CFA Level I · CFA Level I Exam

Discounted Cash Flow (DCF) and Growth Models: formula sheet

Full chapter guide

Key formulas

Single-period DDM: V0 = D1 ÷ (1 + r) + P1 ÷ (1 + r); D1 and P1 both arrive at the end of year 1. Equivalent to (D1 + P1) ÷ (1 + r).
Finite-horizon (multi-period) DDM: V0 = Σ [Dt ÷ (1 + r)^t] for t = 1 to n + Pn ÷ (1 + r)^n; Pn is the expected sale price at the end of year n. Discount it n periods.
General DDM (infinite horizon): V0 = Σ [Dt ÷ (1 + r)^t] for t = 1 to ∞; Value is the present value of all future dividends. Needs a dividend forecast or a growth assumption.
Required return from a one-year price: r = (D1 + P1) ÷ V0 − 1; If V0 is the current market price, this gives the expected return, a holding period return.
Gordon growth value: V0 = D1 ÷ (r − g); Requires r > g. D1 is the dividend expected one year from now, not the dividend just paid.
Next dividend from last dividend: D1 = D0 × (1 + g); Use this when the question gives the most recent dividend D0.
Required return: r = D1 ÷ V0 + g; Dividend yield (on D1) plus growth rate.
Implied growth rate: g = r − D1 ÷ V0; If D0 is given, you can also write g = (V0 × r − D0) ÷ (V0 + D0). This comes from V0 = D0 × (1 + g) ÷ (r − g).
Value at a future time t: Vt = Dt+1 ÷ (r − g); Used as a terminal value in multistage models. Under constant growth, Vt = V0 × (1 + g)^t.
Two-stage DDM (finite high-growth period): V0 = Σ [Dt ÷ (1 + r)^t] for t = 1 to n + Pn ÷ (1 + r)^n; Dt is the forecast dividend in year t. Pn is the terminal value at the end of year n.
Terminal value: Pn = Dn+1 ÷ (r − gL) = Dn × (1 + gL) ÷ (r − gL); Valid only when r > gL. Use the first dividend of the stable stage, not Dn.
High-growth dividends: Dt = D0 × (1 + gS)^t; Applies during the high-growth stage only. After year n, dividends grow at gL.
H-model: V0 = [D0 × (1 + gL) ÷ (r − gL)] + [D0 × H × (gS − gL) ÷ (r − gL)]; H = half the length of the transition period = (length of the linear decline in years) ÷ 2. The first term is the Gordon value; the second is the extra value from above-normal growth. The result is an approximation.
Value as a sum of stages: V0 = PV(stage 1 dividends) + PV(stage 2 dividends) + PV(terminal value); The general idea for a three-stage model. Discount each dividend by its own year.
Retention ratio: b = 1 − dividend payout ratio = (Net income − Dividends) ÷ Net income; Payout ratio = Dividends ÷ Net income. If the question gives dividends per share and EPS, use those.
Sustainable growth rate: g = b × ROE; Assumes constant ROE, constant payout, constant leverage and no new equity issued.
ROE: ROE = Net income ÷ Equity; Use the equity base stated in the question: beginning, average or ending. Check what is given.
DuPont (three-step) ROE: ROE = (Net income ÷ Sales) × (Sales ÷ Total assets) × (Total assets ÷ Equity); Net profit margin × asset turnover × financial leverage.
Growth from DuPont: g = b × net profit margin × asset turnover × financial leverage; Use this to see which driver changes growth.
Gordon growth link: V0 = D1 ÷ (r − g), with D1 = EPS1 × (1 − b); Requires r > g. Using g = b × ROE ties dividends and growth to the same policy.
FCFF from net income: FCFF = NI + NCC + Int × (1 − t) − FCInv − WCInv; NCC = non-cash charges such as depreciation. FCInv = fixed capital investment (capex minus proceeds from asset sales). WCInv = increase in working capital.
FCFF from CFO: FCFF = CFO + Int × (1 − t) − FCInv; Add Int × (1 − t) whenever interest paid is deducted in CFO: always under US GAAP, and under IFRS if interest paid is classified as operating. If IFRS classifies interest paid as financing, do not add it back.
