Analyst Dojo

CFA Level I Financial Statement Analysis formulas

The most formulas of any topic. Ratios do the heavy lifting: liquidity, solvency, activity and profitability, plus the inventory, depreciation, lease and tax adjustments that change them.

201 formulas from the Financial Statement Analysis lessons (11–14% of the exam), 93 to memorize. Each says how deeply to learn it and opens to a quick worked example with the keystrokes for the TI BA II Plus and the HP 12C.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.

Module 1 Introduction to Financial Statement Analysis

Regulatory filings, notes, MD&A and the audit report

Segment and customer share test Use it
s=ST≥10%s = \frac{S}{T} \ge 10\%
Quick example

A segment has revenue of 180 out of combined segment revenue of 1,500. 180 ÷ 1,500 = 12%, at or above 10%, so it is reportable on the revenue test.

On your calculator
  1. 180÷1500= 0.12
  1. 180ENTER1500÷ 0.12

ENTER enter (on the HP, puts the number on the stack)

Reportable-segment coverage test Use it
external revenue of reportable segmentstotal revenue≥75%\frac{\text{external revenue of reportable segments}}{\text{total revenue}} \ge 75\%
Quick example

Three segments pass the 10% test with external revenue of 280, 220 and 150, out of total revenue of 800. (280 + 220 + 150) ÷ 800 = 81.25%, so no more segments are needed.

On your calculator
  1. 280+220+150=÷800= 0.8125
  1. 280ENTER220+150+800÷ 0.8125

ENTER enter (on the HP, puts the number on the stack)

IFRS vs US GAAP, new standards and other information sources

Operating cash flow under the other interest treatment Use it
CFOop=CFOfin−I\text{CFO}_{\text{op}} = \text{CFO}_{\text{fin}} - I
Quick example

An IFRS filer reports operating cash flow of 150 with 21 of interest paid in financing. With interest in operating, as under US GAAP: 150 − 21 = 129. The IFRS figure looks 16.3% higher (21 ÷ 129).

On your calculator
  1. 150−21= 129
  1. 150ENTER21− 129

ENTER enter (on the HP, puts the number on the stack)

Module 2 Analyzing Income Statements

Revenue recognition: the five-step model

Allocating the transaction price Use it
Xi=T×Si∑SX_i = T \times \frac{S_i}{\sum S}
Quick example

A bundle sells for 1,350. Stand-alone prices are 900 for item 1 and 600 for item 2. Item 1 gets 1,350 × 900 ÷ 1,500 = 810; item 2 gets 540.

On your calculator
  1. 900+600=STO1
  2. 1350×900÷RCL1= 810

STO store · RCL recall a stored number

  1. 1350ENTER900×900ENTER600+÷ 810

ENTER enter (on the HP, puts the number on the stack)

Percent complete (cost to cost) Use it
% complete=costs incurred to datetotal expected costs\%\ \text{complete} = \frac{\text{costs incurred to date}}{\text{total expected costs}}
Quick example

Costs to date 15 against total expected costs of 60. 15 ÷ 60 = 25% complete.

On your calculator
  1. 15÷60= 0.25
  1. 15ENTER60÷ 0.25

ENTER enter (on the HP, puts the number on the stack)

Revenue and profit to date Use it
Revenue=P×% complete,Profit=Revenue−costs to date\text{Revenue} = P \times \%\ \text{complete}, \qquad \text{Profit} = \text{Revenue} - \text{costs to date}
Quick example

Price 90, total expected cost 60, costs to date 15. Revenue 90 × 15 ÷ 60 = 22.5; profit 22.5 − 15 = 7.5.

On your calculator
  1. 90×15÷60= revenue 22.5
  2. −15= profit 7.5
  1. 90ENTER15×60÷ revenue 22.5
  2. 15− profit 7.5

ENTER enter (on the HP, puts the number on the stack)

Expense recognition: capitalizing vs expensing

Straight-line depreciation Know the idea
Depreciation=Cost−Salvage valueUseful life\text{Depreciation} = \frac{\text{Cost} - \text{Salvage value}}{\text{Useful life}}
Quick example

Equipment costs 480, salvage value 60, useful life 6 years. (480 − 60) ÷ 6 = 70 a year.

On your calculator
  1. 480−60=÷6= 70
  1. 480ENTER60−6÷ 70

ENTER enter (on the HP, puts the number on the stack)

Interest coverage adjusted for capitalized interest Use it
Coverage=EBITInterest expense+Capitalized interest\text{Coverage} = \frac{EBIT}{\text{Interest expense} + \text{Capitalized interest}}
Quick example

EBIT 90, interest expense 15, capitalized interest 5. Reported coverage 90 ÷ 15 = 6.0×. Adjusted: 90 ÷ (15 + 5) = 4.5×.

On your calculator
  1. 15+5=STO1
  2. 90÷RCL1= 4.5

STO store · RCL recall a stored number

  1. 90ENTER15ENTER5+÷ 4.5

ENTER enter (on the HP, puts the number on the stack)

Non-recurring items, discontinued operations and accounting changes

Discontinued operations, net of tax Use it
After-tax result=Pretax result×(1−t)\text{After-tax result} = \text{Pretax result} \times (1 - t)
Quick example

A sold division lost 40 before tax; the tax rate is 25%. It is shown as a loss of 40 × 0.75 = 30 below continuing operations.

On your calculator
  1. 40×0.75= 30
  1. 40ENTER0.75× 30

ENTER enter (on the HP, puts the number on the stack)

Revised depreciation after a change in estimate Use it
New charge=Carrying amountRemaining useful life\text{New charge} = \frac{\text{Carrying amount}}{\text{Remaining useful life}}
Quick example

An 8,000 machine with an 8-year life has run 3 years (carrying amount 5,000). The life is revised to 10 years in total, so 7 remain: 5,000 ÷ 7 = 714.29 a year, applied from now on.

On your calculator
  1. 5000÷7= 714.29
  1. 5000ENTER7÷ 714.29

ENTER enter (on the HP, puts the number on the stack)

Organic revenue growth Use it
gorg=Revenue1−Acquisitions−Currency effectRevenue0−1g_{org} = \frac{\text{Revenue}_1 - \text{Acquisitions} - \text{Currency effect}}{\text{Revenue}_0} - 1
Quick example

Revenue rises from 800 to 880. Acquisitions added 40 and a weaker currency added 16. (880 − 40 − 16) ÷ 800 − 1 = 3.0%.

On your calculator
  1. 880−40−16=÷800−1= 0.03
  1. 880ENTER40−16−800÷1− 0.03

ENTER enter (on the HP, puts the number on the stack)

Basic EPS and the weighted average number of shares

Basic EPS Memorize
EPS=NI−DpWEPS = \frac{NI - D_p}{W}
Quick example

Net income 5,400, preferred dividends 400, weighted average shares 1,250. (5,400 − 400) ÷ 1,250 = 4.00.

On your calculator
  1. 5400−400=÷1250= 4
  1. 5400ENTER400−1250÷ 4

ENTER enter (on the HP, puts the number on the stack)

Weighted average number of shares Memorize
W=∑shares×months outstanding12W = \sum \text{shares} \times \frac{\text{months outstanding}}{12}
Quick example

1,000 shares all year, 400 issued with 9 months left, 200 bought back with 3 months left. 1,000 + 400 × 9/12 − 200 × 3/12 = 1,250.

On your calculator
  1. 400×9÷12=STO1
  2. 200×3÷12=STO2
  3. 1000+RCL1−RCL2= 1250

STO store · RCL recall a stored number

  1. 1000ENTER400ENTER9×12÷+200ENTER3×12÷− 1250

ENTER enter (on the HP, puts the number on the stack)

Diluted EPS: if-converted and treasury stock methods

Diluted EPS Memorize
EPSd=NI−Dp+Dconv+AW+C+ΔSEPS_d = \frac{NI - D_p + D_{conv} + A}{W + C + \Delta S}
Quick example

Income to common 8,000 on 2,000 shares (basic 4.00). Convertible bonds add back 210 of after-tax interest and 100 shares. 8,210 ÷ 2,100 = 3.91.

On your calculator
  1. 2000+100=STO1
  2. 8000+210=÷RCL1= 3.9095

STO store · RCL recall a stored number

  1. 8000ENTER210+2000ENTER100+÷ 3.9095

ENTER enter (on the HP, puts the number on the stack)

After-tax interest on convertible debt Use it
A=F×c×(1−t)A = F \times c \times (1 - t)
Quick example

Bonds with face value 12,000 and a 5% coupon, tax rate 20%. 12,000 × 0.05 × 0.80 = 480 added back.

On your calculator
  1. 12000×0.05×0.8= 480
  1. 12000ENTER0.05×0.8× 480

ENTER enter (on the HP, puts the number on the stack)

Treasury stock method: incremental shares Memorize
ΔS=N−N×KPavg=N×Pavg−KPavg\Delta S = N - \frac{N \times K}{P_{avg}} = N \times \frac{P_{avg} - K}{P_{avg}}
Quick example

50,000 options, exercise price 18, average price 24. 50,000 × (24 − 18) ÷ 24 = 12,500 new shares.

On your calculator
  1. 24−18=×50000÷24= 12500
  1. 24ENTER18−50000×24÷ 12500

ENTER enter (on the HP, puts the number on the stack)

Dilution test (add-back per new share) Use it
q=A or DconvC,include only if q<basic EPSq = \frac{A \text{ or } D_{conv}}{C}, \quad \text{include only if } q < \text{basic EPS}
Quick example

Basic EPS 2.40. A convertible would add back 380 and create 100 shares: 380 ÷ 100 = 3.80, above 2.40, so it is antidilutive and left out.

On your calculator
  1. 380÷100= 3.8
  1. 380ENTER100÷ 3.8

ENTER enter (on the HP, puts the number on the stack)

Common-size income statements and margin ratios

Gross profit margin Memorize
Gross margin=Revenue−Cost of salesRevenue\text{Gross margin} = \frac{\text{Revenue} - \text{Cost of sales}}{\text{Revenue}}
Quick example

Revenue 500, cost of sales 310. Gross profit 190 ÷ 500 = 38.0%.

On your calculator
  1. 500−310=÷500= 0.38
  1. 500ENTER310−500÷ 0.38

ENTER enter (on the HP, puts the number on the stack)

Operating profit margin Memorize
Operating margin=Operating profitRevenue\text{Operating margin} = \frac{\text{Operating profit}}{\text{Revenue}}
Quick example

Gross profit 190, operating expenses 110, so operating profit 80. 80 ÷ 500 = 16.0%.

On your calculator
  1. 190−110=÷500= 0.16
  1. 190ENTER110−500÷ 0.16

ENTER enter (on the HP, puts the number on the stack)

Pretax margin Memorize
Pretax margin=Pretax incomeRevenue\text{Pretax margin} = \frac{\text{Pretax income}}{\text{Revenue}}
Quick example

Operating profit 80, interest expense 25, so pretax income 55. 55 ÷ 500 = 11.0%.

On your calculator
  1. 80−25=÷500= 0.11
  1. 80ENTER25−500÷ 0.11

ENTER enter (on the HP, puts the number on the stack)

Net profit margin Memorize
Net margin=Net incomeRevenue\text{Net margin} = \frac{\text{Net income}}{\text{Revenue}}
Quick example

Pretax income 55, tax 11, so net income 44. 44 ÷ 500 = 8.8%.

On your calculator
  1. 44÷500= 0.088
  1. 44ENTER500÷ 0.088

ENTER enter (on the HP, puts the number on the stack)

Effective tax rate Use it
Effective tax rate=Income tax expensePretax income\text{Effective tax rate} = \frac{\text{Income tax expense}}{\text{Pretax income}}
Quick example

Tax 11 on pretax income of 55. 11 ÷ 55 = 20%. Not 11 ÷ 500.

On your calculator
  1. 11÷55= 0.2
  1. 11ENTER55÷ 0.2

ENTER enter (on the HP, puts the number on the stack)

Comprehensive income Know the idea
Comprehensive income=Net income+OCI\text{Comprehensive income} = \text{Net income} + \text{OCI}
Quick example

Net income 44 and a currency translation loss of 6 in OCI. 44 − 6 = 38.

