Business 200Lesson 10 of 1515 min

Calculating DCF Results — Discounting, the EV→Equity Bridge, and Diluted Shares

Building the forecast and estimating WACC are only the inputs. The calculation stage — discounting explicit-period FCFFs, adding terminal value, bridging from enterprise value to equity value, and dividing by diluted shares — is where models break in subtle ways. McKinsey's Chapter 12 details the mid-year convention, the stub period, and the exact mechanics of converting EV to per-share intrinsic value.

What you'll learn
  • Apply the mid-year discount convention and explain why it better reflects continuously generated cash flows than end-of-year discounting
  • Compute enterprise value as the sum of PV of explicit-period FCFFs plus PV of terminal value
  • Execute the EV-to-equity bridge by adding non-operating assets and subtracting all debt claims and minority interests
  • Calculate diluted shares outstanding using the treasury stock method for options and warrants
  • Identify and correct the most common mechanical errors in the discounting and bridge calculations

Discounting Mechanics — Mid-Year Convention and Explicit Period

Explicit Period — Mid-Year Convention (WACC=10%)
Factor = 1/(1.10)^(t−0.5)
Y1$85M0.953$81.0M
Y2$97M0.867$84.1M
Y3$110M0.788$86.7M
Y4$123M0.716$88.1M
Y5$136M0.651$88.6M
PV Explicit Period$428.5M
TV = $136M×1.03/(10%−3%)$2040M÷(1.10)^5$1266.8M
Enterprise Value$1695.3M
TV = $1266.8M = 74.7% of EV — typical for growing businesses
EV → Equity Bridge ($M)
Enterprise Value (Operating)$1695M
+ Cash & Investments$120M
+ NOLs (PV)$30M
− Total Debt($450M)
− Capital Leases($55M)
− Pension Deficit($80M)
− Minority Interests($40M)
= Equity Value$1220M
÷ Diluted Shares (73M) =
$16.72 per share
Treasury Stock Method — Diluted Share Count
70.0M
Basic Shares
From 10-K
+1.56M
In-Money Options (net)
TSM: issued − repurchased
+1.5M
Unvested RSUs
All dilutive ($0 exercise)
73.06M
Diluted Total
Used in per-share calc

The DCF calculation requires discounting each year's free cash flow back to the valuation date. The discount factor for year t is 1 / (1 + WACC)^t — but this assumes all cash flows arrive at the end of the year. In reality, businesses generate cash throughout the year. The mid-year convention corrects for this by discounting as if cash flows arrive at the midpoint: discount factor = 1 / (1 + WACC)^(t−0.5). For the terminal value (which is computed at the end of year T), the discount factor remains 1 / (1 + WACC)^T.

YearFCFF ($M)End-Year PV FactorEnd-Year PV ($M)Mid-Year PV FactorMid-Year PV ($M)Difference
Year 1$1001/(1.10)^1 = 0.909$90.91/(1.10)^0.5 = 0.953$95.3+$4.4
Year 2$1001/(1.10)^2 = 0.826$82.61/(1.10)^1.5 = 0.867$86.7+$4.1
Year 3$1001/(1.10)^3 = 0.751$75.11/(1.10)^2.5 = 0.788$78.8+$3.7
Year 4$1001/(1.10)^4 = 0.683$68.31/(1.10)^3.5 = 0.716$71.6+$3.3
Year 5$1001/(1.10)^5 = 0.621$62.11/(1.10)^4.5 = 0.651$65.1+$3.0
Sum (5-year PV)$379.0$397.5+$18.5 (+4.9%)

When a valuation date falls mid-year (e.g., June 30 valuation for a December 31 fiscal year), the first period's cash flow must be discounted for only half a year (the 'stub'). This applies in: (1) M&A transactions where deal close is expected mid-year; (2) any live valuation done at a non-fiscal-year-end date. McKinsey's guidance: annualize the partial year's FCFF proportionally, then apply the stub discount factor. Example: June 30 valuation with WACC = 10%, Year 1 FCFF = $100M (full year). Stub FCFF = $100M × 0.5 = $50M (H2 only). Stub discount factor = 1 / (1.10)^0.25 (because H2 midpoint is 3 months from valuation date). Forgetting the stub period overstates PV by pulling forward future cash flows.