FCFF from EBIT: FCFF = EBIT × (1 − t) + Dep − FCInv − WCInv; Tax is applied to EBIT, so no interest tax shield is included; that is captured in WACC.
FCFF from EBITDA: FCFF = EBITDA × (1 − t) + Dep × t − FCInv − WCInv; Depreciation only matters through its tax shield.
FCFE from FCFF: FCFE = FCFF − Int × (1 − t) + Net borrowing; Net borrowing = debt issued − debt repaid.
FCFE from net income: FCFE = NI + NCC − FCInv − WCInv + Net borrowing; Interest is already deducted in net income, so do not adjust for it.
FCFE from CFO: FCFE = CFO − FCInv + Net borrowing; CFO already includes interest paid under US GAAP, and under IFRS if interest paid is classified as operating. If IFRS interest paid is in financing activities, subtract Int × (1 − t) from CFO to get FCFE.
Firm and equity value: Firm value = Σ FCFFt ÷ (1 + WACC)^t; Equity value = Σ FCFEt ÷ (1 + r)^t; r is the cost of equity. Equity value from FCFF route = Firm value − market value of debt.
Constant growth valuation: Firm value0 = FCFF1 ÷ (WACC − g); Equity value0 = FCFE1 ÷ (r − g); Needs FCFF1 or FCFE1, the next-period flow, and WACC > g (or r > g).
FCFF from net income: FCFF = NI + NCC + Int(1 − t) − FCInv − WCInv; NCC is non-cash charges such as depreciation. FCInv is fixed capital investment. WCInv is the increase in working capital.
FCFF from CFO: FCFF = CFO + Int(1 − t) − FCInv (when interest paid is deducted in CFO); Check where interest paid is classified. If interest is in CFO, add back Int(1 − t). Under IFRS, interest paid may instead sit in financing cash flow. Then CFO is already before interest, so do not add back interest. Adjust only for the tax effect: taxes paid in CFO are lower because of the interest deduction, so subtract Int × t. FCFF = CFO − Int × t − FCInv.
FCFF from EBIT: FCFF = EBIT(1 − t) + Dep − FCInv − WCInv; Use the tax rate on EBIT.
FCFF from EBITDA: FCFF = EBITDA(1 − t) + Dep × t − FCInv − WCInv; Depreciation gives a tax shield.
FCFE from FCFF: FCFE = FCFF − Int(1 − t) + Net borrowing; Net borrowing = new debt issued − debt repaid.
FCFE from net income: FCFE = NI + NCC − FCInv − WCInv + Net borrowing; Interest is already deducted in net income.
FCFE from CFO: FCFE = CFO − FCInv + Net borrowing; Quick route when CFO is given.
Firm value, single stage: Firm value = FCFF₁ ÷ (WACC − g); FCFF₁ = FCFF₀ × (1 + g). Requires WACC > g.
Equity value from firm value: Equity value = Firm value − Market value of debt (+ non-operating cash); Preferred stock is also deducted if present.
Equity value, single stage: Equity value = FCFE₁ ÷ (r − g); r is the cost of equity. FCFE₁ = FCFE₀ × (1 + g).
Terminal value: TVₙ = FCFₙ₊₁ ÷ (discount rate − g_long-run); Value is at time n. Discount it back n periods. Use WACC for FCFF and cost of equity for FCFE.
WACC: WACC = wd × rd × (1 − t) + we × re; Use market-value weights.
CAPM cost of equity: r = Rf + β × (E(Rm) − Rf); (E(Rm) − Rf) is the equity risk premium. Use the rate matching the cash flow currency.
Gordon growth value (DDM): V0 = D1 ÷ (r − g); Needs r > g and constant growth forever. D1 = D0 × (1 + g).
Equity value from FCFE: Equity value = Σ FCFEt ÷ (1 + r)^t; Discount at cost of equity. Constant growth: FCFE1 ÷ (r − g).
Firm value from FCFF: Firm value = Σ FCFFt ÷ (1 + WACC)^t; Constant growth: FCFF1 ÷ (WACC − g).
Equity value from firm value: Equity value = Firm value − Market value of debt (and preferred); Add non-operating cash if it is not already in the cash flows.
WACC: WACC = wd × rd × (1 − t) + wp × rp + we × re; Use target or market-value weights, not book weights.
FCFE from FCFF: FCFE = FCFF − Interest × (1 − t) + Net borrowing; Use when you are given FCFF and debt information.

