FSA Master Formula Sheet

Balance Sheet

Accounting Equation:

$\text{Assets}=\text{Liabilities}+\text{Owners’ Equity}$

$\text{Owners’ Equity}=\text{Contributed Capital}+\text{Retained Earnings}+\text{AOCI}$

${\text{Retained Earnings}}_{end}={\text{RE}}_{beg}+\text{Net Income}-\text{Dividends}$

Working Capital:

$\text{Working Capital}=\text{Current Assets}-\text{Current Liabilities}$

Income Statement

$\text{Gross Profit}=\text{Revenue}-\text{COGS}$

$\text{Operating Income}=\text{Gross Profit}-\text{Operating Expenses}$

$\text{Net Income}=\text{Revenue}-\text{Total Expenses}-\text{Taxes}$

$\text{Comprehensive Income}=\text{Net Income}+\text{OCI}$

Earnings Per Share (EPS)

Basic EPS:

$\text{Basic EPS}=\frac{\text{Net Income}-\text{Preferred Dividends}}{\text{Weighted Average Shares Outstanding}}$

Diluted EPS (Treasury Stock Method for Options/Warrants):

$\text{New shares}=\text{Shares from exercise}-\frac{\text{Exercise Price}\times \text{Shares from exercise}}{\text{Market Price}}$

Only dilutive when market price > exercise price.

Diluted EPS (If-Converted Method for Convertible Bonds):

$\text{Diluted EPS}=\frac{\text{NI}-\text{Pref Div}+\text{Convertible Interest}(1-t)}{\text{WASO}+\text{Convertible Shares}}$

Diluted EPS (If-Converted Method for Convertible Preferred):

$\text{Diluted EPS}=\frac{\text{NI}-\text{Pref Div}+\text{Convertible Pref Div}}{\text{WASO}+\text{Shares from Conversion}}$

Cash Flow Formulas

$\text{Net Change in Cash}=\text{CFO}+\text{CFI}+\text{CFF}$

Indirect Method CFO:

$\text{CFO}=\text{NI}+\text{Non-cash charges (D\&A)}\pm \Delta \text{Working Capital}-\text{Gains}+\text{Losses}$

Direct Method Conversions:

$\text{Cash from customers}=\text{Revenue}-\Delta \text{AR}+\Delta \text{Unearned Revenue}$

$\text{Cash to suppliers}=\text{COGS}+\Delta \text{Inventory}-\Delta \text{AP}$

$\text{Cash operating expenses}=\text{OpEx}+\Delta \text{Prepaid}-\Delta \text{Accrued Liabilities}$

$\text{Cash interest}=\text{Interest Expense}+\Delta \text{Interest Payable}-\text{Amortization of discount}$

$\text{Cash taxes}=\text{Tax Expense}-\Delta \text{DTL}+\Delta \text{DTA}-\Delta \text{Tax Payable}$

Free Cash Flow

FCFF (Free Cash Flow to Firm):

$\text{FCFF}=\text{CFO}+\text{Int}(1-t)-\text{CAPEX}$

$\text{FCFF}=\text{NI}+\text{NCC}+\text{Int}(1-t)-\text{WCInv}-\text{FCInv}$

FCFE (Free Cash Flow to Equity):

$\text{FCFE}=\text{CFO}-\text{CAPEX}+\text{Net Borrowing}$

Inventory

$\text{COGS}=\text{Beginning Inventory}+\text{Purchases}-\text{Ending Inventory}$

Weighted Average Cost:

$\text{WAC per unit}=\frac{\text{Cost of Goods Available for Sale}}{\text{Total Units Available}}$

LIFO Reserve Conversions:

${\text{Inventory}}_{FIFO}={\text{Inventory}}_{LIFO}+\text{LIFO Reserve}$

${\text{COGS}}_{FIFO}={\text{COGS}}_{LIFO}-\Delta \text{LIFO Reserve}$

Depreciation

Straight-Line:

$\text{Depreciation}=\frac{\text{Cost}-\text{Salvage Value}}{\text{Useful Life}}$

Double-Declining Balance:

$\text{Depreciation}=\frac{2}{n}\times \text{Beginning Book Value}$

Units-of-Production:

$\text{Depreciation}=\frac{\text{Cost}-\text{Salvage}}{\text{Total Units}}\times \text{Units Produced}$

PPE Age Estimates:

$\text{Average Age}=\frac{\text{Accumulated Depreciation}}{\text{Annual Depreciation}}$

$\text{Average Useful Life}=\frac{\text{Historical Cost}}{\text{Annual Depreciation}}$

$\text{Remaining Life}=\frac{\text{Net PPE}}{\text{Annual Depreciation}}$

Goodwill and Business Combinations

$\text{Goodwill}=\text{Purchase Price}-(\text{Fair Value of Assets}-\text{Fair Value of Liabilities})$

Bonds and Long-Term Debt

Interest Expense (Effective Interest Method):

$\text{Interest Expense}=\text{Book Value of Bond}\times \text{Market Rate at Issuance}$

Coupon Payment:

$\text{Coupon Payment}=\text{Face Value}\times \text{Coupon Rate}$

Amortization of Discount/Premium:

$\text{Amortization}=\text{Interest Expense}-\text{Coupon Payment}$

• Discount bond: Interest Expense > Coupon Payment (book value increases)
• Premium bond: Interest Expense < Coupon Payment (book value decreases)