Enterprise Value — Explicit Period + Terminal Value

Enterprise Value Calculation

EV = Σ [FCFF_t / (1+WACC)^(t−0.5)] + TV_T / (1+WACC)^T

Sum uses mid-year convention for explicit period FCFFs; terminal value is discounted at full T years since TV is computed at end of forecast period

ComponentYear 1Year 2Year 3Year 4Year 5Terminal
FCFF$85$97$110$123$136
Terminal Value$2,040 (= $136 × 1.03 / (10%−3%))
Discount Factor (mid-year for FCFFs; Year 5 for TV)0.9530.8670.7880.7160.6510.621
PV of Cash Flow$81.0$84.1$86.7$88.1$88.6$1,266.8
Cumulative PV$81.0$165.1$251.8$339.9$428.5$1,695.3

In the above model, TV PV = $1,266.8M of a total EV of $1,695.3M = 74.7% of enterprise value. This is typical — for a growing business, 60%–80% of DCF value comes from terminal value. This concentration is not a flaw in the method; it is the mathematical consequence of the fact that most business value lies in cash flows beyond a 5-year explicit period. But it does mean: small changes in the terminal value assumption (WACC, g, or ROIC in the KVD formula) have enormous impact on EV. This is precisely why terminal value sensitivity analysis is mandatory.

EV to Equity Bridge — From Enterprise Value to Per-Share Value

Enterprise value is the total value of the business to all capital providers. Converting EV to equity value (what common shareholders own) requires adding claims that represent non-operating assets and subtracting claims senior to equity. Each adjustment must be done at market value, not book value — and the adjustments must be consistent with what was included (or excluded) from FCFF.

AdjustmentDirectionAmount (Example)Rationale
Enterprise Value (DCF)Starting point$1,695MPV of all operating cash flows to all capital providers
+ Cash and Short-Term InvestmentsAdd+$120MExcess cash not needed for operations is a non-operating asset that belongs to equity; must not be in FCFF
+ Investments and Affiliates (at market)Add+$45MMinority-owned stakes; include only if not consolidated in FCFF and their cash flows not in the model
+ Tax Loss Carryforwards (PV)Add+$30MNOLs have real economic value — they reduce future cash taxes; often omitted, creating systematic undervaluation
− Total Debt (at market value)Subtract($450M)All interest-bearing debt: term loans, bonds, notes — includes current portion; use market value where possible
− Capital Leases (at PV of future payments)Subtract($55M)Post-IFRS 16/ASC 842: leases are on balance sheet; must be subtracted like debt; lease payments not in FCFF if leases are excluded from NOPAT
− Underfunded Pension Obligations (at market)Subtract($80M)If pension costs are in NOPAT (as they should be), the unfunded PBO is a debt-like claim against equity
− Minority Interests (at market)Subtract($40M)Minority shareholders' claim on consolidated subsidiaries; EV includes 100% of consolidated subsidiary cash flows
− Preferred Stock (at liquidation value)Subtract($0M)Senior equity claim; subtract before arriving at common equity value
= Equity Value to Common ShareholdersResult$1,265MTotal value to common equity holders
÷ Diluted Shares OutstandingDivide75M sharesTreasury stock method; includes options and unvested RSUs
= Intrinsic Value Per ShareResult$16.87Compare to current market price to assess over/undervaluation

Diluted Shares — Treasury Stock Method for Options and RSUs

Dividing equity value by basic shares outstanding ignores the dilutive effect of options, warrants, and convertible securities that, if exercised, would increase the share count and reduce per-share value. The treasury stock method (TSM) is the standard approach for options and computes the net share dilution — the new shares issued minus the shares the company could repurchase with the exercise proceeds.