Quick revision

DDM: value today is the present value of all expected future dividends discounted at the required return on equity.
Gordon Growth Model: P0 = D1 ÷ (r − g), valid only when g is constant forever and r > g.
D1 = D0 × (1 + g). Check which dividend the question gives.
Sustainable growth rate g = retention rate b × ROE, where b = 1 − payout ratio.
Multistage: discount the explicit dividends, then discount the terminal value found at the end of the high-growth stage.
Terminal value at time n = Dn+1 ÷ (r − g), using the stable growth rate after stage one.
FCFF is discounted at WACC and gives firm value. Subtract debt to get equity value.
FCFE is discounted at the required return on equity and gives equity value directly.
FCFF = NI + NCC + Interest × (1 − t) − FCInv − WCInv.
FCFE = FCFF − Interest × (1 − t) + Net borrowing.
Higher r or lower g lowers value, and value is very sensitive when r is close to g.
Use DDM for dividend-paying, stable firms. Use FCFE or FCFF when dividends do not reflect cash generation.

Common mistakes

Leaving out the sale price in a finite holding period question Fix: If the stem gives an end-of-holding-period price, add it as a cash flow in the final year. It stands for the later dividends.
Discounting the final price by one period fewer or more than needed Fix: The year-n price is discounted n periods, the same as the year-n dividend.
Using D0 in the numerator instead of D1. Fix: Always ask whether the dividend is next year's. If it was just paid, multiply by (1 + g) first.
Applying the model when g ≥ r. Fix: Check r > g first. If not, the constant-growth model is not valid for that company.
Forgetting to discount the terminal value Fix: Pn is a value at time n. Divide it by (1 + r)^n and then add it to the present value of the early dividends.
Using Dn instead of Dn+1 in the terminal value Fix: Always grow the last high-growth dividend by (1 + gL) first. Write Dn+1 on your page before dividing.
Using the payout ratio instead of the retention ratio in g = b × ROE. Fix: Always convert: b = 1 − payout. Write b on its own line before multiplying.
Forgetting that g is only sustainable if ROE, payout and leverage stay constant and no new equity is issued. Fix: If a question says the firm issues shares or changes leverage, the formula no longer holds as stated.
Discounting FCFE at WACC or FCFF at the cost of equity. Fix: FCFF is for all capital providers, so WACC. FCFE is for shareholders only, so cost of equity.
Adding back interest to net income when computing FCFE. Fix: Net income is already after interest, which is a real cash cost to shareholders. Only FCFF adds back Int × (1 − t).

Exam tips

Look for the timing words: end of year, at the end of the holding period. They set the exponent on (1 + r).
If the stem gives a sale price, it is almost always meant to be included. Check that you have added it to the final dividend before discounting.
With three options, remove any answer that equals the plain sum of cash flows. A present value must be lower for positive r.
For two or more years, use the cash flow keys rather than discounting by hand. It saves time and avoids rounding slips.
Expect the DDM to be a stepping stone. Questions often build on it with a constant growth or multistage assumption.
Read the wording for D0 versus D1. Examiners often give D0 on purpose.
Eliminate options quickly by checking the denominator: a small r − g should give a large value, so a very low value is likely wrong.
Questions on limitations often ask when the model is unsuitable: no dividends, very high growth, or growth above the required return.