BEC Formulas
Break-Even (Call) = Strike Price + Cost of Option
Break-Even (Put) = Strike Price – Cost of Option
Effective Interest Rate =
!"#$%$&# ()*+ ($% ($%*,+
Interest paid per period =
-$# .%,/$$+& ,0 1,)"
.%*"/*()2 3 456
# ,0 .$%*,+&
Annual Percentage Rate: APR = Effective Interest Rate x # Periods in Year
Effective Annual Percentage Rate:
EAR = (1 + 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒)# 8,9(,:"+*"; .$%*,+& − 1
# 8,9(,:"+*"; .$%*,+&
𝑆𝐴𝑅
𝐸𝐴𝑅 = 61 +
A
−1
# 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑𝑠
Simple Interest: SI = Principal x SAR x # Years
Compound Interest: FV = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙(1 + 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒)<,#)2 .$%*,+&
Required Rate of Return = Nominal Risk-Free Rate + Risk Premiums
=
?
Weighted Average Cost of Capital: WACC = =>? *𝑘= + =>? * 𝑘? * (1 – t)
k @ = cost of equity; k A = cost of debt
E = market value of firm’s equity
D = market value of firm’s debt
@
@>A
A
@>A
= percentage of financing that is equity
= percentage of financing that is debt
t = corporate tax rate
1
Weighted Average Cost of Finance:
WACC = (kdx x wdx) + (kps x wps) + (kre x wcs)
kdx = cost of long-term debt (after tax)
wdx = (weight for) long-term debt (after tax)
kps = cost of preferred stock
wps = (weight for) preferred stock
kre = cost of retained earnings
wcs = (weight for) common stock equity
Weighted Average Interest Rate =
=00$/#*B$ 5"":)2 !"#$%$&# .)C9$"#&
?$D# E:#&#)"+*";
After-tax Cost of Debt = Pretax cost of debt x (1 – Tax rate)
.%$0$%%$+ 4#,/F ?*B*+$"+&
Cost of Preferred Stock = -$# .%,/$$+& ,0 .%$0$%%$+ 4#,/F
Preferred Stock Dividends = Par value x Dividend rate %
Capital Asset Pricing Model: CAPM = 𝑟0 + R 𝛽 𝑥 U𝑅9 − 𝑟0 VW
𝑟0 = risk free rate
𝑅9 = expected market return
𝑅9 − 𝑟0 = market risk premium
?
Discounted Cash Flows: DCF = .! + 𝑔
"
𝑃G = current market value/price
𝐷H = expected dividend per share at end of one year
g = constant rate of growth in dividends
Bond Yield Plus Risk Premium: BYRP = Pretax cost of LT debt + Market Risk Premium
2
6$#:%" ," )&&$#& 3 6$#$"#*,"
Growth Rate: g = HI(6$#:%" ," )&&$#& 3 6$#$"#*,")
Return on Sales: ROS =
!"/,9$ D$0,%$ *"#$%$&# *"/,9$,
*"#$%$&# $3($"&$,)"+ #)3$&
4)2$& ("$#)
-$# !"/,9$
Return on Investment: ROI = 5B$%);$ !"B$&#$+ 8)(*#)2
-$# !"/,9$
Return on Assets: ROA = 5B$%);$ <,#)2 5&&$#&
-$# !"/,9$
Return on Equity: ROE = 5B$%);$ <,#)2 =M:*#C
Degree of Operating Leverage: 𝐷𝑂𝐿 =
Degree of Financial Leverage: 𝐷𝐹𝐿 =
% ∆ =P!<
% ∆ 4)2$&
% ∆ =P< ,% =.4
% ∆ =P!<
Value of a Levered Firm = Value of an unlevered firm + Present value of the interest tax savings
