Analyst Dojo

CFA Level I Corporate Finance formulas

Cost of capital and the capital structure propositions, leverage, working capital and liquidity ratios, and the investment measures NPV and IRR.

51 formulas from the Corporate Finance lessons (6–9% of the exam), 30 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 Organizational Forms, Corporate Issuer Features, and Ownership

Sole proprietorships, partnerships and limited companies compared

Effective ownership through a general partner Use it
E=A×BE = A \times B
Quick example

A fund manager owns 60% of a company that is the general partner and holds 35% of a property partnership. E=0.60×0.35=E = 0.60 \times 0.35 = 21% of the partnership.

On your calculator
  1. 0.6×0.35= 0.21
  1. 0.6ENTER0.35× 0.21

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

Key features of corporations: legal identity, limited liability and double taxation

Total tax on corporate profit (double taxation) Memorize
T=tc+(1−tc)×b×tdT = t_c + (1 - t_c) \times b \times t_d
Quick example

Company tax 28%, dividend tax 15%, all after-tax profit paid out (b=1b = 1). T=0.28+0.72×0.15=T = 0.28 + 0.72 \times 0.15 = 38.8% of pre-tax profit.

On your calculator
  1. 1−0.28=×0.15+0.28= 0.388
  1. 1ENTER0.28−0.15×0.28+ 0.388

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

Public vs private companies, going public and going private

Free float Use it
FF=N−H1−H2N\text{FF} = \frac{N - H_1 - H_2}{N}
Quick example

300 million shares outstanding. Founders hold 90 million and a strategic investor 45 million. (300−90−45)÷300=(300 - 90 - 45) \div 300 = 55%.

On your calculator
  1. 300−90−45=÷300= 0.55
  1. 300ENTER90−45−300÷ 0.55

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

Module 2 Investors and Other Stakeholders

Debt vs equity: the claims and motivations of lenders and shareholders

Return on equity with debt Use it
ROE=EBIT−r×DE\text{ROE} = \frac{\text{EBIT} - r \times D}{E}
Quick example

Assets of 700 funded by debt of 420 at 8% and equity of 280. Operating profit is 21. (21−0.08×420)÷280=(21 - 0.08 \times 420) \div 280 = −4.5%.

On your calculator
  1. 21−(0.08×420)=÷280= −0.045
  1. 21ENTER0.08ENTER420×−280÷ −0.045

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

Leverage spread Use it
ROE=ROA+DE (ROA−r)\text{ROE} = \text{ROA} + \frac{D}{E}\,(\text{ROA} - r)
Quick example

ROA is 12%, debt-to-equity is 1.5 and the interest rate is 6%. ROE = 12% + 1.5 × (12% − 6%) = 21%.

On your calculator
  1. 12−6=×120÷80+12= 21
  1. 12ENTER6−120×80÷12+ 21

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

Payoffs at the debt maturity Use it
Equity=max⁡(V−D, 0),Debt=min⁡(V, D)\text{Equity} = \max(V - D,\ 0), \qquad \text{Debt} = \min(V,\ D)
Quick example

Debt owed is 260. If the firm is worth 205, equity gets max⁡(205−260,0)=\max(205 - 260, 0) = 0 and debt gets min⁡(205,260)=\min(205, 260) = 205.

On your calculator
  1. 205−260= −55, negative, so equity = 0 and debt = 205
  1. 205ENTER260− −55, negative, so equity = 0 and debt = 205

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

ESG factors investors consider

Value of a level cash flow Know the idea
V=CFrV = \frac{CF}{r}
Quick example

A level cash flow of 45 a year forever, discounted at 12%. 45÷0.12=45 \div 0.12 = 375.

On your calculator
  1. 45÷0.12= 375
  1. 45ENTER0.12÷ 375

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

Module 3 Corporate Governance: Conflicts, Mechanisms, Risks, and Benefits

Principal-agent problems and stakeholder conflicts

Economic stake of a share class Use it
Stake=BA+B\text{Stake} = \frac{B}{A + B}
Quick example

Founders hold 24 million Class B shares and the public holds 216 million Class A shares. Stake = 24 ÷ 240 = 10%.

On your calculator
  1. 24÷240= 0.1
  1. 24ENTER240÷ 0.1

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

Voting power of a share class Use it
Voting power=B×vA+B×v\text{Voting power} = \frac{B \times v}{A + B \times v}
Quick example

Same company, but each Class B share carries 5 votes and each Class A share one. Votes: 24 × 5 = 120 against 216. Voting power = 120 ÷ 336 = 35.71%.

