terminal value is commonly estimated using the Perpetuity with Growth model. The model takes the FCFE the year after the end of the forecast period and divides it by the difference between the cost of equity and the pgr. This mathematical trick accounts for all cash flows into perpetuity growing at a constant rate.
Let's go through an example of coding this in R, suppose you have the FCFE in the fifth year of the forecast period as $100. Also assume that the PGR is 3% and cost of equity is 15%. Then in R, we need to first grow the year 5 FCFE by the PGR for one year, then divided by the difference of the cost of equity and perpetuity growth rate to get to $858. Let's.
