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Financial Ratios and Calculations: Definitions and Formulas, Exercises of Cost Accounting

Definitions and formulas for various financial ratios, including the current ratio, quick ratio, debt-to-asset ratio, debt-to-equity ratio, equity multiplier, times interest earned, inventory turnover, receivables turnover, total assets turnover, net profit margin, roa, roe, eps, p/e ratio, market-to-book ratio, dividend payout ratio, retention ratio, net cash flow, operating cash flow, free cash flow, dividend yield, capital gain rate, and holding period return. It also includes formulas for the cost of preferred stock capital, cost of common equity capital, security market line, and present value of annuity.

What you will learn

  • How is the Quick Ratio calculated?
  • What is the definition of the Current Ratio?
  • What is the difference between the Debt-to-Asset Ratio and the Debt-to-Equity Ratio?

Typology: Exercises

2021/2022

Uploaded on 08/05/2022

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Selected Ratios and Definitions
(standard definitions; most formulas use the notations from the Berk, DeMarzo, Harford book)
Current Ratio = Current Assets / Current Liabilities;
Quick Ratio = (Current Assets - Inventory) / Current Liabilities;
Debt-to-Asset Ratio = Total Debt / Total Assets; Debt-to-value ratio = D/(E+D)
Debt-to-Equity = Total Debt / Total Equity;
Equity Multiplier = Total Assets / Total Equity;
Times Interest Earned = EBIT / Interest Payment;
Interest Coverage Ratio = Some Measure of Earnings / Interest;
Inventory Turnover = COGS / Inventory; or, Sales/Average Inventory if COGS data is not available;
Average Age of Inventory = 365 / Inventory Turnover = 365 / (Sales / Inventory);
Receivables Turnover = Annual Sales / Accounts Receivables;
Average Collection Period = 365 / Receivables Turnover = 365 / (Sales / Accounts Receivables);
Total Assets Turnover = Sales / Total Assets;
Net Profit Margin = Net Income / Sales;
ROA = Net Income / Total Assets = total asset turnover * net profit margin;
ROE = Net Income / Equity = ROA * Equity Multiplier = ROA * Total Assets / Equity;
ROE = total asset turnover * net profit margin * equity multiplier;
EPS = Net Income / Number of Common Shares Outstanding;
P/E Ratio = Market Price per Share / EPS;
Market-to-Book Ratio = Market Price per Share / Book Value per Share
Market-to-Book Ratio = Total Market Value of Equity / Total Book Value of Equity;
Dividend Payout Ratio (DPR) = Dividends / Net Income;
Retention Ratio = 1 - Dividend Payout Ratio;
Net Cash Flow = Net Income + Depreciation;
Operating Cash Flow (OCF) = Earnings before Interest and Taxes + Depreciation - Tax;
Free Cash Flow (FCF) = [EBIT x (1- Tax Rate)] + Depreciation CAPEX Change in NWC
Dividend Yield = Dividend per Share / Stock Price = Div1 / P0
Capital Gain Rate = (Price Next Period / Price today) 1 = (P1 / P0) – 1 = (P1 - P0) / P0)
Holding Period Return: HPR = D1/P0 + (P1/P0 -1)
Value of a perpetuity: P = C / r where C is the perpetual cash flow and r is the discount rate
Constant Growth Model:
0
1/( )
E
P
Div r g
=
where Div1 is the next period dividend, rE is the equity cost of
capital and g is the growth rate in dividend.
Cost of Preferred Stock Capital; rpfd = (Divpfd / Ppfd); Cost of Common Equity Capital; rE = (Div1 / PE) + g; or
Security Market Line, SML or CAPM formula:
()
ii
RF M RF
rr r r
β
=
;
)]
( (E[ )
f
ii
f mkt
ER r R r
β
=+−
WACC; rWACC = rE E% + rpfd P% + rD (1 - TC) D%
Single Cash Flow Present Value: PV = C / (1 + r)n; Single Cash Flow Future Value: FVn = C * (1 + r)n
Present Value of Annuity:
0
1
1
1(1 )
N
PV C
rr
=


