recruiting equations

Company Value (Perpetuity Formula)

Cash flow / (discount rate - cash flow growth rate).

Finance Lease - Interest

Interest = discount rate x lease liability.

Change in Operating Lease Asset

Lease expense - interest (represents the "depreciation"/principal portion).

Change in Operating Lease Liability

Discount rate x lease liability (represents the interest/debt portion).

Total Tax Expense (with Deferred Taxes)

Current taxes plus or minus the change in deferred taxes.

Net DTA

DTA - DTL.

Net DTL

DTL - DTA.

Change in Cash from a PP&E; Sale

Book value of PP&E; plus or minus (gain/loss x (1 - tax rate)).

Common Stock

Shares x par value.

APIC (Additional Paid-In Capital)

Shares x (market value - par value).

NWC (Net Working Capital)

Current operational assets - current operational liabilities.

FCF (Free Cash Flow, basic)

CFO - CapEx.

Change in NWC

Old working capital - new working capital (negative because an increase in WC represents a use/decrease of cash).

Leverage Ratio

Total debt / EBITDA - measures debt relative to the ability to repay it.

Interest Coverage Ratio

EBITDA / interest expense - measures how easily a company can pay interest.

ROE (Return on Equity)

Net income (to common) / average common shareholders equity.

ROA (Return on Assets)

NI (to common) / average total assets.

ROIC (Return on Invested Capital)

NOPAT / average invested capital.

NOPAT

EBIT x (1 - tax rate).

DSO (Days Sales Outstanding)

AR / revenue x 365.

DIO (Days Inventory Outstanding)

Inventory / COGS x 365.

DPO (Days Payable Outstanding)

AP / COGS x 365.

CCC (Cash Conversion Cycle)

DIO + DSO - DPO.

Calculating EqV

Market cap = shares outstanding x current share price; alternatively, market value of total assets - market value of total liabilities, or last funding valuation for private companies.

EV − Debt (and debt-like items) + Cash and cash equivalents − Preferred Stock − Noncontrolling Interest + Non-Operating Assets

Calculating EV

EqV − Non-Operating Assets + Debt (and debt-like items) − Cash and cash equivalents + Preferred Stock + Noncontrolling Interest

Treasury Stock Method

If current share price < exercise price, options add nothing. If current share price > exercise price, employees pay exercise price x number of options, and the company uses proceeds to buy back shares.

Common Valuation Multiples

TEV/Revenue, TEV/EBIT, TEV/EBITDA, and P/E (= EqV/NI).

UFCF (Unlevered Free Cash Flow)

Free cash flow to all investors; starts from NOPAT (EBIT x (1 - tax rate)) rather than CFO

FCF to Equity Investors

FCF or LFCF (Levered Free Cash Flow); FCF does not deduct debt, but LFCF does.

FCF (Full Formula)

CFO - CapEx.

UFCF (Full Formula)

NOPAT + D&A; and non-cash adjustments +/- change in NWC - CapEx

LFCF (Full Formula)

NI to common + D&A; +/- change in NWC - CapEx - debt repayments + debt issuances.

Book Value

Total assets - total liabilities.

Net Operating Assets (NOA)

Operating assets - operating liabilities.

Invested Capital

Book value of equity + debt + preferred stock + other investor groups + operating leases.

EV/NOA

Enterprise value relative to net operating assets.

EV/IC

Measures how valuable a company is relative to its accumulated invested capital.

UFCF (DCF Projection Formula)

NOPAT + non-cash adjustments + change in NWC (from CFS) - CapEx.

Cost of Preferred Stock

Similar to cost of debt but with a higher coupon rate typically, and not tax-deductible.

WACC (Weighted Average Cost of Capital)

WACC = (Cost of Equity x %Equity) + (Cost of Debt x %Debt x (1 - tax rate)) + (Cost of Preferred Stock x %Preferred Stock).

Cost of Equity (CAPM)

Cost of Equity = Risk-Free Rate + Equity Risk Premium x Levered Beta.

Unlevered Beta Formula

Unlevered Beta = Levered Beta / (1 + (D/E x (1 - tax rate)) + P/E).

Levered Beta Formula

Levered Beta = Unlevered Beta x (1 + (D/E x (1 - tax rate)) + P/E).

P/E in the Beta Formula

Preferred stock / equity.

Terminal Value (Gordon Growth / Perpetuity Method)

Terminal Value = UFCF in Year 1 of the terminal period / (WACC - terminal UFCF growth rate), used when discount rate and cash flow growth rate are assumed constant thereafter.

Gordon Growth Simplification

Terminal Value = projection-end FCF x (1 + terminal FCF growth rate) / (discount rate - terminal FCF growth rate), avoiding the need to project one extra year of FCF.

Terminal Value (Multiples Method)

Terminal EBITDA/EBIT/NOPAT/FCF x the relevant multiple from comps, applied at a discount.

Converting Multiples Terminal Value to Gordon Growth

Set Terminal Value = final year FCF x (1 + terminal FCF growth rate) / (discount rate - terminal FCF growth rate) and solve.

Implied Terminal FCF Growth Rate

(Terminal Value x discount rate - final year FCF) / (Terminal Value + final year FCF).

Implied Enterprise Value (DCF)

PV of projected FCF + PV of terminal value; apply the EV-to-EqV bridge and divide by diluted share count to reach a per-share value.

APV (Adjusted Present Value)

APV = Unlevered Value + Net PV of Financing Effects, using unlevered beta as the discount rate to avoid double-counting the effect of debt (which would happen if re-levering).

Liquidation Value / Net Asset Value

Implied EqV = market-valued assets - market-valued liabilities.

Purchase EqV

Share price x (1 + control premium) x shares outstanding (public); for private companies, typically a multiple of EBITDA or revenue.

Weighted Average Cost of Acquisition

(% cash used x after-tax cost of cash) + (% debt used x after-tax cost of debt) + (% stock used x cost of stock).

Accretion/Dilution in 100% Stock Deals

Buyer's P/E > Seller's P/E = accretive; Buyer's P/E < Seller's P/E = dilutive; equal P/E = neutral.

Accretion/Dilution Test (WACA Method)

Weighted cost of acquisition < seller’s yield = accretive; weighted cost of acquisition > seller’s yield = dilutive; equal = neutral.

Max New Debt (Private Deal)

(Max debt/EBITDA) x (combined EBITDA - buyer's existing debt).

Combined EqV

Acquirer's EqV + market value of any stock used to fund the deal.

Combined EV

Acquirer's EV + target's purchase EV.

EPS

Net income / share count.

Earnings Yield

1 / (P/E).

P/E Ratio

EqV / NI.

Merger Math (WACC Method)

Compare the weighted cost of acquisition (%cash x after-tax cost of cash + %debt x after-tax cost of debt + %stock x cost of stock) against the seller's earnings yield to see which is higher.

Merger Math (EPS Method) - Formula

Pro-forma EPS = (combined NI + synergies - financing effects) / (buyer shares + new shares issued).

rule of 72

72 / number of holding years = IRR for doubling money

rule of 114

114 / number of holding years = IRR for tripling money

rule of 144

144 / number of holding years = IRR for quadrupling money

Dividend Growth Model (Gordon Growth)

Cost of Equity = (Expected Dividend per Share / Current Share Price) + Dividend Growth Rate