Discounted Cash Flow Valuation

Suppose someone offers to sell you an apple tree. How much is it worth? Not what the wood would fetch, and not what the neighbour paid for hers. It is worth the apples it will produce for the rest of its life — except that a crate of apples twenty years from now is worth less to you today than a crate this afternoon, because you would have to wait, take the risk of a bad season, and give up whatever else you could have done with the money.

Discounted cash flow valuation is that reasoning applied to a business. Forecast the cash it will produce, shrink each future amount to reflect how far away and how uncertain it is, and add up what is left. Everything else in valuation — multiples, comparables, rules of thumb — is a shortcut for this.

The formula, one symbol at a time

$$V_0 = \sum_{t=1}^{N} \frac{CF_t}{(1+r)^t} + \frac{TV_N}{(1+r)^N}.$$

Read it left to right. $V_0$ is what the business is worth today. $CF_t$ is the cash it produces in year $t$. $r$ is the discount rate, the annual return an investor demands for taking this risk. Dividing by $(1+r)^t$ is the discounting step: the further out the year, the bigger the denominator, the smaller the contribution. $TV_N$ is the terminal value, one lump standing in for every year beyond the forecast horizon $N$, because nobody can forecast year 43 individually.

Said plainly: add up every future pound of cash, each one shrunk by how long you have to wait for it.

The compounding explorer below is this machinery running forwards. Push the rate and years sliders and watch how violently the exponent bites — a DCF simply runs the same curve in reverse, so the same sensitivity you see here is the sensitivity your valuation inherits.

The three inputs

Cash flows. Normally unlevered free cash flow, the cash available to lenders and shareholders together, forecast for five to ten years.

The discount rate. For unlevered cash flows this is the weighted average cost of capital: the blended return demanded by everyone who funded the business. Higher risk, higher $r$, lower value.

Terminal value. Usually the Gordon growth form, which assumes cash grows forever at a modest rate $g$:

$$TV_N = \frac{CF_N \,(1+g)}{r - g}.$$

In words: a cash flow growing at $g$ forever, discounted at $r$, is worth next year's cash divided by the gap between the two rates. That gap is small, so the terminal value is enormous and extremely touchy — the single most fragile number in the whole exercise.

A worked example

A company will generate 100 of free cash flow a year for five years. Its WACC is 10% and cash is assumed to grow at 2% forever afterwards. Discount factors are $1/1.1^t$: 0.909, 0.826, 0.751, 0.683, 0.621.

Multiplying gives present values of 90.9, 82.6, 75.1, 68.3 and 62.1, summing to 379.1. Terminal value at the end of year five is $100 \times 1.02 / (0.10 - 0.02) = 1275$, and discounting that back gives $1275 \times 0.621 = 791.7$.

Total enterprise value is $379.1 + 791.7 = 1170.8$. Subtract net debt of 250 and equity is worth 920.8; across 100 million shares that is about $9.21 each.

Look at the split: 792 of the 1,171 — 68% — comes from the terminal value, a single formula about a future nobody forecast.

Second example: what one percentage point does

Same company, discount rate cut from 10% to 9%. The five explicit years rise only slightly, from 379.1 to 389.0. But terminal value becomes $102 / 0.07 = 1457$, and its present value climbs to 947.1. Enterprise value is now 1336.1, equity 1086.1, and the share price $10.86.

A one-point change in an input nobody can pin down moved the answer by 18%. Nothing about the business changed.

Common pitfalls

• Discounting the wrong cash flow with the wrong rate. Unlevered cash flows go with WACC and give enterprise value; equity cash flows go with the cost of equity and give equity value. Mixing them double-counts debt.
• Forgetting the bridge. Enterprise value is not share price. Subtract net debt, then divide by a diluted share count.
• Hockey-stick forecasts. Margins that expand every single year until they hit the terminal formula are how a target price gets reverse-engineered from a conclusion.
• Ignoring mid-year timing. Cash arrives through the year, not on 31 December. The mid-year convention lifts a typical valuation by a few percent.