On your calculator
  1. 44−6= 38
  1. 44ENTER6− 38

ENTER enter (on the HP, puts the number on the stack)

Module 3 Analyzing Balance Sheets

Intangible assets: finite vs indefinite lives

Straight-line amortization and carrying amount Use it
A=CL,Kt=C−A×tA = \frac{C}{L}, \qquad K_t = C - A \times t
Quick example

A software license costs 90 and has a 5-year life. A = 90 ÷ 5 = 18 a year. After 2 years K = 90 − 36 = 54.

On your calculator
  1. 90÷5×2= accumulated amortization, 36
  2. +|-+90= 54

+|- change sign

  1. 90ENTER5÷2× accumulated amortization, 36
  2. CHS90+ 54

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Goodwill: how it is measured and tested

Goodwill Memorize
G=P−(AFV−LFV)G = P - (A_{FV} - L_{FV})
Quick example

Pay 75 for a company whose identifiable assets are worth 130 at fair value and whose liabilities are worth 80. Net identifiable assets 50, so G = 75 − 50 = 25.

On your calculator
  1. 75−130+80= 25
  1. 75ENTER130−80+ 25

ENTER enter (on the HP, puts the number on the stack)

Bargain purchase gain Use it
Gain=(AFV−LFV)−P(when positive)Gain = (A_{FV} - L_{FV}) - P \quad (\text{when positive})
Quick example

Pay 55 for net identifiable assets of 70 at fair value. Gain = 70 − 55 = 15, recognized in profit. No goodwill is recorded.

On your calculator
  1. 70−55= 15
  1. 70ENTER55− 15

ENTER enter (on the HP, puts the number on the stack)

Financial instruments: amortized cost, FVOCI and FVPL

Net income effect of a debt security Use it
ΔNI={I+ΔFVFVPLIFVOCI or amortized cost\Delta NI = \begin{cases} I + \Delta FV & \text{FVPL} \\ I & \text{FVOCI or amortized cost} \end{cases}
Quick example

Coupon income 30 and the bond falls 12 in value. Held at FVPL: profit effect 30 − 12 = 18. At FVOCI or amortized cost: profit effect 30.

On your calculator
  1. 30−12= 18, the FVPL profit effect
  1. 30ENTER12− 18, the FVPL profit effect

ENTER enter (on the HP, puts the number on the stack)

Other comprehensive income effect Use it
ΔOCI={ΔFVFVOCI0FVPL or amortized cost\Delta OCI = \begin{cases} \Delta FV & \text{FVOCI} \\ 0 & \text{FVPL or amortized cost} \end{cases}
Quick example

The same bond at FVOCI: the 12 fall goes to OCI, so OCI is −12 and comprehensive income is 30 − 12 = 18, the same as at FVPL.

On your calculator
  1. 12+|-+30= 18, comprehensive income

+|- change sign

  1. 12CHS30+ 18, comprehensive income

CHS change sign

Non-current liabilities: bonds at amortized cost and deferred taxes

Bond issue price (opening carrying amount) Use it
B0=∑k=1NcF(1+y)k+F(1+y)NB_0 = \sum_{k=1}^{N}\frac{cF}{(1+y)^k} + \frac{F}{(1+y)^N}
Quick example

Face 100, 3% annual coupon, 2 years, market rate 5%. B₀ = 3 ÷ 1.05 + 103 ÷ 1.05² = 96.28.

On your calculator
  1. 2NDCLR TVM with P/Y set to 1
  2. 2N5I/Y3PMT100FV
  3. CPTPV −96.28

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · FV future value · CPT compute · PV present value

  1. fCLEAR FIN
  2. 2n5i3PMT100FV
  3. PV −96.28

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Interest expense (effective interest method) Use it
IEt=Bt−1×yIE_t = B_{t-1} \times y
Quick example

Opening carrying amount 96.28 at a 5% market rate at issue. IE = 96.28 × 5% = 4.81, against a coupon of 3.00.

On your calculator
  1. 96.28×0.05= 4.814
  1. 96.28ENTER0.05× 4.814

ENTER enter (on the HP, puts the number on the stack)

Carrying amount roll-forward Use it
Bt=Bt−1+IEt−cFB_t = B_{t-1} + IE_t - cF
Quick example

Opening 96.28, interest expense 4.81, coupon paid 3.00. Closing = 96.28 + 4.81 − 3.00 = 98.09, drifting toward face value of 100.

On your calculator
  1. 96.28+4.81−3= 98.09
  1. 96.28ENTER4.81+3− 98.09

ENTER enter (on the HP, puts the number on the stack)

Deferred tax liability Use it
DTL=taxable temporary difference×tDTL = \text{taxable temporary difference} \times t
Quick example

Carrying amount of an asset exceeds its tax base by 150 and the tax rate is 25%. DTL = 150 × 0.25 = 37.5.

On your calculator
  1. 150×0.25= 37.5
  1. 150ENTER0.25× 37.5

ENTER enter (on the HP, puts the number on the stack)

Common-size balance sheets, liquidity and solvency ratios

Common-size balance sheet item Memorize
Item %=line itemtotal assets×100\text{Item \%} = \frac{\text{line item}}{\text{total assets}} \times 100
Quick example

Goodwill of 45 in a company with total assets of 1,500. 45 ÷ 1,500 = 3.0%.

On your calculator
  1. 45÷1500= 0.03
  1. 45ENTER1500÷ 0.03

ENTER enter (on the HP, puts the number on the stack)

Current ratio Memorize
Current=current assetscurrent liabilities\text{Current} = \frac{\text{current assets}}{\text{current liabilities}}
Quick example

Current assets 420, current liabilities 350. 420 ÷ 350 = 1.20.

On your calculator
  1. 420÷350= 1.2
  1. 420ENTER350÷ 1.2

ENTER enter (on the HP, puts the number on the stack)

Quick ratio Memorize
Quick=cash+marketable securities+receivablescurrent liabilities\text{Quick} = \frac{\text{cash} + \text{marketable securities} + \text{receivables}}{\text{current liabilities}}
Quick example

Cash 30, securities 20, receivables 110, current liabilities 250. 160 ÷ 250 = 0.64.

On your calculator
  1. 30+20+110÷250= 0.64
  1. 30ENTER20+110+250÷ 0.64

ENTER enter (on the HP, puts the number on the stack)

Cash ratio Memorize
Cash=cash+marketable securitiescurrent liabilities\text{Cash} = \frac{\text{cash} + \text{marketable securities}}{\text{current liabilities}}
Quick example

Cash 30, securities 20, current liabilities 250. 50 ÷ 250 = 0.20.

On your calculator
  1. 30+20÷250= 0.2
  1. 30ENTER20+250÷ 0.2

ENTER enter (on the HP, puts the number on the stack)

Long-term debt-to-equity Memorize
LT D/E=long-term debttotal equity\text{LT D/E} = \frac{\text{long-term debt}}{\text{total equity}}
Quick example

Long-term debt 400, equity 800. 400 ÷ 800 = 0.50.

On your calculator
  1. 400÷800= 0.5
  1. 400ENTER800÷ 0.5

ENTER enter (on the HP, puts the number on the stack)

Debt-to-equity Memorize
D/E=total debttotal equity\text{D/E} = \frac{\text{total debt}}{\text{total equity}}
Quick example

Short-term debt 150, long-term debt 400, equity 800. 550 ÷ 800 = 0.69.

On your calculator
  1. 150+400÷800= 0.6875
  1. 150ENTER400+800÷ 0.6875

ENTER enter (on the HP, puts the number on the stack)

Total debt ratio (debt-to-assets) Memorize
D/TA=total debttotal assets\text{D/TA} = \frac{\text{total debt}}{\text{total assets}}
Quick example

Total debt 550, total assets 1,600. 550 ÷ 1,600 = 0.34.

On your calculator
  1. 550÷1600= 0.3438
  1. 550ENTER1600÷ 0.3438

ENTER enter (on the HP, puts the number on the stack)

Financial leverage Memorize
FL=total assetstotal equity\text{FL} = \frac{\text{total assets}}{\text{total equity}}
Quick example

Total assets 1,600, equity 800. 1,600 ÷ 800 = 2.0: each dollar of equity supports two dollars of assets.

On your calculator
  1. 1600÷800= 2
  1. 1600ENTER800÷ 2

ENTER enter (on the HP, puts the number on the stack)

Module 4 Analyzing Statements of Cash Flows I

How the cash flow statement links to the balance sheet and income statement

Account roll-forward Use it
Bend=Bbegin+additions−deductionsB_{end} = B_{begin} + \text{additions} - \text{deductions}
Quick example

Receivables start at 520, credit revenue is 4,200 and customers pay 4,240. Closing receivables: 520 + 4,200 − 4,240 = 480.

On your calculator
  1. 520+4200−4240= 480
  1. 520ENTER4200+4240− 480

ENTER enter (on the HP, puts the number on the stack)

Inventory purchases Use it
Purchases=COGS+Bend−Bbegin\text{Purchases} = \text{COGS} + B_{end} - B_{begin}
Quick example

COGS is 3,100 and inventory falls from 400 to 350. Purchases: 3,100 + 350 − 400 = 3,050.

On your calculator
  1. 3100+350−400= 3050
  1. 3100ENTER350+400− 3050

ENTER enter (on the HP, puts the number on the stack)

Cash flow from operations: the indirect method

Cash flow from operations (indirect) Memorize
CFO=NI+non-cash charges−gains+losses−Δop. assets+Δop. liabilitiesCFO = NI + \text{non-cash charges} - \text{gains} + \text{losses} - \Delta\text{op. assets} + \Delta\text{op. liabilities}
Quick example

Net income 640, depreciation 210, gain on sale 35. Operating assets up 90 and operating liabilities up 55. 640 + 210 − 35 − 90 + 55 = 780.

On your calculator
  1. 640+210−35−90+55= 780
  1. 640ENTER210+35−90−55+ 780

ENTER enter (on the HP, puts the number on the stack)

The direct method and converting indirect to direct

Cash received from customers Memorize
C=Revenue−ΔAR+ΔUnearned revenueC = \text{Revenue} - \Delta AR + \Delta\text{Unearned revenue}
Quick example

Revenue 7,400, receivables up 80, unearned revenue up 25. 7,400 − 80 + 25 = 7,345.

On your calculator
  1. 7400−80+25= 7345
  1. 7400ENTER80−25+ 7345

ENTER enter (on the HP, puts the number on the stack)

Cash paid to suppliers Memorize
S=COGS+ΔInv−ΔAPS = COGS + \Delta Inv - \Delta AP
Quick example

COGS 4,200, inventory down 60, payables up 35. 4,200 − 60 − 35 = 4,105.

On your calculator
  1. 4200−60−35= 4105
  1. 4200ENTER60−35− 4105

ENTER enter (on the HP, puts the number on the stack)

Cash paid to employees Use it
W=Wage expense−ΔWages payableW = \text{Wage expense} - \Delta\text{Wages payable}
Quick example

Wage expense 900, wages payable up 15. 900 − 15 = 885.

On your calculator
  1. 900−15= 885
  1. 900ENTER15− 885

ENTER enter (on the HP, puts the number on the stack)

Cash paid for other operating expenses Use it
O=Expense+ΔPrepaid−ΔAccrued liabilitiesO = \text{Expense} + \Delta\text{Prepaid} - \Delta\text{Accrued liabilities}
Quick example

Other expenses 450, prepaid up 10, accrued liabilities up 5. 450 + 10 − 5 = 455.

On your calculator
  1. 450+10−5= 455
  1. 450ENTER10+5− 455

ENTER enter (on the HP, puts the number on the stack)

Cash paid for interest Use it
I=Interest expense−ΔInterest payable+premium amort.−discount amort.I = \text{Interest expense} - \Delta\text{Interest payable} + \text{premium amort.} - \text{discount amort.}
Quick example

Interest expense 140, interest payable down 6, discount amortization 4. 140 + 6 − 4 = 142.