Present Value of Interest Tax Savings =
# 3 (%#$%& 3 ?)
%#$%&
t = corporate tax rate
r = interest rate on debt
D = amount of debt
3
Total Debt Ratio =
<,#)2 1*)D*2*#*$&
<,#)2 5&&$#&
Debt-to-equity Ratio =
<,#)2 1*)D*2*#*$&
<,#)2 =M:*#C
<,#)2 5&&$#&
Equity Multiplier = <,#)2 =M:*#C
Times Interest Earned Ratio =
=)%"*";& P$0,%$ !"#$%$&# =3($"&$ & <)3$& (=P!<)
!"#$%$&# =3($"&$
8:%%$"# 5&&$#&
Current Ratio = 8:%%$"# 1*)D*2*#*$&
Quick Ratio =
8)&R & 8)&R =M:*B)2$"#&>4< S)%F$#)D2$ 4$/:%*#*$&>6$/$*B)D2$& ("$#)
8:%%$"# 1*)D*2*#*$&
Cash Conversion Cycle = Days in Inventory + Days Sales in AR – Days of Payables Outstanding
4
8,&# ,0 T,,+& 4,2+
Inventory Turnover = 5B$%);$ !"B$"#,%C
="+*"; !"B$"#,%C
Days in Inventory = (8,&# ,0 T,,+& 4,2+ ÷ VWX )
4)2$& ("$#)
Accounts Receivable Turnover = 5B$%);$ 5//,:"#& 6$/$*B)D2$ ("$#)
Days Sales in Accounts Receivable =
Days Sales in Accounts Receivable =
="+*"; 5//,:"#& 6$/$*B)D$ ("$#)
(4)2$& ("$#) ÷ VWX)
="+*"; 5//,:"#& 6$/$*B)D$ ("$#)
4)2$& ("$#)
x # Days in the Period
8,&# ,0 T,,+& 4,2+
Accounts Payable Turnover = 5B$%);$ 5//,:"#& .)C)D2$
="+*"; 5//,:"#& .)C)D2$
Days of Payables Outstanding = (8,&# ,0 T,,+& 4,2+ ÷ VWX)
4)2$&
Working Capital Turnover = 5B$%);$ Y,%F*"; 8)(*#)2
Average Working Capital =
P$;*""*"; ,0 .$%*,+ Y,%F*"; 8)(*#)2 > ="+ ,0 ($%*,+ Y,%F*"; 8)(*#)2
Z
Reorder Point = Safety Stock + Lead Time x Sales During Lead Time
5
Economic Order Quantity (EOQ) = \
Z4E
EOQ = \
Z 3 5"":)2 4)2$& (:"*#&) 3 8,&# ($% .:%/R)&$ E%+$%
5"":)2 8)%%C*"; 8,&# ($% ["*#
EOQ = Order Size
8
S = Annual Sales (units)
O = Cost per Purchase Order
C = Annual Carrying Cost per Unit
VWG
APR of Quick Payment Discount = .)C .$%*,+I?*&/,:"# .$%*,+ 𝑥
Annuity Present Value =
?*&/,:"#
HGGI?*&/,:"# %
\ ] (H – _`abacd efgha ifjdk`)
%
C = Amount of Annuity (equal future cash flows)
r = Rate of Return
H
Present Value Factor = (H>%)&
t = Number of Years
Present Value of a Perpetuity: P =
?*B*+$"+
6$M:*%$+ 6$#:%"
(Stock Value per Share)
P = Stock Price
D = Dividend
R = Required Return
Constant (Gordon) Growth Dividend Discount Model (DDM) = 𝑃# =
𝑃# = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑃𝑟𝑖𝑐𝑒 (𝑝𝑟𝑖𝑐𝑒 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 t)
𝐷("#$) = 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑜𝑛𝑒 𝑦𝑒𝑎𝑟 𝑎𝑓𝑡𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
.
Price-Earnings Ratio (P/E) = ="
!
.
Trailing P/E Ratio = ="
"
?&'! (H>;)
(6I;)
R = Required Return
G = (Sustainable) Growth Rate
𝑃G = 𝑆𝑡𝑜𝑐𝑘 𝑃𝑟𝑖𝑐𝑒 𝑜𝑟 𝑉𝑎𝑙𝑢𝑒 𝑇𝑜𝑑𝑎𝑦
𝐸H = 𝐸𝑃𝑆 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑖𝑛 𝑜𝑛𝑒 𝑦𝑒𝑎𝑟
𝑃G = 𝑆𝑡𝑜𝑐𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑟 𝑉𝑎𝑙𝑢𝑒 𝑇𝑜𝑑𝑎𝑦
𝐸G = 𝐸𝑃𝑆 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑝𝑎𝑠𝑡 𝑦𝑒𝑎𝑟
6
PEG Ratio =
("
)!
