Growth has to be paid for with reinvestment. The value driver formula makes the return on that reinvestment explicit, and shows what the plain Gordon growth model assumes about it.
The value driver formula sets the terminal value as next year's NOPAT times one minus growth over the return on new invested capital, divided by WACC less growth: TV = NOPAT × (1 − g ÷ RONIC) ÷ (WACC − g). On an illustrative 6,000,000 of NOPAT at a 9.0 per cent WACC and 2.5 per cent growth, it gives 66,666,667 if new investment only earns its cost of capital, against the 78,461,538 a Gordon growth on the last forecast cash flow produces. The Gordon figure is 17.7 per cent higher, because of an assumption it makes without saying so.
Worked in full in Business Valuation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The formula is the one popularised by McKinsey's Valuation, and it exists to tie growth to the investment that pays for it. A business cannot grow its profit 2.5 per cent a year for ever without spending something to do it, and how much it must spend depends on what each new dollar earns. The plain Gordon growth model, applied to the final forecast year's free cash flow, carries that year's reinvestment into perpetuity and so quietly fixes the return on new capital at whatever that ratio implies.
| Input | Value |
|---|---|
| NOPAT in the first year after the forecast | 6,000,000 |
| Net reinvestment in the last forecast year, share of NOPAT | 15.0% |
| WACC | 9.0% |
| Perpetual growth | 2.5% |
| Years to discount the terminal value | 5 |
Net reinvestment is capital expenditure less depreciation plus the increase in working capital, the same lines as in the unlevered free cash flow build. NOPAT is operating profit after tax on an unlevered basis.
Step 1: what the Gordon version assumes. Free cash flow is NOPAT less reinvestment, 6,000,000 × (1 − 15.0%) = 5,100,000, and the Gordon growth terminal value is 5,100,000 over 6.5 per cent, or 78,461,538. Growth is reinvestment rate times the return on new capital, so this pair implies a RONIC of 2.5% ÷ 15.0% = 16.67 per cent, for ever, nearly twice the cost of capital.
Step 2: choose RONIC, then derive the reinvestment.
Reinvestment rate = g ÷ RONIC = 2.5% ÷ 9.0% = 27.78%
Free cash flow = 6,000,000 × (1 − 27.78%) = 4,333,333
TV = 4,333,333 ÷ (9.0% − 2.5%) = 66,666,667
Excel: =NOPAT*(1-g/RONIC)/(WACC-g)
When RONIC equals WACC the answer is exactly NOPAT over WACC, 6,000,000 ÷ 9.0%, with no growth term left in it. Growth that earns only its cost of capital creates no value, so the growth rate drops out. Discounted over five years at 9.0 per cent, a factor of 1.538624, the terminal value is worth 43,328,759 today against 50,994,616 for the Gordon version, a difference of 7,665,857 in enterprise value.
| RONIC | Reinvestment | FCF | Terminal value | TV / NOPAT | vs Gordon |
|---|---|---|---|---|---|
| 9.00% | 27.78% | 4,333,333 | 66,666,667 | 11.11x | −15.0% |
| 12.00% | 20.83% | 4,750,000 | 73,076,923 | 12.18x | −6.9% |
| 16.67% | 15.00% | 5,100,000 | 78,461,538 | 13.08x | 0.0% |
| 20.00% | 12.50% | 5,250,000 | 80,769,231 | 13.46x | 2.9% |
| 30.00% | 8.33% | 5,500,000 | 84,615,385 | 14.10x | 7.8% |
The highlighted row is the Gordon answer, which is the value driver formula with RONIC set, by accident, at 16.67 per cent. Whether that is right is a question about the business: a franchise with pricing power may keep earning well above its cost of capital on new investment; a contractor in a competitive market probably will not. A common middle course is RONIC equal to WACC on new investment while the existing capital keeps its current return, which is what the 66,666,667 row assumes for the increment.
| Growth | RONIC 9.00% | RONIC 12.00% | RONIC 16.67% |
|---|---|---|---|
| 1.5% | 66,666,667 | 70,000,000 | 72,800,000 |
| 2.5% | 66,666,667 | 73,076,923 | 78,461,538 |
| 3.5% | 66,666,667 | 77,272,727 | 86,181,818 |
Growth is worth something only to the extent that RONIC exceeds WACC. At 9 per cent the column does not move at all; at 16.67 per cent two points of growth add 13,381,818. That is why the argument over the perpetual growth rate, which decides most of the gap between a DCF and a multiple, cannot be settled without saying what return the growth earns.
The worst version is growing NOPAT, or EBITDA less tax, with no reinvestment at all. That gives 6,000,000 over 6.5 per cent, 92,307,692, which is 38.5 per cent above the RONIC-equals-WACC value and implies an infinite return on new capital: the company grows for ever without spending. It usually enters a model when depreciation is set equal to capital expenditure in the final year and working capital is held flat, which looks prudent and is the opposite. The milder version is the one above: copying the last forecast year's ratios into perpetuity without checking the RONIC they imply.
The terminal value block and its share of the answer are in the free workbook for this case, with the growth rate each method implies solved in closed form.
One you can defend for a mature business, often equal to WACC on new investment unless the company has durable pricing power. At RONIC equal to WACC growth adds nothing: 6,000,000 of NOPAT at 9.0 per cent gives 66,666,667 whatever the growth rate. At 12.00 per cent and 2.5 per cent growth it gives 73,076,923.
Divide the perpetual growth rate by the reinvestment rate, net investment as a share of NOPAT, in the cash flow being capitalised. A 2.5 per cent growth rate on a cash flow after 15.0 per cent reinvestment implies a RONIC of 16.67 per cent for ever, nearly twice a 9.0 per cent WACC.
Each dollar reinvested earns exactly what investors require, so the present value of the extra profit equals the dollar spent. The value driver formula then reduces to NOPAT divided by WACC: 6,000,000 over 9.0 per cent is 66,666,667 at 1.5, 2.5 or 3.5 per cent growth alike.
This article is one calculation from Business Valuation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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