On your calculator
  1. 140+6−4= 142
  1. 140ENTER6+4− 142

ENTER enter (on the HP, puts the number on the stack)

Cash paid for income taxes Use it
T=Tax expense−ΔTP+ΔDTA−ΔDTLT = \text{Tax expense} - \Delta TP + \Delta DTA - \Delta DTL
Quick example

Tax expense 310, taxes payable up 20, deferred tax liability up 12. 310 − 20 − 12 = 278.

On your calculator
  1. 310−20−12= 278
  1. 310ENTER20−12− 278

ENTER enter (on the HP, puts the number on the stack)

Investing and financing cash flows: asset sales, debt and dividends

Proceeds from the sale of an asset Use it
P=(C−AD)+G(minus a loss)P = (C - AD) + G \quad (\text{minus a loss})
Quick example

Equipment cost 320 with accumulated depreciation 250 is sold at a loss of 12. Book value 70; 70 − 12 = 58.

On your calculator
  1. 320−250−12= 58
  1. 320ENTER250−12− 58

ENTER enter (on the HP, puts the number on the stack)

Capital expenditures (gross PP&E) Use it
Capex=G1−G0+cost of assets soldCapex = G_1 - G_0 + \text{cost of assets sold}
Quick example

Gross PP&E rises from 3,000 to 3,400 and equipment that cost 150 was sold. 3,400 − 3,000 + 150 = 550.

On your calculator
  1. 3400−3000+150= 550
  1. 3400ENTER3000−150+ 550

ENTER enter (on the HP, puts the number on the stack)

Capital expenditures (net PP&E) Use it
Capex=ΔNet PP&E+Depreciation+Book value of assets soldCapex = \Delta\text{Net PP\&E} + \text{Depreciation} + \text{Book value of assets sold}
Quick example

Net PP&E rises from 1,800 to 1,950, depreciation is 260 and sold assets had a book value of 45. 150 + 260 + 45 = 455.

On your calculator
  1. 1950−1800+260+45= 455
  1. 1950ENTER1800−260+45+ 455

ENTER enter (on the HP, puts the number on the stack)

Dividends paid Use it
Div=RE0+NI−RE1Div = RE_0 + NI - RE_1
Quick example

Retained earnings go from 900 to 1,040 with net income of 310. 900 + 310 − 1,040 = 170.

On your calculator
  1. 900+310−1040= 170
  1. 900ENTER310+1040− 170

ENTER enter (on the HP, puts the number on the stack)

Net change in cash Memorize
ΔCash=CFO+CFI+CFF\Delta Cash = CFO + CFI + CFF
Quick example

CFO 640, CFI −520, CFF −90. 640 − 520 − 90 = 30.

On your calculator
  1. 640−520−90= 30
  1. 640ENTER520−90− 30

ENTER enter (on the HP, puts the number on the stack)

Cash flow statements under IFRS vs US GAAP

Operating cash flow on a US GAAP basis Use it
CFOGAAP=CFOIFRS−Ip+RCFO_{GAAP} = CFO_{IFRS} - I_p + R
Quick example

An IFRS filer reports CFO of 800 with 45 of interest paid in financing and 10 of dividends received in investing. 800 − 45 + 10 = 765.

On your calculator
  1. 800−45+10= 765
  1. 800ENTER45−10+ 765

ENTER enter (on the HP, puts the number on the stack)

Module 5 Analyzing Statements of Cash Flows II

Reading a cash flow statement: sources, uses and common-size

Common-size cash flow line Use it
Share=cash flow linetotal inflows (or outflows, or net revenue)\text{Share} = \frac{\text{cash flow line}}{\text{total inflows (or outflows, or net revenue)}}
Quick example

Operating cash flow is 330 and total cash inflows are 750. 330 ÷ 750 = 44.0% of inflows. Against net revenue of 2,200 the same line is 330 ÷ 2,200 = 15.0%.

On your calculator
  1. 330÷750= 0.44, so 44.0%
  1. 330ENTER750÷ 0.44, so 44.0%

ENTER enter (on the HP, puts the number on the stack)

Free cash flow to the firm (FCFF) and to equity (FCFE)

Free cash flow (generic) Know the idea
Free cash flow=CFO−capital expenditures\text{Free cash flow} = CFO - \text{capital expenditures}
Quick example

CFO of 760 and capital expenditures of 470 leave 290 of free cash flow.

On your calculator
  1. 760−470= 290
  1. 760ENTER470− 290

ENTER enter (on the HP, puts the number on the stack)

Net fixed capital investment Use it
FCInv=capital expenditures−proceeds from sale of long-term assetsFCInv = \text{capital expenditures} - \text{proceeds from sale of long-term assets}
Quick example

Capital expenditures of 1,200 and asset sale proceeds of 150 give FCInv of 1,050.

On your calculator
  1. 1200−150= 1050
  1. 1200ENTER150− 1050

ENTER enter (on the HP, puts the number on the stack)

FCFF from CFO Memorize
FCFF=CFO+Int(1−t)−FCInvFCFF = CFO + Int(1 - t) - FCInv
Quick example

CFO 640 (after paying interest of 80), tax rate 35%, FCInv 200. 640 + 80 × 0.65 − 200 = 492.

On your calculator
  1. 80×0.65+640−200= 492
  1. 80ENTER0.65×640+200− 492

ENTER enter (on the HP, puts the number on the stack)

FCFF from net income Memorize
FCFF=NI+NCC+Int(1−t)−FCInv−WCInvFCFF = NI + NCC + Int(1 - t) - FCInv - WCInv
Quick example

NI 410, non-cash charges 130, interest 60 at 20% tax, FCInv 180, WCInv 40. 410 + 130 + 60 × 0.80 − 180 − 40 = 368.

On your calculator
  1. 60×0.8+410+130−180−40= 368
  1. 60ENTER0.8×410+130+180−40− 368

ENTER enter (on the HP, puts the number on the stack)

FCFE from CFO Memorize
FCFE=CFO−FCInv+Net borrowingFCFE = CFO - FCInv + \text{Net borrowing}
Quick example

CFO 640, FCInv 200, new debt 100 and repayments 150 (net borrowing −50). 640 − 200 − 50 = 390.

On your calculator
  1. 640−200+100−150= 390
  1. 640ENTER200−100+150− 390

ENTER enter (on the HP, puts the number on the stack)

FCFE from FCFF Use it
FCFE=FCFF−Int(1−t)+Net borrowingFCFE = FCFF - Int(1 - t) + \text{Net borrowing}
Quick example

FCFF 492, interest 80 at 35% tax, net borrowing −50. 492 − 52 − 50 = 390, the same as from CFO.

On your calculator
  1. 492−(80×0.65)−50= 390
  1. 492ENTER80ENTER0.65×−50− 390

ENTER enter (on the HP, puts the number on the stack)

Cash flow performance and coverage ratios

Cash flow to revenue Memorize
CFOnet revenue\frac{CFO}{\text{net revenue}}
Quick example

CFO 520 on revenue of 4,000. 520 ÷ 4,000 = 13.0%.

On your calculator
  1. 520÷4000= 0.13
  1. 520ENTER4000÷ 0.13

ENTER enter (on the HP, puts the number on the stack)

Cash return on assets Use it
CFOaverage total assets\frac{CFO}{\text{average total assets}}
Quick example

CFO 520, average total assets 5,000. 520 ÷ 5,000 = 10.4%.

On your calculator
  1. 520÷5000= 0.104
  1. 520ENTER5000÷ 0.104

ENTER enter (on the HP, puts the number on the stack)

Cash return on equity Use it
CFOaverage shareholders’ equity\frac{CFO}{\text{average shareholders’ equity}}
Quick example

CFO 520, average equity 2,600. 520 ÷ 2,600 = 20.0%.

On your calculator
  1. 520÷2600= 0.2
  1. 520ENTER2600÷ 0.2

ENTER enter (on the HP, puts the number on the stack)

Cash to income Memorize
CFOoperating income\frac{CFO}{\text{operating income}}
Quick example

CFO 520, operating income 650. 520 ÷ 650 = 0.80.

On your calculator
  1. 520÷650= 0.8
  1. 520ENTER650÷ 0.8

ENTER enter (on the HP, puts the number on the stack)

Cash flow per share Memorize
CFO−preferred dividendscommon shares outstanding\frac{CFO - \text{preferred dividends}}{\text{common shares outstanding}}
Quick example

CFO 520, preferred dividends 20, 250 million common shares. (520 − 20) ÷ 250 = 2.00 per share.

On your calculator
  1. 520−20=÷250= 2
  1. 520ENTER20−250÷ 2

ENTER enter (on the HP, puts the number on the stack)

Debt coverage Memorize
CFOtotal debt\frac{CFO}{\text{total debt}}
Quick example

CFO 520, total debt 1,300. 520 ÷ 1,300 = 0.40.

On your calculator
  1. 520÷1300= 0.4
  1. 520ENTER1300÷ 0.4

ENTER enter (on the HP, puts the number on the stack)

Cash flow interest coverage Memorize
CFO+interest paid+taxes paidinterest paid\frac{CFO + \text{interest paid} + \text{taxes paid}}{\text{interest paid}}
Quick example

CFO 520, interest paid 40, taxes paid 90. (520 + 40 + 90) ÷ 40 = 16.25×.

On your calculator
  1. 520+40+90=÷40= 16.25
  1. 520ENTER40+90+40÷ 16.25

ENTER enter (on the HP, puts the number on the stack)

Reinvestment Memorize
CFOcash paid for long-term assets\frac{CFO}{\text{cash paid for long-term assets}}
Quick example

CFO 520, cash paid for long-term assets 260. 520 ÷ 260 = 2.0.

On your calculator
  1. 520÷260= 2
  1. 520ENTER260÷ 2

ENTER enter (on the HP, puts the number on the stack)

Debt payment Use it
CFOcash paid for long-term debt repayment\frac{CFO}{\text{cash paid for long-term debt repayment}}
Quick example

CFO 520, long-term debt repaid 130. 520 ÷ 130 = 4.0.

On your calculator
  1. 520÷130= 4
  1. 520ENTER130÷ 4

ENTER enter (on the HP, puts the number on the stack)

Dividend payment Use it
CFOdividends paid\frac{CFO}{\text{dividends paid}}
Quick example

CFO 520, dividends paid 104. 520 ÷ 104 = 5.0.

On your calculator
  1. 520÷104= 5
  1. 520ENTER104÷ 5

ENTER enter (on the HP, puts the number on the stack)

Investing and financing Use it
CFOcash outflows for investing and financing\frac{CFO}{\text{cash outflows for investing and financing}}
Quick example

CFO 520 against 260 of asset purchases, 130 of debt repaid and 104 of dividends (494 in all). 520 ÷ 494 = 1.05.

On your calculator
  1. 260+130+104=STO1
  2. 520÷RCL1= 1.0526

STO store · RCL recall a stored number

  1. 260ENTER130+104+STO1
  2. 520RCL1÷ 1.0526

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Module 6 Analysis of Inventories

Lower of cost and net realizable value (and write-down reversals)

Net realizable value Memorize
NRV=Selling price−Costs to complete−Costs to sellNRV = \text{Selling price} - \text{Costs to complete} - \text{Costs to sell}
Quick example

Expected selling price 900, 60 of finishing costs, 40 of selling costs. 900 − 60 − 40 = 800.

On your calculator
  1. 900−60−40= 800
  1. 900ENTER60−40− 800

ENTER enter (on the HP, puts the number on the stack)

Write-down to the lower of cost and NRV Memorize
Write-down=Cost−NRV(only if NRV<Cost)\text{Write-down} = \text{Cost} - NRV \quad (\text{only if } NRV < \text{Cost})
Quick example

Cost 850, NRV 800. The inventory is written down by 850 − 800 = 50. If NRV were 870, there would be no write-down.