𝑃G = Stock Price or Value Today
;
𝐸H = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐸𝑃𝑆
g = Growth Rate = 100 x Expected growth rate
Current Price of Stock = 𝑃G = 𝑃𝐸𝐺 𝑥 𝐸H 𝑥 𝑔
(Using PEG)
.
Price-to-Sales Ratio (P/S) = 4"
𝑃G = Stock Price or Value Today
!
Current Price of Stock = 𝑃G =
𝑆H = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑆𝑎𝑙𝑒𝑠 𝑖𝑛 𝑜𝑛𝑒 𝑦𝑒𝑎𝑟
."
4!
𝑥 𝑆H
(Using P/S)
.
Price-to-Cash-Flow Ratio (P/CF) = 8l"
!
Current Price of Stock = 𝑃G =
."
8l!
𝑃G = Stock Price or Value Today
𝐶𝐹H = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑜𝑛𝑒 𝑦𝑒𝑎𝑟
𝑥 𝐶𝐹H
(Using P/CF)
.
Price-to-Book Ratio (P/B) = P"
"
𝑃G = Stock Price or Value Today
𝐵G = 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑜𝑚𝑚𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 (𝑡𝑜𝑑𝑎𝑦)
Depreciation Tax Shield = Depreciation x Tax Rate
Net Present Value:
Step 1: Calculate after-tax cash flows = Annual Net Cash Flow x (1 – Tax Rate)
Step 2: Add (+) Depreciation Benefit = Depreciation x Tax Rate
Step 3: Multiply (x) result by appropriate PV of an annuity (assuming cash flows are an annuity)
Step 4: Subtract (-) initial cash outflow
= NPV
7
.%$&$"# m)2:$ ,0 8)&R l2,n&
Profitability Index = 8,&# (.m),0 *"*#*)2 *"B$&#9$"#
-$# !"*#*)2 !"B$&#9$"#
Payback Period = 5B$%);$ !"/%$9$"#)2 8)&R l2,n∗
H
Present Value Factor = (H>%)*
*Where cash flow per period is even
r = interest rate
n = number of years
Present Value Factor of Annuity =
Economic Return % =
HI.m l)/#,%
%
?*B*+$"+> ∆ 4#,/F .%*/$
!"*#*)2 !"B$&#9$"#
Free Cash Flow = Net Income + Noncash Expenses – Increase in WC – Capital Expenditures
/
/
/
/
/>(
PVFCF = (H>%)! + (H>%)+ + (H>%), + (H>%)- + ⋯ (H>%)&
c = coupon payment
r = discount/market rate
t = # of periods/payouts
p = principal
Valuing Intangible Assets:
Income Approach:
Value = Expected FCF x Discount Factor
Valuing Tangible Assets:
Cost Method:
Net Book Value = Original Cost to Buy Asset – Accumulated
Depreciation
Replacement Cost:
Value = Cost to Replace + Assembly + Transportation
8
PV of After-Tax Lease Payment = Lease Payment x PV Factor
= Lease Payment x (1-T)
Prime Cost = Direct Labor + Direct Materials
Conversion Cost = Direct Labor + OH Applied
Traditional Costing:
P:+;$#$+ EB$%R$)+ 8,&#&
Step 1: Overhead Rate = =&#*9)#$+ 8,&# ?%*B$%
Step 2: Applied Overhead = Actual Cost Driver x Overhead Rate
Beginning Raw Materials
+ Purchase of Raw Materials
Raw Materials Available for Use
- Raw Materials Used
Ending Raw Materials
Beginning WIP
+ Raw Materials Used
+ DL & OH Used
.
WIP Available to be Finished
- Transferred to Finished Goods
Ending WIP
Beginning Finished Goods
+ Transferred from WIP
Finished Goods Available for Sale
- COGS
Ending Finished Goods
Cost of Goods Manufactured = Begin. WIP + RM Used + DL (Actual) + OH Applied – End WIP
Cost of Goods Sold = Begin. Finished Goods + COGM – Ending Finished Goods
Cost of Goods Sold = Beginning Inventory + Purchases – Ending Inventory
Cost of Goods Available for Sale = Begin. Finished Goods + COGM
9
Equivalent Units:
Weighted Average:
FIFO:
Units Completed
+ (Ending WIP x % Completed)
Equivalent Units
(Beginning WIP x % to be completed)
+ (Units Completed – Beginning WIP)
+ (Ending WIP x % completed)
.