Income Taxes

$\text{Tax Expense}=\text{Taxes Payable}+\Delta \text{DTL}-\Delta \text{DTA}$

$\text{DTL}=(\text{Carrying Amount}-\text{Tax Base})\times t$

$\text{DTA}=(\text{Tax Base}-\text{Carrying Amount})\times t$

$\text{Effective Tax Rate}=\frac{\text{Income Tax Expense}}{\text{Pretax Income}}$

Activity Ratios

$\text{Inventory Turnover}=\frac{\text{COGS}}{\text{Average Inventory}}$

$\text{DOH}=\frac{365}{\text{Inventory Turnover}}$

$\text{Receivables Turnover}=\frac{\text{Revenue}}{\text{Average AR}}$

$\text{DSO}=\frac{365}{\text{Receivables Turnover}}$

$\text{Payables Turnover}=\frac{\text{Purchases}}{\text{Average AP}}$

$\text{Days Payable}=\frac{365}{\text{Payables Turnover}}$

$\text{Total Asset Turnover}=\frac{\text{Revenue}}{\text{Average Total Assets}}$

$\text{Fixed Asset Turnover}=\frac{\text{Revenue}}{\text{Average Net Fixed Assets}}$

$\text{Working Capital Turnover}=\frac{\text{Revenue}}{\text{Average Working Capital}}$

$\text{CCC}=\text{DOH}+\text{DSO}-\text{Days Payable}$

Liquidity Ratios

$\text{Current Ratio}=\frac{\text{Current Assets}}{\text{Current Liabilities}}$

$\text{Quick Ratio}=\frac{\text{Cash}+\text{ST Investments}+\text{Receivables}}{\text{Current Liabilities}}$

$\text{Cash Ratio}=\frac{\text{Cash}+\text{ST Investments}}{\text{Current Liabilities}}$

$\text{Defensive Interval}=\frac{\text{Cash}+\text{ST Investments}+\text{Receivables}}{\text{Daily Cash Expenditures}}$

Solvency Ratios

$\text{Debt-to-Assets}=\frac{\text{Total Debt}}{\text{Total Assets}}$

$\text{Debt-to-Equity}=\frac{\text{Total Debt}}{\text{Total Equity}}$

$\text{Debt-to-Capital}=\frac{\text{Total Debt}}{\text{Total Debt}+\text{Total Equity}}$

$\text{Financial Leverage}=\frac{\text{Average Total Assets}}{\text{Average Equity}}$

$\text{Interest Coverage}=\frac{\text{EBIT}}{\text{Interest Expense}}$

$\text{Fixed Charge Coverage}=\frac{\text{EBIT}+\text{Lease Payments}}{\text{Interest}+\text{Lease Payments}}$

Profitability Ratios

$\text{Gross Profit Margin}=\frac{\text{Gross Profit}}{\text{Revenue}}$

$\text{Operating Margin}=\frac{\text{EBIT}}{\text{Revenue}}$

$\text{Net Profit Margin}=\frac{\text{Net Income}}{\text{Revenue}}$

$\text{ROA}=\frac{\text{Net Income}}{\text{Average Total Assets}}$

$\text{ROE}=\frac{\text{Net Income}}{\text{Average Equity}}$

DuPont Analysis

3-Factor:

$\text{ROE}=\frac{\text{NI}}{\text{Revenue}}\times \frac{\text{Revenue}}{\text{Avg Assets}}\times \frac{\text{Avg Assets}}{\text{Avg Equity}}$

5-Factor (Extended):

$\text{ROE}=\frac{\text{NI}}{\text{EBT}}\times \frac{\text{EBT}}{\text{EBIT}}\times \frac{\text{EBIT}}{\text{Revenue}}\times \frac{\text{Revenue}}{\text{Avg Assets}}\times \frac{\text{Avg Assets}}{\text{Avg Equity}}$

where:

• $\frac{\text{NI}}{\text{EBT}}$ = Tax burden
• $\frac{\text{EBT}}{\text{EBIT}}$ = Interest burden
• $\frac{\text{EBIT}}{\text{Revenue}}$ = EBIT margin
• $\frac{\text{Revenue}}{\text{Avg Assets}}$ = Asset turnover
• $\frac{\text{Avg Assets}}{\text{Avg Equity}}$ = Financial leverage

Cash Flow Ratios

$\text{CF-to-Revenue}=\frac{\text{CFO}}{\text{Revenue}}$

$\text{Cash Return on Assets}=\frac{\text{CFO}}{\text{Avg Total Assets}}$

$\text{Cash Return on Equity}=\frac{\text{CFO}}{\text{Avg Equity}}$

$\text{Cash-to-Income}=\frac{\text{CFO}}{\text{Operating Income}}$

$\text{Debt Coverage}=\frac{\text{CFO}}{\text{Total Debt}}$

$\text{Interest Coverage (cash)}=\frac{\text{CFO}+\text{Interest}+\text{Taxes}}{\text{Interest Paid}}$

$\text{Reinvestment}=\frac{\text{CFO}}{\text{Cash for LT Assets}}$

See Also

• Financial Ratios
• Cash Flow Analysis
• Inventory Valuation
• Income Taxes Accounting