On your calculator
  1. 850−800= 50
  1. 850ENTER800− 50

ENTER enter (on the HP, puts the number on the stack)

US GAAP market value (LIFO and retail methods) Use it
Market=middle value of (NRV−m, RC, NRV)\text{Market} = \text{middle value of } \bigl(NRV - m,\ RC,\ NRV\bigr)
Quick example

Cost 700, NRV 650, normal margin 60, replacement cost 620. Floor 650 − 60 = 590, so market is 620 and the write-down is 700 − 620 = 80.

On your calculator
  1. 650−60= floor 590, so replacement cost 620 sits between floor and ceiling
  2. 700−620= 80
  1. 650ENTER60− floor 590, so replacement cost 620 sits between floor and ceiling
  2. 700ENTER620− 80

ENTER enter (on the HP, puts the number on the stack)

IFRS reversal of a write-down Memorize
Reversal=min⁡(NRVnew−Carrying amount, Original write-down)\text{Reversal} = \min\bigl(NRV_{new} - \text{Carrying amount},\ \text{Original write-down}\bigr)
Quick example

Cost 90 was written down to 70 (a write-down of 20). New NRV is 78. Reversal = min(78 − 70, 20) = 8, so the carrying amount is 78.

On your calculator
  1. 78−70= 8, below the 20 write-down, so reverse 8
  1. 78ENTER70− 8, below the 20 write-down, so reverse 8

ENTER enter (on the HP, puts the number on the stack)

FIFO, LIFO and weighted average when prices rise or fall

Cost of goods sold identity Memorize
COGS=Beginning inventory+Purchases−Ending inventoryCOGS = \text{Beginning inventory} + \text{Purchases} - \text{Ending inventory}
Quick example

Beginning inventory 600, purchases 3,900, ending inventory 750. 600 + 3,900 − 750 = 3,750.

On your calculator
  1. 600+3900−750= 3750
  1. 600ENTER3900+750− 3750

ENTER enter (on the HP, puts the number on the stack)

Weighted average cost per unit Memorize
Average cost=Cost of goods available for saleUnits available for sale\text{Average cost} = \frac{\text{Cost of goods available for sale}}{\text{Units available for sale}}
Quick example

80 units at 9 and 120 at 11 are available. (720 + 1,320) ÷ 200 = 10.20 a unit, so selling 150 units costs 10.20 × 150 = 1,530.

On your calculator
  1. (80×9)+(120×11)=÷200= 10.2
  1. 80ENTER9×120ENTER11×+200÷ 10.2

ENTER enter (on the HP, puts the number on the stack)

Cash tax saved by LIFO Use it
Tax saved=(COGSLIFO−COGSFIFO)×t\text{Tax saved} = (COGS_{LIFO} - COGS_{FIFO}) \times t
Quick example

LIFO cost of sales is 240 higher than FIFO. At a 30% tax rate, LIFO pays 72 less tax, so operating cash flow is 72 higher.

On your calculator
  1. 240×0.3= 72
  1. 240ENTER0.3× 72

ENTER enter (on the HP, puts the number on the stack)

FIFO inventory from LIFO inventory Use it
InventoryFIFO=InventoryLIFO+LIFO reserveInventory_{FIFO} = Inventory_{LIFO} + \text{LIFO reserve}
Quick example

LIFO inventory 600 and a LIFO reserve of 90 give FIFO inventory of 690.

On your calculator
  1. 600+90= 690
  1. 600ENTER90+ 690

ENTER enter (on the HP, puts the number on the stack)

FIFO cost of sales from LIFO cost of sales Use it
COGSFIFO=COGSLIFO−(Reserveend−Reservestart)COGS_{FIFO} = COGS_{LIFO} - (\text{Reserve}_{end} - \text{Reserve}_{start})
Quick example

LIFO cost of sales 3,000. The reserve rose from 70 to 90. FIFO cost of sales = 3,000 − 20 = 2,980.

On your calculator
  1. 3000−90+70= 2980
  1. 3000ENTER90−70+ 2980

ENTER enter (on the HP, puts the number on the stack)

FIFO equity from LIFO equity Know the idea
EquityFIFO=EquityLIFO+LIFO reserve×(1−t)Equity_{FIFO} = Equity_{LIFO} + \text{LIFO reserve} \times (1 - t)
Quick example

A reserve of 90 at a 30% tax rate adds 90 × 0.70 = 63 to equity on a FIFO basis.

On your calculator
  1. 1−0.3=×90= 63
  1. 1ENTER0.3−90× 63

ENTER enter (on the HP, puts the number on the stack)

Inventory disclosures, turnover and days of inventory

Average inventory Use it
Inventoryavg=Inventorybegin+Inventoryend2Inventory_{avg} = \frac{Inventory_{begin} + Inventory_{end}}{2}
Quick example

Inventory of 520 at the start of the year and 680 at the end. (520 + 680) ÷ 2 = 600.

On your calculator
  1. 520+680=÷2= 600
  1. 520ENTER680+2÷ 600

ENTER enter (on the HP, puts the number on the stack)

Inventory turnover Memorize
Inventory turnover=Cost of salesAverage inventory\text{Inventory turnover} = \frac{\text{Cost of sales}}{\text{Average inventory}}
Quick example

Cost of sales 2,940 and average inventory 420. 2,940 ÷ 420 = 7.0 times.

On your calculator
  1. 2940÷420= 7
  1. 2940ENTER420÷ 7

ENTER enter (on the HP, puts the number on the stack)

Days of inventory on hand Memorize
DOH=365Inventory turnoverDOH = \frac{365}{\text{Inventory turnover}}
Quick example

Turnover of 7.0 gives 365 ÷ 7.0 = 52.1 days.

On your calculator
  1. 365÷7= 52.14
  1. 365ENTER7÷ 52.14

ENTER enter (on the HP, puts the number on the stack)

Gross profit margin Use it
Gross profit margin=Revenue−Cost of salesRevenue\text{Gross profit margin} = \frac{\text{Revenue} - \text{Cost of sales}}{\text{Revenue}}
Quick example

Revenue 4,000 and cost of sales 2,940. (4,000 − 2,940) ÷ 4,000 = 26.5%.

On your calculator
  1. 4000−2940=÷4000= 0.265
  1. 4000ENTER2940−4000÷ 0.265

ENTER enter (on the HP, puts the number on the stack)

Inventory before the valuation allowance Use it
Inventorygross=Inventorynet+Valuation allowanceInventory_{gross} = Inventory_{net} + \text{Valuation allowance}
Quick example

Net inventory 910 and a valuation allowance of 60 mean inventory at cost of 970.

On your calculator
  1. 910+60= 970
  1. 910ENTER60+ 970

ENTER enter (on the HP, puts the number on the stack)

Module 7 Analysis of Long-Term Assets

Purchased, internally developed and acquired intangibles

IFRS development spending: capitalized and expensed Use it
C=M (13−k),X=M (k−1)C = M\,(13 - k), \qquad X = M\,(k - 1)
Quick example

A project costs 9,000 a month. All IFRS criteria are first met at the start of month 8. Capitalized = 9,000 × (13 − 8) = 45,000; expensed = 9,000 × 7 = 63,000.

On your calculator
  1. 13−8=×9000= 45000
  1. 13ENTER8−9000× 45000

ENTER enter (on the HP, puts the number on the stack)

Return on assets Use it
ROA=Net incomeTotal assetsROA = \frac{\text{Net income}}{\text{Total assets}}
Quick example

Profit of 120 on assets of 800 gives 120 ÷ 800 = 15.0%. A lower profit and a lower asset base can move ROA either way.

On your calculator
  1. 120÷800= 0.15
  1. 120ENTER800÷ 0.15

ENTER enter (on the HP, puts the number on the stack)

Goodwill from a business combination Use it
Goodwill=Price paid−Fair value of net identifiable assetsGoodwill = \text{Price paid} - \text{Fair value of net identifiable assets}
Quick example

Price 640. Identifiable assets at fair value 520 (including 90 of unrecorded customer relationships), liabilities 130. Net identifiable assets = 390; goodwill = 640 − 390 = 250.

On your calculator
  1. 520−130= 390
  2. +|-+640= 250

+|- change sign

  1. 520ENTER130− 390
  2. CHS640+ 250

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Impairment and derecognition of PP&E and intangibles

Recoverable amount (IFRS) Memorize
RA=max⁡(FVLCS, VIU)RA = \max(FVLCS,\ VIU)
Quick example

Fair value less costs to sell 540, value in use 585. The recoverable amount is the higher, 585.

IFRS impairment loss Memorize
L=CA−RAL = CA - RA
Quick example

Carrying amount 640, recoverable amount 585. Loss = 640 − 585 = 55. If CA is below RA, no loss.

On your calculator
  1. 640−585= 55
  1. 640ENTER585− 55

ENTER enter (on the HP, puts the number on the stack)

US GAAP impairment loss Memorize
L={CA−FVif CA>UCF0otherwiseL = \begin{cases} CA - FV & \text{if } CA > UCF \\ 0 & \text{otherwise} \end{cases}
Quick example

Carrying amount 640, undiscounted cash flows 615, fair value 590. 640 > 615, so impaired: loss = 640 − 590 = 50.

On your calculator
  1. 640−615= 25, positive, so not recoverable
  2. 640−590= 50
  1. 640ENTER615− 25, positive, so not recoverable
  2. 640ENTER590− 50

ENTER enter (on the HP, puts the number on the stack)

Gain or loss on sale Memorize
G=P−(C−AD)G = P - (C - AD)
Quick example

Cost 460, accumulated depreciation 330, sold for 150. Carrying amount 130; gain = 150 − 130 = 20.

On your calculator
  1. 460−330= carrying amount 130
  2. +|-+150= 20

+|- change sign

  1. 460ENTER330− carrying amount 130
  2. CHS150+ 20

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Largest IFRS reversal Use it
Reversal=min⁡(RA, CAno impairment)−CAnowReversal = \min(RA,\ CA_{\text{no impairment}}) - CA_{\text{now}}
Quick example

Carrying amount now 18,000. Without the earlier impairment it would be 26,000. Recoverable amount is 21,000. Reversal = min(21,000, 26,000) − 18,000 = 3,000.

On your calculator
  1. 21000−18000= 3000
  1. 21000ENTER18000− 3000

ENTER enter (on the HP, puts the number on the stack)

PP&E disclosures, fixed asset turnover and asset age

Estimated total useful life Use it
T=Gross PP&EDepreciation expenseT = \frac{\text{Gross PP\&E}}{\text{Depreciation expense}}
Quick example

Gross PP&E 6,800 and depreciation 400 a year. T = 6,800 ÷ 400 = 17.0 years.

On your calculator
  1. 6800÷400= 17
  1. 6800ENTER400÷ 17

ENTER enter (on the HP, puts the number on the stack)

Estimated average age Memorize
Age=Accumulated depreciationDepreciation expenseAge = \frac{\text{Accumulated depreciation}}{\text{Depreciation expense}}
Quick example

Accumulated depreciation 2,600 and depreciation 400 a year. Age = 2,600 ÷ 400 = 6.5 years.

On your calculator
  1. 2600÷400= 6.5
  1. 2600ENTER400÷ 6.5

ENTER enter (on the HP, puts the number on the stack)

Estimated remaining useful life Memorize
Rem=Net PP&EDepreciation expenseRem = \frac{\text{Net PP\&E}}{\text{Depreciation expense}}
Quick example

Gross 6,800, accumulated depreciation 2,600, depreciation 400. Net PP&E = 4,200; remaining life = 4,200 ÷ 400 = 10.5 years.

On your calculator
  1. 6800−2600= 4200
  2. ÷400= 10.5
  1. 6800ENTER2600− 4200
  2. 400÷ 10.5

ENTER enter (on the HP, puts the number on the stack)

Fixed asset turnover Memorize
FAT=RevenueAverage net PP&EFAT = \frac{\text{Revenue}}{\text{Average net PP\&E}}
Quick example

Revenue 6,300. Net PP&E 3,900 at the start and 4,500 at the end, average 4,200. FAT = 6,300 ÷ 4,200 = 1.50 times.