Equivalent Units
Cost Per Equivalent Unit:
Weighted Average:
FIFO:
P$;*""*"; 8,&# > 8:%%$"# 8,&#
=M:*B)2$"# ["*#&
8:%%$"# 8,&# E"2C
=M:*B)2$"# ["*#&
Sales Value at Split-Off = Final Selling Price – Identifiable Costs Incurred After Split-Off
E:#(:#
Total Factor Productivity Ratio (TFP) = <,#)2 8,&#
E:#(:#
Partial Productivity Ratio (PPR) = 4($/*0*/ p:)"#*#C ,0 S)#$%*)2 ,% 1)D,%
High-Low Method:
1. 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑈𝑛𝑖𝑡 =
!"#$%&' )*'+, -*&' . /*0%&' )*'+, -*&'
!"#$%&' 1*,23% . /*0%&' 1*,23%
2. Variable Cost = Highest or Lowest Volume x Variable Cost per Unit
3. Fixed Costs = Total Costs – Variable Cost
10
Linear Regression Model:
y = a +Bx
y = dependent variable (variable we are trying to explain)
x = independent variable (the regressor) explains y
a = y-axis intercept of the regression line
B = slope of the regression line
Absorption Costing:
Revenue
Less: COGS
Gross Margin
Less: Operating Expenses
Net Income
Flexible Budget:
Contribution/Variable/Direct Costing:
Revenue
Less: Variable Costs
Contribution Margin
Less: Fixed Costs
Net Income
Total Cost = Fixed Costs + (VC per unit x # of units)
Contribution Margin (CM) = Revenue – Variable Costs
Unit Contribution Margin (UCM) = Unit Sales Price – Variable Cost per Unit
Contribution Margin Ratio (CMR) =
8,"#%*D:#*," S)%;*"
6$B$":$
Controllable Margin = Contribution Margin – Controllable “fixed” Costs
Gross Margin (%) =
T%,&& S)%;*"
-$# 4)2$&
Gross Profit = Selling Price – Total Costs (COGS+OH)
l*3$+ SEq
Fixed Costs per Unit = ["*#& .%,+:/$+
Change in Income = Change in Inventory Units x Fixed Costs per Unit
11
<,#)2 l*3$+ 8,&#&
Break-Even Point (Units) = ["*# 8,"#%*D:#*," S)%;*"
Break-Even Point ($) = Unit Price x Break-Even Point (units)
Break-Even Point ($) =
<,#)2 l*3$+ 8,&#&
8,"#%*D:#*," S)%;*" 6)#*,
Target Profit:
Sales (Units) =
l*3$+ 8,&#& > .%$#)3 .%,0*#
["*# 8,"#%*D:#*," S)%;*"
Sales ($) = Variable Costs + Fixed Costs + Pretax Profits
Sales ($) =
l*3$+ 8,&#& > .%$#)3 .%,0*#
8,"#%*D:#*," S)%;*" 6)#*,
Sales Price per Unit =
l*3$+ 8,&#& > m)%*)D2$ 8,&#& > .%$#)3 .%,0*#
# ,0 ["*#& 4,2+
Margin of Safety ($) = Total Sales ($) – Breakeven Sales ($)
Margin of Safety (%) =
S)%;*" ,0 4)0$#C ($)
<,#)2 4)2$&
Target Cost = Market Price – Required Profit
12
ROI =
!"#$%&
!"'&()%&") +,-.),/
ROI = Profit Margin x Investment Turnover
Investment Capital = Total Assets – Operating Liabilities
Investment Capital = Interest Bearing Debt + Equity
-$# !"/,9$
ROA = 5B$%);$ <,#)2 5&&$#&
Average Total Assets =
8:%%$"# s$)% > .%*,% s$)%
Z
-$# !"/,9$
ROE = =M:*#C ()B$%);$)
Net Profit Margin =
-$# !"/,9$
4)2$&
Asset Turnover = 5&&$#& ()B$%);$)
4)2$&
5&&$#&
Financial Leverage = =M:*#C
DFL = 1 +
?$D#
=M:*#C
DuPont ROE = Net Profit Margin x Asset Turnover x Financial Leverage