On your calculator
  1. 24×5=STO1 120 votes
  2. ÷(216+RCL1)= 0.3571

STO store · RCL recall a stored number

  1. 24ENTER5×ENTERENTER216+÷ 0.3571

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

Corporate governance mechanisms for each stakeholder group

Elections needed to win a board majority Use it
Y=⌈MS⌉Y = \left\lceil \frac{M}{S} \right\rceil
Quick example

A board of 9 elects one third (3 seats) a year. A majority is 5 seats. 5÷3=1.675 \div 3 = 1.67, rounded up: 2 annual elections.

On your calculator
  1. 5÷3= 1.6667, so round up to 2
  1. 5ENTER3÷ 1.6667, so round up to 2

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

Module 4 Working Capital and Liquidity

The cash conversion cycle and working capital

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

DOH is 58 days, DSO is 33 days and DPO is 44 days. CCC = 58 + 33 − 44 = 47 days.

On your calculator
  1. 58+33−44= 47
  1. 58ENTER33+44− 47

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

Days sales outstanding Memorize
DSO=Accounts receivableSales/365\text{DSO} = \frac{\text{Accounts receivable}}{\text{Sales} / 365}
Quick example

Receivables 135, sales 1,825. Sales per day = 5, so DSO = 135 ÷ 5 = 27 days.

On your calculator
  1. 135×365÷1825= 27
  1. 135ENTER365×1825÷ 27

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

Days of inventory on hand Memorize
DOH=InventoryCOGS/365\text{DOH} = \frac{\text{Inventory}}{\text{COGS} / 365}
Quick example

Inventory 150, cost of goods sold 1,095. COGS per day = 3, so DOH = 150 ÷ 3 = 50 days.

On your calculator
  1. 150×365÷1095= 50
  1. 150ENTER365×1095÷ 50

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

Days payable outstanding Memorize
DPO=Accounts payableCOGS/365\text{DPO} = \frac{\text{Accounts payable}}{\text{COGS} / 365}
Quick example

Payables 99, cost of goods sold 1,095. DPO = 99 ÷ 3 = 33 days.

On your calculator
  1. 99×365÷1095= 33
  1. 99ENTER365×1095÷ 33

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

Total working capital Memorize
Total working capital=Current assets−Current liabilities\text{Total working capital} = \text{Current assets} - \text{Current liabilities}
Quick example

Current assets 300, current liabilities 160. Total working capital = 140.

On your calculator
  1. 300−160= 140
  1. 300ENTER160− 140

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

Net working capital Memorize
NWC=(CA−cash−securities)−(CL−short-term debt)\text{NWC} = (\text{CA} - \text{cash} - \text{securities}) - (\text{CL} - \text{short-term debt})
Quick example

Current assets 300 (of which cash 40, securities 20); current liabilities 160 (of which short-term debt 50); sales 1,040. NWC = (300 − 60) − (160 − 50) = 130, which is 12.5% of sales.

On your calculator
  1. 300−40−20−160+50= 130
  2. ÷1040= 0.125
  1. 300ENTER40−20−160−50+ 130
  2. 1040÷ 0.125

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

Liquidity: sources, drags and pulls, and liquidity ratios

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

Current assets 360, current liabilities 240. Current ratio = 360 ÷ 240 = 1.50.

On your calculator
  1. 360÷240= 1.5
  1. 360ENTER240÷ 1.5

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

Quick ratio Memorize
Quick ratio=Cash+Marketable securities+ReceivablesCurrent liabilities\text{Quick ratio} = \frac{\text{Cash} + \text{Marketable securities} + \text{Receivables}}{\text{Current liabilities}}
Quick example

Cash 40, securities 10, receivables 90, current liabilities 125. Quick ratio = 140 ÷ 125 = 1.12.

On your calculator
  1. 40+10+90=÷125= 1.12
  1. 40ENTER10+90+125÷ 1.12

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

Cash ratio Memorize
Cash ratio=Cash+Marketable securitiesCurrent liabilities\text{Cash ratio} = \frac{\text{Cash} + \text{Marketable securities}}{\text{Current liabilities}}
Quick example

Cash 18, securities 12, current liabilities 100. Cash ratio = 30 ÷ 100 = 0.30.