On your calculator
  1. 3900+4500=÷2= 4200
  2. STO1
  3. 6300÷RCL1= 1.5

STO store · RCL recall a stored number

  1. 3900ENTER4500+2÷ 4200
  2. STO1
  3. 6300ENTERRCL1÷ 1.5

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Capital expenditure to depreciation Use it
CapEx ratio=Capital expenditureDepreciation expenseCapEx\ ratio = \frac{\text{Capital expenditure}}{\text{Depreciation expense}}
Quick example

Capital expenditure 450, depreciation 500. 450 ÷ 500 = 0.90: the asset base is shrinking.

On your calculator
  1. 450÷500= 0.9
  1. 450ENTER500÷ 0.9

ENTER enter (on the HP, puts the number on the stack)

Module 8 Topics in Long-Term Liabilities and Equity

Leases: finance vs operating and lessee accounting (IFRS vs US GAAP)

Lease liability at inception Use it
L0=P×1−(1+r)−NrL_0 = P \times \frac{1 - (1+r)^{-N}}{r}
Quick example

Payments of 12,000 at each year-end for 6 years, discounted at 7%. L₀ = 12,000 × 4.76654 = 57,198. The right-of-use asset starts at the same amount.

On your calculator
  1. 2NDCLR TVM
  2. 6N7I/Y12000PMT
  3. CPTPV −57,198.48

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · CPT compute · PV present value

  1. fCLEAR FIN
  2. 6n7i12000PMT
  3. PV −57,198.48

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · PV present value

Interest on the lease liability Use it
It=r×Lt−1I_t = r \times L_{t-1}
Quick example

Opening liability 240,000 at a 5% discount rate. Interest = 240,000 × 0.05 = 12,000. The rest of the payment repays principal.

On your calculator
  1. 240000×0.05= 12000
  1. 240000ENTER0.05× 12000

ENTER enter (on the HP, puts the number on the stack)

Year-1 expense, IFRS and US GAAP finance lease Use it
E1=ROU0N+r×L0E_1 = \frac{ROU_0}{N} + r \times L_0
Quick example

Same lease as above (L₀ = 57,198, 6 years, 7%). Depreciation 57,198 ÷ 6 = 9,533 plus interest 4,004 = 13,537, against a cash payment of 12,000.

On your calculator
  1. 2NDCLR TVM
  2. 6N7I/Y12000PMT
  3. CPTPV −57,198.48
  4. +|-×(1÷6+0.07)= 13,536.97

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · CPT compute · PV present value · +|- change sign

  1. fCLEAR FIN
  2. 6n7i12000PMT
  3. PV −57,198.48
  4. CHS1ENTER6÷0.07+× 13,536.97

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · PV present value · CHS change sign · ENTER enter (on the HP, puts the number on the stack)

US GAAP operating lease cost Use it
Eop=total lease paymentsNE_{op} = \frac{\text{total lease payments}}{N}
Quick example

Payments of 10,000, 11,000 and 12,000 over three years. Total 33,000 ÷ 3 = 11,000 a year, every year, in operating expenses.

On your calculator
  1. 10000+11000+12000=÷3= 11000
  1. 10000ENTER11000+12000+3÷ 11000

ENTER enter (on the HP, puts the number on the stack)

Lessor accounting: finance vs operating leases

Lease receivable at commencement Use it
R0=∑t=1NPt(1+r)tR_0 = \sum_{t=1}^{N} \frac{P_t}{(1+r)^t}
Quick example

Three year-end payments of 40,000, rate implicit in the lease 10%. R₀ = 99,474.

On your calculator
  1. 2NDCLR TVM
  2. 3N10I/Y40000PMT
  3. CPTPV −99,474.08

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · CPT compute · PV present value

  1. fCLEAR FIN
  2. 3n10i40000PMT
  3. PV −99,474.08

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · PV present value

Selling profit Use it
S=R0−CS = R_0 - C
Quick example

Receivable (PV of payments) 99,474 and the equipment carried at 90,000. Selling profit = 99,474 − 90,000 = 9,474, recognized at commencement.

On your calculator
  1. 99474−90000= 9474
  1. 99474ENTER90000− 9474

ENTER enter (on the HP, puts the number on the stack)

Lessor interest income Use it
It=r×Rt−1I_t = r \times R_{t-1}
Quick example

Opening receivable 99,474 at a 10% implicit rate. Interest income = 99,474 × 0.10 = 9,947. The rest of the 40,000 receipt reduces the receivable.

On your calculator
  1. 99474×0.1= 9947.4
  1. 99474ENTER0.1× 9947.4

ENTER enter (on the HP, puts the number on the stack)

Defined contribution vs defined benefit pension plans

Funded status Memorize
F=A−DF = A - D
Quick example

Plan assets 3,100 and defined benefit obligation 3,450. F = 3,100 − 3,450 = −350, so the balance sheet shows a net pension liability of 350.

On your calculator
  1. 3100−3450= −350
  1. 3100ENTER3450− −350

ENTER enter (on the HP, puts the number on the stack)

Net interest (IFRS) Memorize
NI=r×(D0−A0)NI = r \times (D_0 - A_0)
Quick example

Opening obligation 2,000, opening plan assets 1,700, discount rate 4.5%. Net interest (NI) = 0.045 × 300 = 13.5, an expense because the plan is in deficit. A surplus gives net interest income.

On your calculator
  1. 2000−1700=×0.045= 13.5
  1. 2000ENTER1700−0.045× 13.5

ENTER enter (on the HP, puts the number on the stack)

Pension cost in profit or loss (IFRS) Memorize
C=S+Q+NIC = S + Q + NI
Quick example

Current service cost 80, past service cost 10, net interest 13.5. C = 80 + 10 + 13.5 = 103.5.

On your calculator
  1. 80+10+13.5= 103.5
  1. 80ENTER10+13.5+ 103.5

ENTER enter (on the HP, puts the number on the stack)

Remeasurement of plan assets (IFRS, OCI) Use it
Remeasurement=actual return−r×A0\text{Remeasurement} = \text{actual return} - r \times A_0
Quick example

Opening plan assets 1,700, discount rate 4.5% (interest income 76.5 inside net interest), actual return 120. Remeasurement = 120 − 76.5 = +43.5 gain, to OCI.

On your calculator
  1. 1700×0.045=+|-+120= 43.5

+|- change sign

  1. 1700ENTER0.045×CHS120+ 43.5

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Pension cost in profit or loss (US GAAP) Use it
C=S+r D0−ER+amortizationC = S + r\,D_0 - ER + \text{amortization}
Quick example

Service cost 80, 4.5% interest cost on a 2,000 obligation (90), expected return 7% on 1,700 (119), amortization of past service cost and OCI losses 5. C = 80 + 90 − 119 + 5 = 56.

On your calculator
  1. 2000×0.045=+80−(1700×0.07)+5= 56
  1. 2000ENTER0.045×80+1700ENTER0.07×−5+ 56

ENTER enter (on the HP, puts the number on the stack)

Share-based compensation: stock grants, options and SARs

Annual compensation expense (equity-settled) Memorize
E=N×FTE = \frac{N \times F}{T}
Quick example

48,000 options with a grant-date fair value of 5.50, vesting after 4 years. E = 48,000 × 5.50 ÷ 4 = 66,000 a year. For restricted stock, F is the share price at grant.

On your calculator
  1. 48000×5.5÷4= 66000
  1. 48000ENTER5.5×4÷ 66000

ENTER enter (on the HP, puts the number on the stack)

Run-off of unrecognized cost Use it
E=UWE = \frac{U}{W}
Quick example

The notes show 420m of unrecognized cost to be recognized over a weighted-average 2.8 years. About 420 ÷ 2.8 = 150m a year for two years, leaving 420 − 300 = 120m for the third.

On your calculator
  1. 420÷2.8= 150
  1. 420ENTER2.8÷ 150

ENTER enter (on the HP, puts the number on the stack)

Module 9 Analysis of Income Taxes

Accounting profit vs taxable income: temporary and permanent differences

Deferred tax from a temporary difference Use it
DT=∣ CA−TB ∣×tDT = |\,CA - TB\,| \times t
Quick example

A machine has a carrying amount of 1,000 and a tax base of 760; the tax rate is 20%. The asset is above its tax base, so (1,000 − 760) × 20% = 48 DTL.

On your calculator
  1. 1000−760=×0.2= 48
  1. 1000ENTER760−0.2× 48

ENTER enter (on the HP, puts the number on the stack)

Tax base of a liability Use it
TBliability=CA−amounts deductible in futureTB_{liability} = CA - \text{amounts deductible in future}
Quick example

A warranty provision of 80 that tax law lets you deduct only when the repairs are paid: 80 − 80 = 0. Carrying amount 80 is above the tax base of 0, so a deductible difference and a DTA.

On your calculator
  1. 80−80= 0
  1. 80ENTER80− 0

ENTER enter (on the HP, puts the number on the stack)

Deferred tax assets and liabilities

Taxes payable Use it
TP=TI×tTP = TI \times t
Quick example

Taxable income of 1,200 at a 30% tax rate: 1,200 × 0.30 = 360 of income tax payable.

On your calculator
  1. 1200×0.3= 360
  1. 1200ENTER0.3× 360

ENTER enter (on the HP, puts the number on the stack)

Income tax expense Memorize
TE=TP+ΔDTL−ΔDTATE = TP + \Delta DTL - \Delta DTA
Quick example

Taxes payable are 640. The DTL fell by 30 and the DTA rose by 12. Expense = 640 + (−30) − 12 = 598.

On your calculator
  1. 640+30+|-−12= 598

+|- change sign

  1. 640ENTER30CHS+12− 598

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Remeasuring a deferred tax balance Use it
ΔB=D×(t1−t0)\Delta B = D \times (t_1 - t_0)
Quick example

A taxable temporary difference of 400 and a rate cut from 30% to 24%. 400 × (24% − 30%) = −24: the DTL falls by 24, and tax expense falls by 24.

On your calculator
  1. 24−30=×400÷100= −24
  1. 24ENTER30−400×100÷ −24

ENTER enter (on the HP, puts the number on the stack)

Valuation allowance Memorize
VA=G×u,net DTA=G−VAVA = G \times u, \quad \text{net DTA} = G - VA
Quick example

A gross DTA of 350 of which 30% is unlikely to be used. VA = 350 × 0.30 = 105; net DTA = 245.

On your calculator
  1. 350×0.3= 105
  1. 350ENTER0.3× 105

ENTER enter (on the HP, puts the number on the stack)

Effective, statutory and cash tax rates

Effective tax rate Memorize
ETR=income tax expensepretax incomeETR = \frac{\text{income tax expense}}{\text{pretax income}}
Quick example

Pretax income 4,500 and income tax expense 1,071. 1,071 ÷ 4,500 = 23.8%.

On your calculator
  1. 1071÷4500= 0.238
  1. 1071ENTER4500÷ 0.238

ENTER enter (on the HP, puts the number on the stack)

Cash tax rate Memorize
CTR=cash taxes paidpretax incomeCTR = \frac{\text{cash taxes paid}}{\text{pretax income}}
Quick example

Pretax income 4,500 and cash taxes paid 891. 891 ÷ 4,500 = 19.8%, below the 23.8% effective rate.

On your calculator
  1. 891÷4500= 0.198
  1. 891ENTER4500÷ 0.198

ENTER enter (on the HP, puts the number on the stack)

Effective rate from the geographic mix Use it
ETR=∑iwi tiETR = \sum_i w_i \, t_i
Quick example

Half the profit is earned at 12% and half at 28%. 0.5 × 12% + 0.5 × 28% = 20%.

On your calculator
  1. 0.5×12=STO1
  2. 0.5×28=+RCL1= 20

STO store · RCL recall a stored number

  1. 0.5ENTER12×0.5ENTER28×+ 20

ENTER enter (on the HP, puts the number on the stack)

Income tax disclosures and the tax rate reconciliation

Effective rate from the reconciliation Use it
ETR=S+∑reconciling itemsETR = S + \sum \text{reconciling items}
Quick example

Statutory 30%, non-deductible costs +1.2, lower foreign rates −5.0, research credits −0.7. 30 + 1.2 − 5.0 − 0.7 = 25.5%.