+

; Future Value of Annuity:
1
(1 ) 1
N
N
FV C
r
r
=

+−

Calculators
Allowed; HP 10B, HP 10bii, HP 10BII+, TI BAII, TI BAII Plus, and TI BAII Plus Professional calculators;
or any four function calculators
Not allowed; Graphing or Programmable calculators; iPhones with HP-10B or other emulators

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Selected Ratios and Definitions

(standard definitions; most formulas use the notations from the Berk, DeMarzo, Harford book)

Current Ratio = Current Assets / Current Liabilities; Quick Ratio = (Current Assets - Inventory) / Current Liabilities; Debt-to-Asset Ratio = Total Debt / Total Assets; Debt-to-value ratio = D/(E+D) Debt-to-Equity = Total Debt / Total Equity; Equity Multiplier = Total Assets / Total Equity; Times Interest Earned = EBIT / Interest Payment; Interest Coverage Ratio = Some Measure of Earnings / Interest; Inventory Turnover = COGS / Inventory; or, Sales/Average Inventory if COGS data is not available; Average Age of Inventory = 365 / Inventory Turnover = 365 / (Sales / Inventory); Receivables Turnover = Annual Sales / Accounts Receivables; Average Collection Period = 365 / Receivables Turnover = 365 / (Sales / Accounts Receivables); Total Assets Turnover = Sales / Total Assets; Net Profit Margin = Net Income / Sales; ROA = Net Income / Total Assets = total asset turnover * net profit margin; ROE = Net Income / Equity = ROA * Equity Multiplier = ROA * Total Assets / Equity; ROE = total asset turnover * net profit margin * equity multiplier;

EPS = Net Income / Number of Common Shares Outstanding; P/E Ratio = Market Price per Share / EPS; Market-to-Book Ratio = Market Price per Share / Book Value per Share Market-to-Book Ratio = Total Market Value of Equity / Total Book Value of Equity; Dividend Payout Ratio (DPR) = Dividends / Net Income; Retention Ratio = 1 - Dividend Payout Ratio;

Net Cash Flow = Net Income + Depreciation; Operating Cash Flow (OCF) = Earnings before Interest and Taxes + Depreciation - Tax; Free Cash Flow (FCF) = [EBIT x (1- Tax Rate)] + Depreciation – CAPEX – Change in NWC

Dividend Yield = Dividend per Share / Stock Price = Div 1 / P 0 Capital Gain Rate = (Price Next Period / Price today) – 1 = (P 1 / P 0 ) – 1 = (P 1 - P 0 ) / P 0 ) Holding Period Return: HPR = D 1 /P 0 + (P 1 /P 0 -1) Value of a perpetuity: P = C / r where C is the perpetual cash flow and r is the discount rate

Constant Growth Model: P 0 = Div 1 / ( rE − g )where Div 1 is the next period dividend, r E is the equity cost of

capital and g is the growth rate in dividend.

Cost of Preferred Stock Capital; r pfd = (Div pfd / P pfd ); Cost of Common Equity Capital; r E = (Div 1 / P E ) + g; or

Security Market Line, SML or CAPM formula: ri = rRF + β i × ( rM − rRF ); E R ( i ) = rf + β i (E[ Rmkt ]− rf )

WACC; r WACC = r E E% + r pfd P% + r D (1 - T C ) D%

Single Cash Flow Present Value: PV = C / (1 + r)n; Single Cash Flow Future Value: FVn = C * (1 + r) n

Present Value of Annuity: (^0)

(1 ) N

PV C

r r

; Future Value of Annuity:

FVN C (1 r ) N 1

r

Calculators

  • Allowed; HP 10B, HP 10bii, HP 10BII+, TI BAII, TI BAII Plus, and TI BAII Plus Professional calculators; or any four function calculators
  • Not allowed; Graphing or Programmable calculators; iPhones with HP-10B or other emulators