DCF review: trace cash flow, terminal value and equity

Check a DCF by following cash from the operating forecast to the terminal year, discounting every amount from its actual date, and completing the bridge from operating value to equity. A correct terminal-value formula does not rescue the wrong cash-flow definition or an undiscounted amount added to today's value.

Match the cash flow with the discount rate

Free cash flow to the firm, or FCFF, is cash available to the capital providers after operating taxes and reinvestment, before debt financing flows. Discount it at a matching weighted average cost of capital. Free cash flow to equity is a different claim and uses a cost of equity. Aswath Damodaran's valuation notes distinguish the firm and equity approaches.

For a simple FCFF build, assume annual operating profit before interest and tax of $100,000, a 25% operating tax assumption, depreciation of $10,000, capital spending of $20,000 and an increase in noncash operating working capital of $15,000. FCFF is 100,000 × (1 − 25%) + 10,000 − 20,000 − 15,000 = $50,000. The tax rate is a teaching input, not a jurisdictional tax estimate.

Check the signs. An increase in operating working capital uses cash in this example; depreciation is added back because it reduced profit without being a current cash payment. Do not deduct interest or loan principal again from this FCFF and then discount it at an enterprise rate. Check that the cash flows and rate use the same currency and nominal or real basis.

Calculate the explicit forecast and terminal amount

Assume a valuation immediately before year one, annual cash flows received at each year-end, a 10% annual discount rate and 2% perpetual growth after year three. Forecast FCFF is $50,000, $60,000 and $70,000. These values and rates are illustrative, not a forecast for a real company.

The terminal cash flow is year four's FCFF: $70,000 × 1.02 = $71,400. Terminal value at the end of year three is $71,400 ÷ (10% − 2%) = $892,500. Its present value is $892,500 ÷ 1.10³ = $670,548.46. The formula starts with the next year's cash flow and places the terminal amount at the end of the explicit period; see Damodaran's DCF teaching materials.

Use the unrounded values when adding the components. The operating enterprise value is $818,181.82 after rounding the final result. Adding the undiscounted $892,500 instead would materially overstate it. Discounting the terminal amount for four years would also be wrong under this convention: year-four cash starts the perpetuity, but terminal value is dated at year three.

Complete the equity bridge

Assume $30,000 excess cash not already included in the operating value, $200,000 debt and $10,000 other non-equity claims. In this simplified bridge:

With an assumed 100,000 relevant shares, that is about $6.38 per share. The share count and claim adjustments must fit the actual security and dilution treatment. Do not add all cash automatically if some is needed to support operations, or subtract a claim already incorporated elsewhere in the cash flows.

Inspect the assumptions that dominate the answer

The discounted terminal amount supplies about 81.96% of operating value in this case. That makes the continuing-business assumptions decisive. Ask whether year-three margins are sustainable, whether capital spending and working capital support growth, and whether a temporary cash release has been carried forward forever.

The perpetual-growth formula requires the discount rate to exceed growth. At 12% rather than 10%, holding year-four cash of $71,400 and growth of 2% fixed, terminal value at its own date falls to $714,000. A complete comparison must also rediscount the explicit and terminal cash flows at 12%; changing only the denominator leaves an inconsistent valuation.

Use the actuals-versus-assumptions guide to check the forecast's starting data, the capital-spending guide for reinvestment mechanics, and the two-driver sensitivity method to show how assumptions move value. A sensitivity range is not a probability interval or a recommendation to buy a security.