On your calculator
  1. 30+1.2−5−0.7= 25.5
  1. 30ENTER1.2+5−0.7− 25.5

ENTER enter (on the HP, puts the number on the stack)

Sustainable tax rate Use it
ETRs=ETR−one-off itemsETR_s = ETR - \text{one-off items}
Quick example

Reported rate 18.4% includes a one-off valuation allowance release of −2.6 points. 18.4 − (−2.6) = 21.0% is the rate to forecast with.

On your calculator
  1. 18.4−2.6+|-= 21

+|- change sign

  1. 18.4ENTER2.6CHS− 21

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Module 10 Financial Reporting Quality

Why managers misreport, and what stops them

Interest coverage Use it
C=EBITInterest expenseC = \frac{EBIT}{\text{Interest expense}}
Quick example

Operating profit of 640 and interest expense of 160 give coverage of 640 ÷ 160 = 4.0×. A covenant minimum of 3.5× leaves 80 of operating profit as headroom (3.5 × 160 = 560).

On your calculator
  1. 640÷160= 4
  1. 640ENTER160÷ 4

ENTER enter (on the HP, puts the number on the stack)

Non-GAAP measures and other presentation choices

Analyst-adjusted earnings Use it
NIadj=NI+∑accepted add-backsNI_{adj} = NI + \sum \text{accepted add-backs}
Quick example

Net income is 200. Management adds back amortization of acquired intangibles (15) and a restructuring charge booked every year (40). Accepting only the amortization gives 200 + 15 = 215, not 255.

On your calculator
  1. 200+15= 215
  1. 200ENTER15+ 215

ENTER enter (on the HP, puts the number on the stack)

EBITDA from net income Use it
EBITDA=NI+interest+taxes+depreciation and amortizationEBITDA = NI + \text{interest} + \text{taxes} + \text{depreciation and amortization}
Quick example

Net income 90, taxes 30, interest 25, depreciation and amortization 45: 90 + 30 + 25 + 45 = 190.

On your calculator
  1. 90+30+25+45= 190
  1. 90ENTER30+25+45+ 190

ENTER enter (on the HP, puts the number on the stack)

How accounting choices and estimates manage earnings, cash flow and the balance sheet

Straight-line depreciation Know the idea
D=C−SLD = \frac{C - S}{L}
Quick example

A machine costing 880 with salvage value 40 and a 6-year life: (880 − 40) ÷ 6 = 140 a year.

On your calculator
  1. 880−40=÷6= 140
  1. 880ENTER40−6÷ 140

ENTER enter (on the HP, puts the number on the stack)

Depreciation after extending the life of an asset Use it
Dnew=C−S−k DoldL1−kD_{new} = \frac{C - S - k\,D_{old}}{L_1 - k}
Quick example

A 1,500 asset with no salvage value and a 10-year life is two years old. The total life is raised to 14 years. Depreciation to date is 300, so (1,500 − 300) ÷ 12 = 100 a year, down from 150.

On your calculator
  1. 1500÷10×2=STO1
  2. 1500−RCL1=÷12= 100

STO store · RCL recall a stored number

  1. 1500ENTER10÷2×STO1
  2. 1500ENTERRCL1−12÷ 100

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number

Profit effect of a lower bad-debt allowance Use it
Δ=AR×(a0−a1)\Delta = AR \times (a_0 - a_1)
Quick example

Receivables of 4,500 and an allowance cut from 4% to 2.5%: 4,500 × 1.5% = 67.5 more pretax profit, and receivables carried 67.5 higher.

On your calculator
  1. 4500×0.015= 67.5
  1. 4500ENTER0.015× 67.5

ENTER enter (on the HP, puts the number on the stack)

Warning signs of earnings manipulation

Days sales outstanding Use it
DSO=ReceivablesRevenue×365DSO = \frac{\text{Receivables}}{\text{Revenue}} \times 365
Quick example

Year-end receivables of 330 on revenue of 2,400: 330 ÷ 2,400 × 365 = 50.2 days. Compare the trend and the peers, not one year.

On your calculator
  1. 330÷2400×365= 50.1875
  1. 330ENTER2400÷365× 50.1875

ENTER enter (on the HP, puts the number on the stack)

Cash flow to net income Memorize
q=CFONIq = \frac{CFO}{NI}
Quick example

Net income 240 and cash flow from operations 180: 180 ÷ 240 = 0.75. Below 1, so check the accruals.

On your calculator
  1. 180÷240= 0.75
  1. 180ENTER240÷ 0.75

ENTER enter (on the HP, puts the number on the stack)

Inventory turnover Use it
T=COGSInventoryT = \frac{COGS}{\text{Inventory}}
Quick example

Cost of goods sold of 882 on year-end inventory of 280: 882 ÷ 280 = 3.15 times, down from 4.2.

On your calculator
  1. 882÷280= 3.15
  1. 882ENTER280÷ 3.15

ENTER enter (on the HP, puts the number on the stack)

Module 11 Financial Analysis Techniques

Analysis tools: common-size, trend, cross-sectional and the limits of ratios

Vertical common-size item Use it
Item %=line itembase×100\text{Item \%} = \frac{\text{line item}}{\text{base}} \times 100
Quick example

Inventory is 186 on a balance sheet with total assets of 1,550. The base of a common-size balance sheet is total assets: 186 ÷ 1,550 = 12.0%.

On your calculator
  1. 186÷1550= 0.12
  1. 186ENTER1550÷ 0.12

ENTER enter (on the HP, puts the number on the stack)

Horizontal common-size index Use it
Indext=itemtitembase\text{Index}_t = \frac{\text{item}_t}{\text{item}_{\text{base}}}
Quick example

Selling expenses were 85 in the base year and 102 two years later. 102 ÷ 85 = 1.20, so they are 20% above the base year.

On your calculator
  1. 102÷85= 1.2
  1. 102ENTER85÷ 1.2

ENTER enter (on the HP, puts the number on the stack)

Compound growth rate Use it
g=(XnX0)1/n−1g = \left(\frac{X_n}{X_0}\right)^{1/n} - 1
Quick example

Net income grows from 250 to 360 over 4 years. (360 ÷ 250)^(1/4) − 1 = 9.5% a year.

On your calculator
  1. 360÷250=y^x0.25=−1= 0.0954

y^x power

  1. 360ENTER250÷0.25y^x1− 0.0954

ENTER enter (on the HP, puts the number on the stack) · y^x power

Trailing 12 months (TTM) Use it
TTM=last fiscal year+current YTD−prior-year YTD\text{TTM} = \text{last fiscal year} + \text{current YTD} - \text{prior-year YTD}
Quick example

Last fiscal year earnings 600. Six months this year 330 against 290 for the same six months last year. TTM = 600 + 330 − 290 = 640.

On your calculator
  1. 600+330−290= 640
  1. 600ENTER330+290− 640

ENTER enter (on the HP, puts the number on the stack)

Activity ratios: turnover, days and the cash conversion cycle

Inventory turnover Memorize
Inventory turnover=COGSaverage inventory\text{Inventory turnover} = \frac{\text{COGS}}{\text{average inventory}}
Quick example

COGS 1,800. Inventory 210 at the start and 290 at the end, so the average is 250. 1,800 ÷ 250 = 7.2 times.

On your calculator
  1. 1800÷(210+290)×2= 7.2
  1. 1800ENTER210ENTER290+÷2× 7.2

ENTER enter (on the HP, puts the number on the stack)

Receivables turnover Memorize
Receivables turnover=revenueaverage receivables\text{Receivables turnover} = \frac{\text{revenue}}{\text{average receivables}}
Quick example

Revenue 2,600. Receivables 240 at the start and 280 at the end, so the average is 260. 2,600 ÷ 260 = 10.0 times.

On your calculator
  1. 2600÷(240+280)×2= 10
  1. 2600ENTER240ENTER280+÷2× 10

ENTER enter (on the HP, puts the number on the stack)

Purchases Memorize
Purchases=COGS+ending inventory−beginning inventory\text{Purchases} = \text{COGS} + \text{ending inventory} - \text{beginning inventory}
Quick example

COGS 1,800, inventory 210 at the start and 290 at the end. 1,800 + 290 − 210 = 1,880.

On your calculator
  1. 1800+290−210= 1880
  1. 1800ENTER290+210− 1880

ENTER enter (on the HP, puts the number on the stack)

Payables turnover Memorize
Payables turnover=purchasesaverage trade payables\text{Payables turnover} = \frac{\text{purchases}}{\text{average trade payables}}
Quick example

Purchases 1,880. Payables 220 at the start and 250 at the end, so the average is 235. 1,880 ÷ 235 = 8.0 times.

On your calculator
  1. 1880÷(220+250)×2= 8
  1. 1880ENTER220ENTER250+÷2× 8

ENTER enter (on the HP, puts the number on the stack)

Days from turnover Memorize
Days=365turnover\text{Days} = \frac{365}{\text{turnover}}
Quick example

Inventory turnover of 7.2. DOH = 365 ÷ 7.2 = 50.7 days. The same step gives DSO from receivables turnover and days of payables from payables turnover.

On your calculator
  1. 365÷7.2= 50.69
  1. 365ENTER7.2÷ 50.69

ENTER enter (on the HP, puts the number on the stack)

Cash conversion cycle Memorize
CCC=DOH+DSO−days of payables\text{CCC} = \text{DOH} + \text{DSO} - \text{days of payables}
Quick example

DOH 52, DSO 34, days of payables 41. 52 + 34 − 41 = 45 days.

On your calculator
  1. 52+34−41= 45
  1. 52ENTER34+41− 45

ENTER enter (on the HP, puts the number on the stack)

Working capital turnover Use it
Working capital turnover=revenueaverage working capital\text{Working capital turnover} = \frac{\text{revenue}}{\text{average working capital}}
Quick example

Revenue 2,600. Working capital (current assets − current liabilities) 140 at the start and 180 at the end, average 160. 2,600 ÷ 160 = 16.25.

On your calculator
  1. 2600÷(140+180)×2= 16.25
  1. 2600ENTER140ENTER180+÷2× 16.25

ENTER enter (on the HP, puts the number on the stack)

Fixed asset turnover Use it
Fixed asset turnover=revenueaverage net fixed assets\text{Fixed asset turnover} = \frac{\text{revenue}}{\text{average net fixed assets}}
Quick example

Revenue 900. Net fixed assets 280 at the start and 320 at the end, average 300. 900 ÷ 300 = 3.0.

On your calculator
  1. 900÷(280+320)×2= 3
  1. 900ENTER280ENTER320+÷2× 3

ENTER enter (on the HP, puts the number on the stack)

Total asset turnover Memorize
Total asset turnover=revenueaverage total assets\text{Total asset turnover} = \frac{\text{revenue}}{\text{average total assets}}
Quick example

Revenue 2,600. Total assets 1,900 at the start and 2,100 at the end, average 2,000. 2,600 ÷ 2,000 = 1.3.

On your calculator
  1. 2600÷(1900+2100)×2= 1.3
  1. 2600ENTER1900ENTER2100+÷2× 1.3

ENTER enter (on the HP, puts the number on the stack)

Liquidity and solvency ratios: can the company pay?

Current ratio Memorize
Current ratio=current assetscurrent liabilities\text{Current ratio} = \frac{\text{current assets}}{\text{current liabilities}}
Quick example

Current assets 910, current liabilities 650. 910 ÷ 650 = 1.40.

On your calculator
  1. 910÷650= 1.4
  1. 910ENTER650÷ 1.4

ENTER enter (on the HP, puts the number on the stack)

Quick ratio Memorize
Quick ratio=cash+short-term investments+receivablescurrent liabilities\text{Quick ratio} = \frac{\text{cash} + \text{short-term investments} + \text{receivables}}{\text{current liabilities}}
Quick example

Cash 90, short-term investments 40, receivables 210, current liabilities 400. 340 ÷ 400 = 0.85.

