Reverse DCF: Method

Reverse DCF: What Growth Does a Price Assume?

What it does

A discounted cash flow (DCF) model normally runs forward: you forecast how fast a company's cash flow will grow, and the model returns a value. The forecast is the hard part, and the answer is only as good as the guess. A reverse DCF runs the same model backward. It takes the one number that is known, today's share price, and solves for the growth rate that would make the model return exactly that price. The result is a description of the price: "this price is consistent with free cash flow growing 8.8 percent a year for ten years". The page does not say whether that growth will happen or what the price should be.

The method

Step 1: the market's value of the business. Market equity value E = P × S, the share price times the shares outstanding. Enterprise value EV = E + net debt, where net debt is debt less cash and investments. Enterprise value is the price of the whole business, whoever finances it; with net cash (negative net debt) it is less than the equity value.

Step 2: the model. Free cash flow (FCF) is cash from operations less capital spending: the cash left for lenders and shareholders. With FCF₀ last year's free cash flow, g the growth rate of the next N years, r the discount rate (the yearly return investors require, the cost of capital) and g_T the terminal growth rate of all later years:

FCF_t = FCF₀ (1 + g)^t for t = 1 … N
TV = FCF_N (1 + g_T) / (r − g_T), the terminal value at year N: the worth, at that date, of a cash flow growing at g_T for ever (the Gordon growth formula)
EV_model(g) = FCF₁/(1 + r) + FCF₂/(1 + r)² + … + FCF_N/(1 + r)^N + TV/(1 + r)^N

Dividing by (1 + r)^t is discounting: 1 received in t years is worth 1/(1 + r)^t today, because that amount invested at r grows to 1 by then. Written in one line, with q = (1 + g)/(1 + r):

EV_model(g) = FCF₀ q (1 − q^N)/(1 − q) + FCF₀ (1 + g)^N (1 + g_T) / [(r − g_T)(1 + r)^N]

Step 3: solve. The implied growth is the g at which EV_model(g) = EV. The equation has no algebraic solution for N above one year, but the model value rises steadily with g, so there is exactly one answer. The page scans g in steps of one point to find the two rates between which the model value crosses the market value, then applies Newton's method (g_next = g − [EV_model(g) − EV]/slope) from the middle of that interval, taking a bisection step if a Newton step leaves it. The trials are tabulated.

Reported with it. The share of value in the terminal term, PV(TV)/EV; the free cash flow of year N that the price assumes; and the implied growth recomputed with the discount rate moved ±1 and ±2 points and the terminal growth ±1 point.

Advanced options. Fade: over the last M of the N years (M at most N − 1) the growth of year N − M + k is g + (g_T − g) k/M, a straight-line decline that reaches g_T in year N; the rate solved for is the starting growth. Revenue and margin: revenue grows at g (with the fade, if any) and FCF_t = revenue_t × m_t, with the margin m_t = m₀ + (m_N − m₀) t/N; the solved rate is then the growth of revenue, and the form works for a company whose cash flow is negative today. Forward check: the same model at a growth you enter, giving (EV_model − net debt)/S per share.

What it assumes

One growth rate for the whole explicit period (or a straight-line fade), then one terminal rate for ever. One discount rate for all years. Cash flows arriving at the end of each year. Last year's free cash flow as a representative starting point. Net debt as the only claim ahead of the shareholders: leases, pensions, preferred stock, minority interests and employee options are left out unless you add them to the net debt. The share count as it stands today.

When it misleads

The answer moves with the discount rate. The discount rate is an input nobody observes. In the default case one point more or less moves the implied growth by more than two points (see the table on the results page). The implied growth is "the growth the price assumes if investors require this return", never the growth alone.

Most of the value is often in the terminal term. When more than half of the value comes from years beyond the explicit period, the result rests on the terminal growth and on r − g_T, a small difference of two estimates. As g_T approaches r the terminal value grows without limit.

An unusual starting year distorts everything. A free cash flow depressed by a recession or a large investment programme produces a high implied growth that is partly just a return to normal; a peak year does the opposite. Share-based pay is a cost that free cash flow does not show. Use the revenue and margin form, or a normalised cash flow, when last year is not representative.

One rate cannot describe every path. Many different growth paths have the same value. The implied rate is the constant-growth equivalent, not a prediction of any year. A longer explicit period lowers the implied rate, a shorter one raises it.

Not for every company. Banks and insurers (whose debt is raw material, so free cash flow and net debt are not meaningful) and companies with no prospect of positive cash flow do not fit the model.

Worked example

The default case uses figures from Apple Inc.'s Form 10-K for the fiscal year ended 30 September 2023, in millions of dollars: shares outstanding 15,553 (15,552,752,000 on the cover, rounded); debt 5,985 + 9,822 + 95,281 = 111,088 and cash and marketable securities 29,965 + 31,590 + 100,544 = 162,099, so net debt = −51,011; free cash flow = 110,543 − 10,959 = 99,584. The share price of 175.00 is a round illustrative figure for the days after the filing, not a quotation; the discount rate of 9 percent and the terminal growth of 3 percent are illustrative.

E = 175 × 15,553 = 2,721,775. EV = 2,721,775 − 51,011 = 2,670,764, or 26.8 times the free cash flow.

Try g = 8.5 percent: the model gives 2,603,764, too low by 67,000. Newton's step moves to 8.836 percent (too high by 864), then to 8.8318 percent, where the model gives 2,670,764.

At g = 8.832 percent: FCF₁ = 99,584 × 1.08832 = 108,379, worth 108,379/1.09 = 99,430 today; FCF₂ = 117,951, worth 99,277; … FCF₁₀ = 232,140, worth 98,058. The ten present values sum to 987,429. TV = 232,140 × 1.03/(0.09 − 0.03) = 3,985,065, worth 3,985,065/1.09¹⁰ = 1,683,335 today. Total 987,429 + 1,683,335 = 2,670,764, the market enterprise value.

So at this price and these rates the model needs free cash flow to grow 8.83 percent a year for ten years, reaching 232,140 (2.33 times the 2023 figure), with 63 percent of the value in the terminal term. With a discount rate of 8 percent the implied growth is 6.33 percent; with 10 percent it is 11.10 percent. For comparison, the free cash flow grew from 92,953 in fiscal 2021 to 99,584 in fiscal 2023, 3.5 percent a year.

A calculator for education and analysis, not investment advice.