On your calculator
  1. 18+12=÷100= 0.3
  1. 18ENTER12+100÷ 0.3

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

Cash flow from operations Use it
CFO=Cash from customers+Interest and dividends received−Cash paid to employees and suppliers−Taxes paid−Interest paid\text{CFO} = \text{Cash from customers} + \text{Interest and dividends received} - \text{Cash paid to employees and suppliers} - \text{Taxes paid} - \text{Interest paid}
Quick example

Customers 900, interest and dividends received 10, employees and suppliers 610, taxes 45, interest paid 25. CFO = 900 + 10 − 610 − 45 − 25 = 230.

On your calculator
  1. 900+10−610−45−25= 230
  1. 900ENTER10+610−45−25− 230

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

Free cash flow Use it
FCF=CFO−Investment in long-term assets\text{FCF} = \text{CFO} - \text{Investment in long-term assets}
Quick example

CFO 230, investment in long-term assets 150. FCF = 80.

On your calculator
  1. 230−150= 80
  1. 230ENTER150− 80

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

Net proceeds after liquidation costs Use it
Net proceeds=∑iFVi×(1−ci)\text{Net proceeds} = \sum_i \text{FV}_i \times (1 - c_i)
Quick example

Treasury bills 25 (cost 0%), receivables 60 (5%), inventory 30 (25%). Net proceeds = 25 + 57 + 22.5 = 104.5; liquidation costs 10.5.

On your calculator
  1. 25+(60×0.95)+(30×0.75)= 104.5
  1. 60ENTER0.95×25+30ENTER0.75×+ 104.5

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

Cost of trade credit and short-term funding choices

Effective annual rate of trade credit Memorize
EAR=(1+d1−d)365/(N−D)−1\text{EAR} = \left(1 + \frac{d}{1 - d}\right)^{365 / (N - D)} - 1
Quick example

Terms 3/10, net 40, so d = 3%, N = 40, D = 10. EAR = (1 + 3/97)^(365/30) − 1 = 44.9%.

On your calculator
  1. 3÷97+1=y^x(365÷30)=−1= 0.4486

y^x power

  1. 3ENTER97÷1+365ENTER30÷y^x1− 0.4486

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

Cost in cash of forgoing a discount Use it
Cost=d×Payables\text{Cost} = d \times \text{Payables}
Quick example

Forgoing a 3% discount on payables of 6 million costs 3% × 6 = 0.18 million.

On your calculator
  1. 6×0.03= 0.18
  1. 6ENTER0.03× 0.18

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

Amount to sell to raise a cash need Use it
Amount sold=Cash needed1−c\text{Amount sold} = \frac{\text{Cash needed}}{1 - c}
Quick example

Cash needed 40, receivables sold at an 8% discount. Sell 40 ÷ 0.92 = 43.48; the cost is 3.48.

On your calculator
  1. 40÷0.92= 43.4783
  1. 40ENTER0.92÷ 43.4783

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

Module 5 Capital Investments and Capital Allocation

Types of capital investments

Maintenance capital expenditures (estimate) Memorize
Maintenance capex≈Depreciation and amortization\text{Maintenance capex} \approx \text{Depreciation and amortization}
Quick example

A company reports depreciation and amortization of USD 410 million. Its maintenance capex is estimated at about USD 410 million.

Growth capital expenditures (estimate) Memorize
Growth capex≈Total capex−D&A\text{Growth capex} \approx \text{Total capex} - \text{D\&A}
Quick example

Total capex is USD 780 million and D&A is USD 410 million. Growth capex ≈ 780 − 410 = USD 370 million.

On your calculator
  1. 780−410= 370
  1. 780ENTER410− 370

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

The capital allocation process, NPV and IRR

Net present value Memorize
NPV=∑t=0TCFt(1+r)tNPV = \sum_{t=0}^{T} \frac{CF_t}{(1+r)^t}
Quick example

Invest 50 now; after-tax inflows of 20, 25 and 30 in years 1 to 3; r = 10%. NPV = −50 + 20/1.10 + 25/1.10² + 30/1.10³ = +11.38. Accept.