On your calculator
  1. 90+40+210÷400= 0.85
  1. 90ENTER40+210+400÷ 0.85

ENTER enter (on the HP, puts the number on the stack)

Cash ratio Memorize
Cash ratio=cash+short-term investmentscurrent liabilities\text{Cash ratio} = \frac{\text{cash} + \text{short-term investments}}{\text{current liabilities}}
Quick example

Cash 90, short-term investments 40, current liabilities 400. 130 ÷ 400 = 0.325.

On your calculator
  1. 90+40÷400= 0.325
  1. 90ENTER40+400÷ 0.325

ENTER enter (on the HP, puts the number on the stack)

Defensive interval ratio Memorize
DIR=cash+short-term investments+receivablesdaily cash expenditures\text{DIR} = \frac{\text{cash} + \text{short-term investments} + \text{receivables}}{\text{daily cash expenditures}}
Quick example

Cash, investments and receivables total 420. Annual cash expenses (after removing depreciation) are 2,555, or 7 a day. 420 ÷ 7 = 60.0 days.

On your calculator
  1. 420×365÷2555= 60
  1. 420ENTER365×2555÷ 60

ENTER enter (on the HP, puts the number on the stack)

Debt-to-assets ratio Memorize
Debt-to-assets=total debttotal assets\text{Debt-to-assets} = \frac{\text{total debt}}{\text{total assets}}
Quick example

Debt (short-term plus long-term borrowings) 540, total assets 1,800. 540 ÷ 1,800 = 0.30.

On your calculator
  1. 540÷1800= 0.3
  1. 540ENTER1800÷ 0.3

ENTER enter (on the HP, puts the number on the stack)

Debt-to-capital ratio Memorize
Debt-to-capital=total debttotal debt+total equity\text{Debt-to-capital} = \frac{\text{total debt}}{\text{total debt} + \text{total equity}}
Quick example

Debt 540, equity 960. 540 ÷ (540 + 960) = 0.36.

On your calculator
  1. 540÷(540+960)= 0.36
  1. 540ENTER540ENTER960+÷ 0.36

ENTER enter (on the HP, puts the number on the stack)

Debt-to-equity ratio Memorize
Debt-to-equity=total debttotal equity\text{Debt-to-equity} = \frac{\text{total debt}}{\text{total equity}}
Quick example

Debt 540, equity 960. 540 ÷ 960 = 0.56.

On your calculator
  1. 540÷960= 0.5625
  1. 540ENTER960÷ 0.5625

ENTER enter (on the HP, puts the number on the stack)

Financial leverage ratio Memorize
Financial leverage=average total assetsaverage total equity\text{Financial leverage} = \frac{\text{average total assets}}{\text{average total equity}}
Quick example

Average assets 1,800 and average equity 750. 1,800 ÷ 750 = 2.40: each unit of equity supports 2.40 of assets.

On your calculator
  1. 1800÷750= 2.4
  1. 1800ENTER750÷ 2.4

ENTER enter (on the HP, puts the number on the stack)

Net debt Use it
Net debt=total debt−cash−marketable securities\text{Net debt} = \text{total debt} - \text{cash} - \text{marketable securities}
Quick example

Debt 1,280, cash and marketable securities 320. Net debt = 960.

On your calculator
  1. 1280−320= 960
  1. 1280ENTER320− 960

ENTER enter (on the HP, puts the number on the stack)

Debt-to-EBITDA Memorize
Debt-to-EBITDA=total (or net) debtEBITDA\text{Debt-to-EBITDA} = \frac{\text{total (or net) debt}}{\text{EBITDA}}
Quick example

Debt 1,280, cash 320, EBITDA 400. Gross: 1,280 ÷ 400 = 3.2 years. Net: 960 ÷ 400 = 2.4 years.

On your calculator
  1. 1280÷400= 3.2
  1. 1280ENTER400÷ 3.2

ENTER enter (on the HP, puts the number on the stack)

Interest coverage Memorize
Interest coverage=EBITinterest payments\text{Interest coverage} = \frac{\text{EBIT}}{\text{interest payments}}
Quick example

EBIT 500, interest 80. 500 ÷ 80 = 6.25 times.

On your calculator
  1. 500÷80= 6.25
  1. 500ENTER80÷ 6.25

ENTER enter (on the HP, puts the number on the stack)

Fixed charge coverage Memorize
Fixed charge coverage=EBIT+lease paymentsinterest payments+lease payments\text{Fixed charge coverage} = \frac{\text{EBIT} + \text{lease payments}}{\text{interest payments} + \text{lease payments}}
Quick example

EBIT 500, interest 80, lease payments 60. (500 + 60) ÷ (80 + 60) = 4.0 times.

On your calculator
  1. (500+60)÷(80+60)= 4
  1. 500ENTER60+80ENTER60+÷ 4

ENTER enter (on the HP, puts the number on the stack)

Profitability ratios: margins and returns on capital

Gross profit margin Memorize
Gross margin=gross profitrevenue\text{Gross margin} = \frac{\text{gross profit}}{\text{revenue}}
Quick example

Revenue 2,000, cost of goods sold (COGS) 1,300. Gross profit 700. 700 ÷ 2,000 = 35.0%.

On your calculator
  1. 2000−1300=÷2000= 0.35
  1. 2000ENTER1300−2000÷ 0.35

ENTER enter (on the HP, puts the number on the stack)

Operating profit margin Memorize
Operating margin=operating incomerevenue\text{Operating margin} = \frac{\text{operating income}}{\text{revenue}}
Quick example

Operating income 260 on revenue of 2,000. 260 ÷ 2,000 = 13.0%.

On your calculator
  1. 260÷2000= 0.13
  1. 260ENTER2000÷ 0.13

ENTER enter (on the HP, puts the number on the stack)

Pretax margin Memorize
Pretax margin=EBTrevenue\text{Pretax margin} = \frac{\text{EBT}}{\text{revenue}}
Quick example

EBT (after interest) 220 on revenue of 2,000. 220 ÷ 2,000 = 11.0%.

On your calculator
  1. 220÷2000= 0.11
  1. 220ENTER2000÷ 0.11

ENTER enter (on the HP, puts the number on the stack)

Net profit margin Memorize
Net margin=net incomerevenue\text{Net margin} = \frac{\text{net income}}{\text{revenue}}
Quick example

Net income 165 on revenue of 2,000. 165 ÷ 2,000 = 8.25%.

On your calculator
  1. 165÷2000= 0.0825
  1. 165ENTER2000÷ 0.0825

ENTER enter (on the HP, puts the number on the stack)

Operating ROA Memorize
Operating ROA=operating income (EBIT)average total assets\text{Operating ROA} = \frac{\text{operating income (EBIT)}}{\text{average total assets}}
Quick example

EBIT 260, average total assets 1,600. 260 ÷ 1,600 = 16.25%.

On your calculator
  1. 260÷1600= 0.1625
  1. 260ENTER1600÷ 0.1625

ENTER enter (on the HP, puts the number on the stack)

Return on assets (ROA) Memorize
ROA=net incomeaverage total assets\text{ROA} = \frac{\text{net income}}{\text{average total assets}}
Quick example

Net income 165, average total assets 1,600. 165 ÷ 1,600 = 10.31%.

On your calculator
  1. 165÷1600= 0.1031
  1. 165ENTER1600÷ 0.1031

ENTER enter (on the HP, puts the number on the stack)

ROA with interest added back Use it
ROAadj=NI+interest×(1−t)average total assets\text{ROA}_{adj} = \frac{\text{NI} + \text{interest} \times (1 - t)}{\text{average total assets}}
Quick example

Net income 165, interest 40, tax rate 25%, average assets 1,600. (165 + 40 × 0.75) ÷ 1,600 = 195 ÷ 1,600 = 12.19%.

On your calculator
  1. 40×0.75+165=÷1600= 0.1219
  1. 40ENTER0.75×165+1600÷ 0.1219

ENTER enter (on the HP, puts the number on the stack)

Return on invested capital (ROIC) Memorize
ROIC=EBIT×(1−t)average (short-term debt + long-term debt + equity)\text{ROIC} = \frac{\text{EBIT} \times (1 - t)}{\text{average (short-term debt + long-term debt + equity)}}
Quick example

EBIT 260, tax rate 25%, average invested capital 1,300. 260 × 0.75 = 195, and 195 ÷ 1,300 = 15.0%.

On your calculator
  1. 260×0.75÷1300= 0.15
  1. 260ENTER0.75×1300÷ 0.15

ENTER enter (on the HP, puts the number on the stack)

Return on total capital (pre-tax) Use it
Return on total capital=EBITaverage (debt + equity)\text{Return on total capital} = \frac{\text{EBIT}}{\text{average (debt + equity)}}
Quick example

EBIT 260, average debt plus equity 1,300. 260 ÷ 1,300 = 20.0%.

On your calculator
  1. 260÷1300= 0.2
  1. 260ENTER1300÷ 0.2

ENTER enter (on the HP, puts the number on the stack)

Return on equity (ROE) Memorize
ROE=net incomeaverage total equity\text{ROE} = \frac{\text{net income}}{\text{average total equity}}
Quick example

Net income 165, average total equity 750. 165 ÷ 750 = 22.0%.

On your calculator
  1. 165÷750= 0.22
  1. 165ENTER750÷ 0.22

ENTER enter (on the HP, puts the number on the stack)

Return on common equity Memorize
ROCE=net income−preferred dividendsaverage common equity\text{ROCE} = \frac{\text{net income} - \text{preferred dividends}}{\text{average common equity}}
Quick example

Net income 165, preferred dividends 15, average common equity 650. (165 − 15) ÷ 650 = 23.1%.

On your calculator
  1. 165−15÷650= 0.2308
  1. 165ENTER15−650÷ 0.2308

ENTER enter (on the HP, puts the number on the stack)

DuPont analysis: three-step and five-step ROE

ROE from ROA and leverage Memorize
ROE=ROA×average total assetsaverage total equity\text{ROE} = \text{ROA} \times \frac{\text{average total assets}}{\text{average total equity}}
Quick example

ROA 6.0% and financial leverage 2.2. ROE = 6.0% × 2.2 = 13.2%.

On your calculator
  1. 0.06×2.2= 0.132
  1. 0.06ENTER2.2× 0.132

ENTER enter (on the HP, puts the number on the stack)

Three-step DuPont Memorize
ROE=NIrevenue×revenueaverage assets×average assetsaverage equity\text{ROE} = \frac{\text{NI}}{\text{revenue}} \times \frac{\text{revenue}}{\text{average assets}} \times \frac{\text{average assets}}{\text{average equity}}
Quick example

Net margin 4.5%, total asset turnover 1.4, financial leverage 2.5. ROE = 0.045 × 1.4 × 2.5 = 15.75%.

On your calculator
  1. 0.045×1.4×2.5= 0.1575
  1. 0.045ENTER1.4×2.5× 0.1575

ENTER enter (on the HP, puts the number on the stack)

Tax burden Memorize
Tax burden=NIEBT=1−effective tax rate\text{Tax burden} = \frac{\text{NI}}{\text{EBT}} = 1 - \text{effective tax rate}
Quick example

Net income 84, EBT 120. 84 ÷ 120 = 0.70, an effective tax rate of 30%.

On your calculator
  1. 84÷120= 0.7
  1. 84ENTER120÷ 0.7

ENTER enter (on the HP, puts the number on the stack)

Interest burden Memorize
Interest burden=EBTEBIT\text{Interest burden} = \frac{\text{EBT}}{\text{EBIT}}
Quick example

EBT 136, EBIT 160. 136 ÷ 160 = 0.85: interest takes 15% of EBIT.

On your calculator
  1. 136÷160= 0.85
  1. 136ENTER160÷ 0.85

ENTER enter (on the HP, puts the number on the stack)

Five-step DuPont Memorize
ROE=NIEBT×EBTEBIT×EBITrevenue×revenueavg. assets×avg. assetsavg. equity\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}}
Quick example

Tax burden 0.70, interest burden 0.85, EBIT margin 8%, asset turnover 1.25, leverage 2.0. ROE = 0.70 × 0.85 × 0.08 × 1.25 × 2.0 = 11.9%.