Treasury Stock Method — Net Dilutive Shares

Net Dilutive Shares = Options Outstanding − (Exercise Proceeds / Current Share Price)

Exercise Proceeds = Options Outstanding × Exercise Price. Net shares are added only when options are in-the-money (Exercise Price < Current Price)

ComponentCount/AmountCalculationDiluted Shares Added
Basic Shares Outstanding70.0MFrom 10-K cover page70.0M (base)
In-the-Money Options (Tranche A)3.0M optionsExercise Price $10, Current Price $16.87 — TSM: 3.0M − (3.0M × $10 / $16.87) = 3.0M − 1.78M+1.22M
In-the-Money Options (Tranche B)2.0M optionsExercise Price $14, Current Price $16.87 — TSM: 2.0M − (2.0M × $14 / $16.87) = 2.0M − 1.66M+0.34M
Out-of-Money Options (Tranche C)1.5M optionsExercise Price $20, Current Price $16.87 — Out of money; not dilutive+0M
Unvested RSUs1.5M unitsRSUs have $0 exercise price — all dilutive: 1.5M − (1.5M × $0 / $16.87) = 1.5M+1.5M
Convertible Notes— (none)If present: convert at conversion price, add net shares from conversion+0M
Total Diluted Shares73.06M70.0M + 1.22M + 0.34M + 0M + 1.5M73.06M
Intrinsic Value (Equity / Diluted)$1,265M / 73.06M$17.31 per diluted share

Strictly, TSM should use the intrinsic value per share (the DCF output) as the 'current price' — not the traded market price — because you are computing dilution from the perspective of the DCF, not the market. In practice, if intrinsic value ≈ market price (which it should be in an efficient market), the difference is immaterial. For companies significantly above or below intrinsic value, using intrinsic value is technically correct — it may require one iteration since diluted shares affects per-share intrinsic value which affects the diluted share count. McKinsey accepts market price as a practical simplification for most applications.

Key Takeaways

  • Mid-year convention: discount FCFF at 1/(1+WACC)^(t−0.5) rather than 1/(1+WACC)^t — better reflects continuously generated cash flows and adds approximately 4%–5% to the PV of explicit-period FCFFs
  • Enterprise value = PV of explicit-period FCFFs (mid-year) + PV of terminal value (end-year T); TV typically represents 60%–80% of total EV for growing businesses
  • EV-to-equity bridge: add non-operating assets (cash, investments, NOLs, PV of tax shields if APV), subtract all debt-like claims (financial debt, capital leases, underfunded pensions, minority interests, preferred stock)
  • Diluted shares: use treasury stock method for options (net shares = options outstanding − exercise proceeds/share price); add all in-the-money instruments; RSUs are fully dilutive (exercise price = $0)
  • Critical consistency check: items excluded from FCFF (e.g., cash excluded from NOPAT, lease payments if leases are in NOPAT) must be added or subtracted in the bridge — the bridge adjustments must mirror the FCFF construction choices

Quiz — 3 Questions

Answer one at a time
Question 1 of 30 answered

A 5-year DCF model produces explicit-period FCFFs of $50M, $60M, $70M, $80M, $90M. WACC = 12%. Terminal value (end of Year 5) = $1,200M. Using mid-year discounting for explicit-period cash flows and end-year for TV, what is enterprise value?

AEV ≈ $890M
BEV ≈ $940M. Mid-year PV factors: Yr1: 1/(1.12)^0.5=0.9449; Yr2: 1/(1.12)^1.5=0.8437; Yr3: 1/(1.12)^2.5=0.7533; Yr4: 1/(1.12)^3.5=0.6726; Yr5: 1/(1.12)^4.5=0.6005. PV FCFFs: $50×0.9449=$47.2; $60×0.8437=$50.6; $70×0.7533=$52.7; $80×0.6726=$53.8; $90×0.6005=$54.0. Sum = $258.3M. PV of TV: $1,200/(1.12)^5 = $1,200/1.7623 = $680.9M. Total EV = $258.3M + $680.9M = $939.2M ≈ $940M
CEV ≈ $1,050M
DEV ≈ $760M (no mid-year convention)