15.1 DCF Structure, WACC, and Mid-Year Convention

Why DCF Structure Matters for FMVA

The 2026 FMVA core path splits discounted-cash-flow work across DCF Valuation Modeling Fundamentals and Applied DCF Valuation Modeling. Together with Introduction to Business Valuation, that cluster is the valuation slice of the final (about 10% of exam weight, sitting on the finance domain that already tested CAPM and WACC). A DCF on the exam is a structure-plus-arithmetic task: forecast unlevered free cash flow (UFCF) from a three-statement model, discount it at the weighted average cost of capital (WACC), add terminal value, and land on enterprise value (EV). This section builds the explicit-period engine, the WACC that discounts it, and the mid-year convention. Section 15.2 adds terminal value and the equity bridge.

CFI's study emphasis for this pair of cores is consistent: know CAPM, know WACC, know how a DCF is wired, and know the mid-year convention. Those four items show up in multiple-choice stems and in Excel case studies. Elective leveraged-buyout or deal-process models are required for credential eligibility but are not tested on the final.

From a 3-Statement Model to a 3–5+ Year UFCF Forecast

A DCF does not invent cash flow in a vacuum. UFCF is a derived schedule from the three-statement model you already built: EBIT from the income statement, tax computed as if unlevered, add-back of depreciation and amortization, the change in operating net working capital, and capex. Chapter 14 locked the formula:

UFCF = NOPAT + D&A − capex − ΔNWC

with NOPAT = EBIT × (1 − t).

The explicit forecast period is typically three to five or more years. Three years is the minimum you should be ready to compute by hand on a timed item. Five years is the workhorse in CFI-style models. Stretch to seven or ten only when the firm is still mid-ramp — negative UFCF, rising margins, heavy growth capex — and is not yet in a state you would capitalize in perpetuity. The test is not "five because the template has five columns." The test is: by the last explicit year, are growth, margin, and reinvestment stable enough that a terminal-value formula is not a lie?

Worked stub — Alder Coatings, figures in $ millions, rounded. Last historical year (Year 0) had revenue of $1,000 million. The three-statement forecast grows revenue 8%, 7%, 6%, 5%, then 4%; EBIT margin expands from 15.5% toward 16.3%; the tax rate is 25%; net working capital stays at 12% of revenue so ΔNWC tracks growth rather than a one-off inventory spike.

Check Year 1: 125 + 42 − 10 − 55 = 102. Capex exceeds D&A in the early years (growth capex). By Year 5 they have nearly converged (55 versus 52), which is the kind of steady-state signal terminal value wants. Do not discount EBITDA as if it were cash. Do not drop ΔNWC. Do not start from net income and call the result UFCF — that path already deducted interest and will not pair with WACC.

WACC as the Discount Rate, with Re from CAPM

CFI's WACC is:

WACC = (E/V) × Re + (D/V) × Rd × (1 − T)

If preferred is material, add (P/V) × Rp with no (1 − T) shield. E, D, and P are market values; V is their sum. Rd is yield to maturity, not the coupon. Re comes from the capital asset pricing model (CAPM):

Re = Rf + β × (Rm − Rf)

Alder Coatings' market stack for the rate: equity market cap $1,200 million, debt at market $800 million, no preferred inside WACC. V = $2,000 million. E/V = 60%, D/V = 40%. Case inputs: Rf = 4.0%, levered beta = 1.60, equity risk premium = 5.0%, so Re = 4.0 + 1.60 × 5.0 = 12.0%. Rd = 6.0%. Statutory tax rate T = 25%.

WACC = 0.60 × 12.0% + 0.40 × 6.0% × (1 − 0.25) = 7.20% + 1.80% = 9.00%.

That 9% is the rate this chapter uses for every present-value cell. Pairing rules from Chapter 3 still apply: UFCF with WACC lands on enterprise value. Discounting the same UFCF at Re would understate EV because Re is larger than WACC. Discounting levered free cash flow to equity (FCFE) at WACC mixes a residual cash flow with an all-capital rate. A small preferred claim will appear in the equity bridge in section 15.2; if that preferred were large relative to V, it would also belong here as an unshielded WACC slice.