On your calculator
  1. 0.7×0.85×0.08×1.25×2= 0.119
  1. 0.7ENTER0.85×0.08×1.25×2× 0.119

ENTER enter (on the HP, puts the number on the stack)

Industry-specific ratios and using ratios to forecast

Coefficient of variation Know the idea
CV=standard deviationaverage\text{CV} = \frac{\text{standard deviation}}{\text{average}}
Quick example

Operating income has a standard deviation of 12 around an average of 80. CV = 12 ÷ 80 = 0.15. A higher CV means a riskier income stream.

On your calculator
  1. 12÷80= 0.15
  1. 12ENTER80÷ 0.15

ENTER enter (on the HP, puts the number on the stack)

Net interest margin Use it
NIM=net interest incomeinterest-earning assets\text{NIM} = \frac{\text{net interest income}}{\text{interest-earning assets}}
Quick example

Net interest income 420 on interest-earning assets of 14,000. 420 ÷ 14,000 = 3.0%.

On your calculator
  1. 420÷14000= 0.03
  1. 420ENTER14000÷ 0.03

ENTER enter (on the HP, puts the number on the stack)

Capital adequacy ratio Know the idea
Capital adequacy=capitalrisk-weighted assets\text{Capital adequacy} = \frac{\text{capital}}{\text{risk-weighted assets}}
Quick example

Capital 1,260 against risk-weighted assets of 10,500. 1,260 ÷ 10,500 = 12.0%.

On your calculator
  1. 1260÷10500= 0.12
  1. 1260ENTER10500÷ 0.12

ENTER enter (on the HP, puts the number on the stack)

Same-store sales growth Use it
Same-store growth=sales at stores open in both periods, this yearsales at the same stores, last year−1\text{Same-store growth} = \frac{\text{sales at stores open in both periods, this year}}{\text{sales at the same stores, last year}} - 1
Quick example

Stores open in both years sold 1,070 this year against 1,000 last year. 1,070 ÷ 1,000 − 1 = 7.0%, whatever the new stores added.

On your calculator
  1. 1070÷1000−1= 0.07
  1. 1070ENTER1000÷1− 0.07

ENTER enter (on the HP, puts the number on the stack)

Occupancy rate Use it
Occupancy=rooms soldrooms available\text{Occupancy} = \frac{\text{rooms sold}}{\text{rooms available}}
Quick example

8,400 room-nights sold of 12,000 available. 8,400 ÷ 12,000 = 70.0%.

On your calculator
  1. 8400÷12000= 0.7
  1. 8400ENTER12000÷ 0.7

ENTER enter (on the HP, puts the number on the stack)

Average daily rate Use it
ADR=room revenuerooms sold\text{ADR} = \frac{\text{room revenue}}{\text{rooms sold}}
Quick example

Room revenue 1,008,000 from 8,400 room-nights sold. 1,008,000 ÷ 8,400 = 120 per room.

On your calculator
  1. 1008000÷8400= 120
  1. 1008000ENTER8400÷ 120

ENTER enter (on the HP, puts the number on the stack)

Average revenue per user Use it
ARPU=revenueaverage number of users\text{ARPU} = \frac{\text{revenue}}{\text{average number of users}}
Quick example

Revenue of 54m from an average of 1.2m subscribers. 54 ÷ 1.2 = 45 per user a year.

On your calculator
  1. 54÷1.2= 45
  1. 54ENTER1.2÷ 45

ENTER enter (on the HP, puts the number on the stack)

Forecast balance from a days ratio Use it
Balance=days ratio×forecast flow365\text{Balance} = \frac{\text{days ratio} \times \text{forecast flow}}{365}
Quick example

Forecast COGS 4,380 and 45 days of inventory on hand. Inventory = 45 × 4,380 ÷ 365 = 540.

On your calculator
  1. 4380÷365×45= 540
  1. 4380ENTER365÷45× 540

ENTER enter (on the HP, puts the number on the stack)

Module 12 Introduction to Financial Statement Modeling

Building a sales-based pro forma income statement

Forecast revenue from its drivers Memorize
R1=R0(1+V)(1+PM)(1+FX)R_1 = R_0 (1 + V)(1 + PM)(1 + FX)
Quick example

Revenue of 1,200 with volume +4%, price/mix +5% and currency −3%. 1,200 × 1.04 × 1.05 × 0.97 = 1,271.1.

On your calculator
  1. 1200×1.04×1.05×0.97= 1271.09
  1. 1200ENTER1.04×1.05×0.97× 1271.09

ENTER enter (on the HP, puts the number on the stack)

Organic growth Memorize
O=(1+V)(1+PM)−1O = (1 + V)(1 + PM) - 1
Quick example

Volume +5% and price/mix +2%; currency and a small acquisition are left out. 1.05 × 1.02 − 1 = 7.1%, not 7%.

On your calculator
  1. 1.05×1.02−1= 0.071
  1. 1.05ENTER1.02×1− 0.071

ENTER enter (on the HP, puts the number on the stack)

Cost with a fixed and a variable part Use it
C=F+c×RC = F + c \times R
Quick example

Fixed costs of 120 plus 25% of revenue, with revenue of 800. 120 + 0.25 × 800 = 320.

On your calculator
  1. 800×0.25+120= 320
  1. 800ENTER0.25×120+ 320

ENTER enter (on the HP, puts the number on the stack)

Pro forma EPS Use it
EPS=(EBIT−I)(1−t)sharesEPS = \frac{(EBIT - I)(1 - t)}{\text{shares}}
Quick example

EBIT 150, interest 10, effective tax rate 20%, 50 shares. (150 − 10) × 0.80 ÷ 50 = 2.24.

On your calculator
  1. 150−10=×0.8÷50= 2.24
  1. 150ENTER10−0.8×50÷ 2.24

ENTER enter (on the HP, puts the number on the stack)

Forecasting working capital, capex, cash flow and the balance sheet

Receivables from days sales outstanding Memorize
AR=DSO×Revenue365AR = \frac{DSO \times \text{Revenue}}{365}
Quick example

Revenue of 2,920 and a DSO of 36 days. 36 × 2,920 ÷ 365 = 288.

On your calculator
  1. 36×2920÷365= 288
  1. 36ENTER2920×365÷ 288

ENTER enter (on the HP, puts the number on the stack)

Inventory and payables from days Memorize
Inv=DIO×COGS365,AP=DPO×COGS365Inv = \frac{DIO \times COGS}{365}, \quad AP = \frac{DPO \times COGS}{365}
Quick example

Cost of sales of 1,825 and 80 days of inventory. 80 × 1,825 ÷ 365 = 400. Payables use the same cost of sales base.

On your calculator
  1. 80×1825÷365= 400
  1. 80ENTER1825×365÷ 400

ENTER enter (on the HP, puts the number on the stack)

Net working capital Use it
NWC=AR+Inv−APNWC = AR + Inv - AP
Quick example

Receivables 288, inventory 400, payables 250. 288 + 400 − 250 = 438. A rise in this figure is a use of cash.

On your calculator
  1. 288+400−250= 438
  1. 288ENTER400+250− 438

ENTER enter (on the HP, puts the number on the stack)

Forecast cash flow from operations Use it
CFO=NI+depreciation−ΔNWCCFO = NI + \text{depreciation} - \Delta NWC
Quick example

Net income 300, depreciation 80, net working capital up 25. 300 + 80 − 25 = 355.

On your calculator
  1. 300+80−25= 355
  1. 300ENTER80+25− 355

ENTER enter (on the HP, puts the number on the stack)

Account roll-forward Memorize
Closing=Opening+additions−reductions\text{Closing} = \text{Opening} + \text{additions} - \text{reductions}
Quick example

Retained earnings: opening 500, net income 120, dividends 45. 500 + 120 − 45 = 575. For PP&E, additions are capex and reductions are depreciation.

On your calculator
  1. 500+120−45= 575
  1. 500ENTER120+45− 575

ENTER enter (on the HP, puts the number on the stack)

Porter's five forces: how competition shapes prices and costs

Return on invested capital (ROIC) Memorize
ROIC=EBIT (1−t)operating assets−operating liabilitiesROIC = \frac{EBIT\,(1 - t)}{\text{operating assets} - \text{operating liabilities}}
Quick example

EBIT 150, tax rate 20%, operating assets 1,400, operating liabilities 400. 150 × 0.80 ÷ (1,400 − 400) = 120 ÷ 1,000 = 12.0%.

On your calculator
  1. 1400−400=STO1
  2. 150×0.8÷RCL1= 0.12

STO store · RCL recall a stored number

  1. 150ENTER0.8×1400ENTER400−÷ 0.12

ENTER enter (on the HP, puts the number on the stack)

Forecasting sales and costs with inflation or deflation

Volume response to a price change Memorize
ΔV≈−e×ΔP\Delta V \approx -e \times \Delta P
Quick example

A 4% price rise with elasticity 0.75. Volume changes by −0.75 × 4% = −3.0%.

On your calculator
  1. 0.75×0.04=+|- −0.03

+|- change sign

  1. 0.75ENTER0.04×CHS −0.03

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Revenue change from a price change Memorize
ΔR=(1+ΔP)(1+ΔV)−1\Delta R = (1 + \Delta P)(1 + \Delta V) - 1
Quick example

Price +10% with elasticity 1.2 gives volume −12%. 1.10 × 0.88 − 1 = −3.2%. Revenue falls because demand is elastic.

On your calculator
  1. 1.2×0.1=+|-+1=×1.1−1= −0.032

+|- change sign

  1. 1ENTER1.2ENTER0.1×−1.1×1− −0.032

ENTER enter (on the HP, puts the number on the stack)

Weighted cost inflation Use it
πcost=∑iwi πi\pi_{cost} = \sum_i w_i\,\pi_i
Quick example

Materials are 60% of costs and inflate 8%, labor is 30% at 4%, energy is 10% at 12%. 4.8 + 1.2 + 1.2 = 7.2%.

On your calculator
  1. 0.6×8=STO1
  2. 0.3×4=STO2
  3. 0.1×12=+RCL1+RCL2= 7.2

STO store · RCL recall a stored number

  1. 0.6ENTER8×0.3ENTER4×+0.1ENTER12×+ 7.2

ENTER enter (on the HP, puts the number on the stack)

Gross margin with no pass-through Use it
GMnew=1−c (1+π)GM_{new} = 1 - c\,(1 + \pi)
Quick example

Cost of sales is 55% of sales and costs rise 10% with prices unchanged. 1 − 0.55 × 1.10 = 39.5%, down from 45.0%.

On your calculator
  1. 1−(0.55×1.1)= 0.395
  1. 1ENTER0.55ENTER1.1×− 0.395

ENTER enter (on the HP, puts the number on the stack)

The forecast horizon, normalized earnings and long-term forecasts

Average holding period Use it
Holding period=1portfolio turnover\text{Holding period} = \frac{1}{\text{portfolio turnover}}
Quick example

Annual portfolio turnover of 40% means an average holding period of 1 ÷ 0.40 = 2.5 years. A 3 to 5 year horizon implies turnover of about 20% to 33%.

On your calculator
  1. 1÷0.4= 2.5
  1. 1ENTER0.4÷ 2.5

ENTER enter (on the HP, puts the number on the stack)

Normalized margin Use it
mnorm=1n∑i=1nmim_{norm} = \frac{1}{n}\sum_{i=1}^{n} m_i
Quick example

Six years of operating margin: 6%, −1%, 4%, 11%, 9%, 1%. Total 30 ÷ 6 = 5.0%.

On your calculator
  1. 6+1+|-+4+11+9+1=÷6= 5

+|- change sign

  1. 6ENTER1CHS+4+11+9+1+6÷ 5

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Terminal value with constant growth Use it
TVn=CFn(1+g)r−gTV_n = \frac{CF_n (1 + g)}{r - g}
Quick example

Final-year cash flow 50, growth 2%, discount rate 8%. 50 × 1.02 ÷ (0.08 − 0.02) = 850.

On your calculator
  1. 50×1.02÷(0.08−0.02)= 850
  1. 50ENTER1.02×0.08ENTER0.02−÷ 850

ENTER enter (on the HP, puts the number on the stack)

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