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Contrast what FCFF, FCFE, dividend and residual income models each need as inputs

CFA® Level I · Equities · Discounted Cash Flow (DCF) and Growth Models · EQ.12.a

The idea

Discounted cash flow models differ mainly in which cash flow they discount and at what rate. The dividend discount model uses forecast dividends at the cost of equity, which suits steady payers. The free cash flow to equity model uses cash left for shareholders after investment and net borrowing, FCFE = CFO - FCInv + net borrowing, also at the cost of equity. The free cash flow to firm model uses cash available to all capital providers at the weighted average cost of capital, giving firm value, from which debt is subtracted to reach equity. The residual income model starts from current book value and adds the present value of earnings above the equity charge, RI = (ROE - r) x beginning book value. Matching cash flow and discount rate is what keeps each model consistent.

Formulas

Free cash flow to the firm from operating cash flow

FCFF = CFO + I × (1 − t) − FCInv

FCFF
free cash flow to the firm
CFO
operating cash flow, struck after interest
I
interest paid
t
the tax rate
FCInv
fixed capital investment, spending on plant and equipment

This is the version where interest sits in operating cash flow (US GAAP). If a firm shows interest paid in financing, nothing is added back: FCFF = CFO − FCInv.

Residual income

RI = (ROE − r) × B₀ and V₀ = B₀ + PV of RI

RI
residual income
ROE
return on equity
r
the required return on equity
B₀
book value of equity at the start of the year
V₀
the value of the equity today
PV
present value of the future residual incomes

Residual income is profit above the charge for the owners' capital. Use beginning book value.

A practice question

From the question bank, with the reason each wrong option is wrong.

Free cash flow to the firm is discounted at the:

  1. weighted average cost of capital - correct
  2. required return on equityWhy not: The cost of equity matches FCFE, which is the cash flow left for shareholders only.
  3. yield on government bondsWhy not: A risk-free government yield ignores the risk borne by the providers of capital to the firm.

FCFF is cash available to both debt and equity holders, so it is discounted at the WACC, which blends their required returns. The result is firm value, from which debt is subtracted to find equity value.

A harder one

A company reports cash flow from operations of 900, fixed capital investment of 350 and net borrowing of 120. Its free cash flow to equity is:

  1. 430Why not: Subtracting net borrowing. New borrowing is cash that becomes available to shareholders, so it is added.
  2. 550Why not: Ignoring net borrowing, which gives FCFE only for a firm with no change in its debt.
  3. 670 - correct

FCFE = CFO - FCInv + net borrowing = 900 - 350 + 120 = 670.

The hardest tier

A company pays no dividends and has negative free cash flow because of heavy investment, but it is profitable and has positive book value. The most suitable model is the:

  1. dividend discount modelWhy not: With no dividends there is nothing to discount, so the value would rest entirely on a distant, guessed payout.
  2. FCFE modelWhy not: Negative free cash flow for years pushes nearly all the value into the terminal value, where it is least reliable.
  3. residual income model - correct

The residual income model uses book value and earnings, both available and positive here, so more of the value is recognised early and depends less on a long-dated terminal estimate.

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