6.2 The three statements as one system

Motivation

Most accounting frauds are inconsistencies between the statements: profits that never become cash, cash that earns no interest, assets that grow without revenue. If you know the identities that must hold, you know where to look.

6.2.1Linking identities#

Setup

Year $t$ ends at date $t$ . Notation:

$A_t$ total assets, $L_t$ total liabilities, $E_t$ book equity.
$NI_t$ net income (profit after tax, PAT). $EBIT_t$ operating profit. $\tau$ tax rate. $Int_t$ interest expense.
$d_t$ net distributions to shareholders: dividends + buybacks − new equity issued.
$NOA_t$ net operating assets: operating assets minus operating liabilities (fixed assets + net working capital). $ND_t$ net debt: debt minus cash and liquid investments.
$CFO, CFI, CFF$ : cash flow from operating, investing and financing activities.

Proposition 6.1Linking identities

Under clean-surplus accounting (every change in equity other than transactions with owners passes through net income):

A_t = L_t + E_t, \tag{6.1}

E_t = E_{t-1} + NI_t - d_t, \tag{6.2}

\text{Cash}_t - \text{Cash}_{t-1} = CFO_t + CFI_t + CFF_t, \tag{6.3}

NOA_t = ND_t + E_t. \tag{6.4}

Proof

(6.1) is the definition of equity as the residual claim. (6.2) is the clean-surplus assumption. (6.3) holds because every cash movement is classified into exactly one of the three activities. For (6.4), split assets into operating assets $OA$ and cash-like financial assets $FA$ , and liabilities into operating liabilities $OL$ (payables, provisions) and debt $D$ . Then (6.1) reads $OA + FA = OL + D + E$ , so $OA - OL = (D - FA) + E$ , which is $NOA = ND + E$ .∎

In Ind AS reporting (Indian Accounting Standards, converged with IFRS), "other comprehensive income" breaks clean surplus slightly (for example actuarial gains on gratuity plans). For valuation the gap is usually small; check the statement of changes in equity.

6.2.2Free cash flows#

Definitionfree cash flows

\begin{aligned} \text{NOPAT}_t &= EBIT_t (1-\tau), \\ \text{FCFF}_t &= \text{NOPAT}_t + \text{D\&A}_t - \text{Capex}_t - \Delta NWC_t, \end{aligned} \tag{6.5}

where $\Delta NWC$ is the increase in non-cash net working capital. Since $NOA$ rises by capex minus depreciation plus the working-capital build, $\text{FCFF}_t = \text{NOPAT}_t - \Delta NOA_t$ : operating profit after tax minus net investment. Free cash flow to equity is

\text{FCFE}_t = \text{FCFF}_t - Int_t(1-\tau) + \Delta ND_t. \tag{6.6}

Proposition 6.2Free cash flow is what capital providers receive

If $NI_t = (EBIT_t - Int_t)(1-\tau)$ (no non-operating items), then

\text{FCFF}_t = \underbrace{Int_t(1-\tau) - \Delta ND_t}_{\text{to lenders, net}} + \underbrace{d_t}_{\text{to shareholders, net}}, \qquad \text{FCFE}_t = d_t.

Proof

$\text{NOPAT}_t = EBIT_t(1-\tau) = NI_t + Int_t(1-\tau)$ . From (6.4), $\Delta NOA_t = \Delta ND_t + \Delta E_t$ , and from (6.2), $\Delta E_t = NI_t - d_t$ . Hence $\text{FCFF}_t = NI_t + Int_t(1-\tau) - \Delta ND_t - NI_t + d_t = Int_t(1-\tau) - \Delta ND_t + d_t.$ Substituting in (6.6) gives $\text{FCFE}_t = d_t$ .∎

Two consequences. First, valuing the firm by discounting FCFF at the weighted cost of all capital, then subtracting net debt, is the same exercise as valuing the equity by discounting what shareholders receive, if the discount rates are consistent. Second, "profit" that never appears as FCFF or as an increase in genuinely realisable net assets is not value. A company that reports rising PAT while CFO stays flat is building receivables, inventory or capitalised costs. Section 6.8 turns this into a score.

6.2.3From enterprise value to equity#

Enterprise-value bridge Equity value $= EV - \text{debt} + \text{cash and liquid investments} - \text{minority interests} + \text{non-operating assets}$ (stakes in associates, surplus land). In Indian groups, listed subsidiaries and cross-holdings make this bridge material; value them at market and apply a holding-company discount only if you can justify one.

Worked example

A listed consumer company reports (₹ cr): EBIT 400, D&A 60, capex 150, increase in working capital 30, interest 40, net new borrowing 50. Use the concessional corporate tax rate of 25.17% (22% base rate plus surcharge and cess; verify the current rate). Then NOPAT $= 400 \times 0.7483 = 299.3$ , FCFF $= 299.3 + 60 - 150 - 30 = 179.3$ , and FCFE $= 179.3 - 40 \times 0.7483 + 50 = 199.4$ . By Proposition 6.2 the company must, in aggregate, have paid ₹199.4 cr to shareholders or added that much to cash (in which case net debt rose by less than the ₹50 cr of new borrowing; redo the identity with cash inside $ND$ ). If the AR shows dividends of ₹50 cr and no buyback, ask where the other ₹149 cr went. The answer is usually in the cash balance; in a Satyam (6.12.2), the cash did not exist.

Practitioner notes

Ind AS 116 (leases) moved operating leases onto the balance sheet from FY20. Lease payments now sit partly in financing cash flow, which flatters CFO for retailers and airlines. For comparability, subtract lease payments from CFO or treat lease liabilities as debt consistently in both FCFF and WACC.