DuPont ROE = ROA x Financial Leverage
-$# !"/,9$
Tax Burden = .%$#)3 !"/,9$
.%$#)3 !"/,9$
Interest Burden = =)%"*";& P$0,%$ !"#$%$&# & <)3 (=P!<)
=P!<
EBIT Margin = 4)2$&
Extended DuPont = Tax Burden x EBIT Margin x Asset Turnover x Financial Leverage
Residual Income = Net Income – Required Return on Equity
Where: Required Return = Net Book Value (Equity) x Hurdle Rate
Net Operating Profit After Tax (NOPAT) = EBIT x (1 - Tax Rate)
Economic Value (EVA) = NOPAT – Required Return ($)
Where: Required Return = Investment x WAAC
13
Budgeted Production = Budgeted Sales + Desired Ending Inventory – Beginning Inventory
DM Purchase Budget:
# Units to be Purchased = Units of DM Needed + Desired End. Inventory – Begin. Inventory
Cost of DM to be Purchased = Units of DM to be Purchased x Cost per Unit
DM Usage Budget:
DM Usage = Begin. Inventory @ Cost + Purchases @ Cost – End. Inventory @ Cost
DL Budget:
Total # Hours Needed = Budgeted Production (units) x Hours Required to Produce Each Unit
Total Wages = Total # Hours Needed x Hourly Wage Rate
COGM&S Budget:
COGS = COGM + Begin. FG Inventory – End. FG Inventory
Cash Budget Format:
Beginning Cash
+ Cash Collections from Sales
- Cash Disbursements for Purchases & Operating
= Computed Ending Cash
- Cash Requirements to Sustain Operations
= Working Capital Loan to Maintain Cash Requirements
Standard Direct Costs = Standard Price x Standard Quantity
Standard Indirect Costs = Standard (predetermined) Application Rate x Standard Quantity
DM Price Variance = Actual Quantity Purchased x (Actual Price – Standard Price)
DM Quantity Usage Variance = Standard Price x (Actual Quantity Used – Standard Quantity Allowed)
DL Rate Variance = Actual Hours Worked x (Actual Rate – Standard Rate)
DL Efficiency Variance = Standard Rate x (Actual Hours Worked – Standard Hours Allowed)
14
Real GDP =
Multiplier =
-,9*")2 T?.
T?. ?$02)#,%
𝑥 100
H
HIS)%;*")2 .%,($"&*#C #, 8,"&:9$ (S.8)
Change in Real GDP = Multiplier x Change in Spending
Unemployment Rate =
# ,0 ["$9(2,C$+
<,#)2 1)D,% l,%/$
Consumer Price Index (CPI) =
Inflation Rate =
𝑥 100
8:%%$"# 8,&# ,0 S)%F$# P)&F$#
P)&$ s$)% 8,&# ,0 S)%F$# P)&F$#
𝑥 100
8.!./00$*& 2$034# I 8.!20340 2$034#
8.!20340 2$034#
Real Interest Rate = Nominal Interest Rate - Inflation Rate
Nominal Interest Rate = Real Interest Rate + Inflation Rate
Price Elasticity of Demand (𝐸4 ) =
Price Elasticity of Supply (𝐸4 ) =
% 8R)";$ *" p:)"#*#C ?$9)"+$+
% 8R)";$ *" .%*/$
% 8R)";$ *" p:)"#*#C 4:((2*$+
% 8R)";$ *" .%*/$
Cross Elasticity of Demand (Supply) (𝐶% ) =
% 8R";$ *" # ["*#& ,0 t ?$9)"+$+ (&:((2*$+)
Interest Elasticity of Demand (Supply) (𝐼% ) =
% 8R)";$ *" .%*/$ ,0 s
% 8R)";$ *" # ["*#& ,0 t ?$9)"+$+ (4:((2*$+)
% 8R)";$ *" !"/,9$
15