6.4 Growth, reinvestment and return on capital

Motivation

As a director you know growth costs money: hiring ahead of revenue, inventory, capex. The same holds for a listed company, and the price of growth is set by the return earned on the capital it consumes. This section makes that exact.

6.4.1Growth from reinvestment#

Setup

Let $IC_t$ be invested capital ( $= NOA_t$ ), $\text{NOPAT}_t$ after-tax operating profit, net investment $I_t = IC_t - IC_{t-1}$ , reinvestment rate $RR = I_t/\text{NOPAT}_t$ , and return on new invested capital $\text{RONIC}$ : each rupee invested in year $t$ adds RONIC rupees of NOPAT from year $t+1$ onward. In steady state we write ROIC for RONIC.

Proposition 6.5Growth equals reinvestment rate times return

If the reinvestment rate and RONIC are constant, NOPAT grows at

g = RR \times \text{RONIC}. \tag{6.10}

The equity analogue is $g_{EPS} = b \times ROE$ , with $b$ the retention ratio.

Proof

$\text{NOPAT}_{t+1} = \text{NOPAT}_t + \text{RONIC}\cdot I_t = \text{NOPAT}_t(1 + \text{RONIC}\cdot RR)$ .∎

Proposition 6.6Value-driver formula

If NOPAT grows at constant $g < W$ funded by reinvestment at constant RONIC, the value of operations is

V_0 = \frac{\text{NOPAT}_1\left(1 - \dfrac{g}{\text{RONIC}}\right)}{W - g}. \tag{6.11}

Proof

By (6.10) the reinvestment rate is $RR = g/\text{RONIC}$ , so $\text{FCFF}_t = \text{NOPAT}_t(1 - RR) = \text{NOPAT}_1(1+g)^{t-1}(1 - g/\text{RONIC})$ . This is a growing perpetuity with first flow $\text{NOPAT}_1(1-g/\text{RONIC})$ ; apply (6.8).∎

This is the "key value driver formula" of Koller, Goedhart & Wessels (ch. 3). It says that value depends on three things only: profits, growth, and the return on the capital that growth consumes.

6.4.2When growth creates value#

Proposition 6.7Growth creates value iff ROIC > WACC

Holding $\text{NOPAT}_1$ and $W$ fixed, for $g < W$ ,

\frac{\partial V_0}{\partial g} = \frac{\text{NOPAT}_1\,(1 - W/\text{RONIC})}{(W-g)^2}, \tag{6.12}

which is positive if $\text{RONIC} > W$ , zero if $\text{RONIC} = W$ , and negative if $\text{RONIC} < W$ . Equivalently,

V_0 = \underbrace{\frac{\text{NOPAT}_1}{W}}_{\text{no-growth value}} + \underbrace{\frac{\text{NOPAT}_1}{W}\cdot\frac{g\,(\text{RONIC} - W)}{\text{RONIC}\,(W-g)}}_{\text{value of growth}}. \tag{6.13}

Proof

Write $V(g) = N(1 - g/R)/(W-g)$ with $N = \text{NOPAT}_1$ , $R = \text{RONIC}$ . By the quotient rule, $V'(g) = N\,\frac{-(1/R)(W-g) + (1 - g/R)}{(W-g)^2} = N\,\frac{1 - W/R}{(W-g)^2}$ , since the $g/R$ terms cancel. The denominator is positive, so the sign is that of $R - W$ . For (6.13), put the right-hand side over the common denominator $RW(W-g)$ : the numerator is $N[R(W-g) + g(R-W)] = N[RW - gW] = NW(R-g)$ , so the sum equals $N(R-g)/(R(W-g)) = N(1-g/R)/(W-g)$ .∎

When $\text{RONIC} = W$ , $V_0 = \text{NOPAT}_1/W$ whatever the growth: growth that earns exactly its cost of capital is worthless. When $\text{RONIC} < W$ , growing faster destroys value; the faster, the worse.

6.4.3Same growth, different returns#

Worked example

₹500 cr of next-year NOPAT, WACC 12%, growth 8%:

RONIC	Reinvestment rate $g/\text{RONIC}$	FCFF$_1$	Value (₹ cr)	Implied EV/NOPAT
30%	26.7%	366.7	9,166.7	18.3×
12%	66.7%	166.7	4,166.7	8.3×
8%	100%	0	0	0

The same 8% growth is worth ₹9,167 cr, ₹4,167 cr or nothing, depending on the return on the capital it uses. In the third row the company reinvests every rupee it earns and pays nothing out, forever. This is many Indian infrastructure and commodity businesses in the 2003–08 capex boom (6.10).

Economic profit Define EVA (economic value added) $= (\text{ROIC} - W)\times IC_{t-1}$ . Under the assumptions of 6.6, value of operations $= IC_0 + \text{PV(future EVA)}$ ; you will prove this in Problem 6.5. A business trades above invested capital only if it is expected to earn above its cost of capital.

Practitioner notes

Distinguish ROIC on existing capital from RONIC. A franchise like an FMCG brand can have 60%+ ROIC on historical capital and a much lower return on a new adjacent category. The formula needs RONIC.
Indian reported ROCE often includes surplus cash in capital employed, which understates operating returns for cash-rich IT companies and overstates them for firms with large off-balance-sheet obligations. Recompute.
For banks and NBFCs replace ROIC/WACC with ROE/cost of equity, and capital with book equity (6.6, justified P/B).