Nominal with nominal. If the three-statement forecast includes inflation in revenue and costs, WACC is a nominal rate (Rf is a nominal Treasury yield). Discounting inflation-inclusive cash flows at a real rate overstates value. Discounting real (inflation-stripped) cash flows at a nominal WACC understates it. On the FMVA final, unless a stem says "real," treat both the cash flows and the 9% as nominal.

Year-End versus Mid-Year, and Why XNPV Is Better

The bar chart is the timing drill in this section, not Alder's five-year stub. Year-end convention assumes each year's UFCF arrives on fiscal year-end (think December 31). Discount factors are 1 / (1 + WACC)^1, 1 / (1 + WACC)^2, 1 / (1 + WACC)^3, and so on. That is conservative: you delay every dollar to the last day of the year.

Mid-year convention assumes cash arrives throughout the year, so the average dollar arrives at the midpoint. Exponents become 0.5, 1.5, 2.5, …. CFI expects you to know this shift and to apply it consistently to explicit cash flows and terminal value (the next section's trap). Algebraically, the mid-year present value of a year-end schedule equals the year-end present value times (1 + WACC)^0.5. You can either change every exponent or multiply the finished year-end EV by the square root of one plus WACC. Do not do both.

Worked Comparison at 9%: Three Years of UFCF

To isolate timing, take three round unlevered cash flows — $120, $135, and $150 million — and discount them at 9%. Alder's five-year stub continues in section 15.2; this three-year strip is the exam-style timing drill.

(1.09)^2 = 1.1881 and (1.09)^3 = 1.295029. Square root of 1.09 = 1.04403, so (1.09)^1.5 = 1.13799 and (1.09)^2.5 = 1.24041.

Year-end

Mid-year

Cross-check: 339.55 × 1.04403 = 354.50. Mid-year is $14.95 million, or about 4.4%, higher than year-end — not a small rounding difference once terminal value is layered on. On a case study, if the stem says cash flows occur evenly through the year or "use the mid-year convention," the 0.5 / 1.5 / 2.5 exponents are required. If the stem is silent and the template uses Year 1, 2, 3 factors, stay on year-end. Do not mix: Year 1 at 0.5 and Year 2 at 2.0 is an integrity error.

Alder Year 1–3 UFCF of 102, 117, and 128 would follow the same exponents at the same 9%. The round 120 / 135 / 150 strip exists so you can reproduce the $339.55 versus $354.50 totals without a spreadsheet in under two minutes — CFI's pacing guidance is under three minutes per typical multiple-choice item.

XNPV with Actual Dates

Even mid-year is an approximation. The better Excel tool is XNPV, which CFI frequently ranks as its #1 Excel formula. XNPV(rate, values, dates) discounts each cash flow by the actual day count from the valuation date. If you value Alder on 30 June 2026 and the cash flows are modeled at each 31 December, Year 1 is only about a half-year away — XNPV will use 184/365, not a blanket 0.5 or 1.0. A 15 March close with a 31 December cash-flow flag is neither a clean year-end nor a clean mid-year; XNPV is the function that respects that calendar.

XIRR is the sibling that solves for the rate given dated cash flows. NPV and IRR assume equal periods starting one period from today; they mis-state value when the first "year" is a stub or when you have a mid-year close. For the FMVA Excel case, if dates sit on the sheet, XNPV beats NPV. If the sheet is a clean annual model with a convention toggle, use (1 + WACC)^(-t) with t = 1, 2, 3 or 0.5, 1.5, 2.5.

Pairing, Integrity, and Exam Traps

Traps the final likes:

• Discounting UFCF at Re (too high a rate on an all-capital cash flow → EV too low).
• Using book E and D in WACC, then discounting market cash flows.
• Applying (1 − T) to preferred or to Re.
• Using the coupon as Rd when yield to maturity is given.
• Year-end factors in a mid-year case, or mid-year on explicit years but year-end on terminal value.
• Mixing real growth with a nominal WACC.
• Treating the undiscounted sum of five years of UFCF as the value of the firm — you have not discounted, and you have not added terminal value.

The next section puts Alder's five UFCF years together with Gordon and exit-multiple terminal values, then bridges EV to a per-share number. Do not jump from Year 1 UFCF of $102 million to a price target. The explicit period is an input. Timing (year-end, mid-year, or XNPV) is a modeling choice you must state. Terminal value is usually most of the answer.