On your calculator
  1. CF2NDCLR WORK
  2. 50+|-ENTER↓20ENTER↓↓25ENTER↓↓30ENTER
  3. NPV10ENTER↓CPT 11.38

CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · +|- change sign · ENTER enter (on the HP, puts the number on the stack) · NPV net present value · CPT compute

  1. fCLEAR REG
  2. 50CHSgCF020gCFj25gCFj30gCFj
  3. 10i
  4. fNPV 11.38

f gold shift key · CLEAR REG clear all registers · CHS change sign · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · i interest rate per period · NPV net present value

Internal rate of return Memorize
0=∑t=0TCFt(1+IRR)t0 = \sum_{t=0}^{T} \frac{CF_t}{(1+IRR)^t}
Quick example

Invest 60 now; inflows of 20, 30 and 35 in years 1 to 3. The IRR is 17.81%. Against a 10% hurdle rate, accept.

On your calculator
  1. CF2NDCLR WORK
  2. 60+|-ENTER↓20ENTER↓↓30ENTER↓↓35ENTER
  3. IRRCPT 17.81

CF cash flow worksheet · 2ND second function (the shifted label above a key) · CLR WORK clear the worksheet · +|- change sign · ENTER enter (on the HP, puts the number on the stack) · IRR internal rate of return · CPT compute

  1. fCLEAR REG
  2. 60CHSgCF020gCFj30gCFj35gCFj
  3. fIRR 17.81

f gold shift key · CLEAR REG clear all registers · CHS change sign · g blue shift key · CF0 cash flow at time zero · CFj cash flow j · IRR internal rate of return

Return on invested capital (ROIC)

Return on invested capital Memorize
ROIC=(1−t)×Operating profitAverage (long-term liabilities + equity)\text{ROIC} = \frac{(1-t)\times \text{Operating profit}}{\text{Average (long-term liabilities + equity)}}
Quick example

Operating profit 360, tax rate 30%, long-term liabilities plus equity 2,300 at the start and 2,500 at the end. After-tax profit = 252; average capital = 2,400. ROIC = 252 ÷ 2,400 = 10.5%.

On your calculator
  1. 2300+2500=÷2=STO1 2400
  2. 360×0.7=÷RCL1= 0.105

STO store · RCL recall a stored number

  1. 2300ENTER2500+2÷STO1 2400
  2. 360ENTER0.7×RCL1÷ 0.105

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

ROIC as margin times turnover Memorize
ROIC=After-tax operating profitSales×SalesAverage invested capital\text{ROIC} = \frac{\text{After-tax operating profit}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Average invested capital}}
Quick example

After-tax operating profit 252, sales 1,800, average invested capital 2,400. Margin = 14%; turnover = 0.75. ROIC = 14% × 0.75 = 10.5%.

On your calculator
  1. 252÷1800= 0.14
  2. ×0.75= 0.105
  1. 252ENTER1800÷ 0.14
  2. 0.75× 0.105

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

Capital allocation principles and pitfalls

After-tax operating cash flow Memorize
CF=(Revenue−Cash costs)(1−t)+Depreciation×tCF = (\text{Revenue} - \text{Cash costs})(1-t) + \text{Depreciation}\times t
Quick example

Revenue 360, cash costs 230, depreciation 40, tax rate 30%. CF = 130 × 0.70 + 40 × 0.30 = 91 + 12 = 103.

On your calculator
  1. 360−230=×0.7=STO1 91
  2. 40×0.3=+RCL1= 103

STO store · RCL recall a stored number

  1. 360ENTER230−0.7×40ENTER0.3×+ 103

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

Real options in capital investments

Project NPV with real options Memorize
Project NPV=NPVwithout options−Option cost+Option value\text{Project NPV} = \text{NPV}_{\text{without options}} - \text{Option cost} + \text{Option value}
Quick example

NPV without options is 8.0, the option costs 1.0 to hold and is worth 3.5. Project NPV = 8.0 − 1.0 + 3.5 = 10.5.

On your calculator
  1. 8−1+3.5= 10.5
  1. 8ENTER1−3.5+ 10.5

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

Module 6 Capital Structure

Weighted-average cost of capital (WACC)

Weighted-average cost of capital Memorize
WACC=wd rd (1−t)+wp rp+we reWACC = w_d\, r_d\,(1 - t) + w_p\, r_p + w_e\, r_e
Quick example

Debt 25% at a pre-tax 8%, equity 75% at 13%, tax rate 30%. WACC = 0.25 × 8% × 0.70 + 0.75 × 13% = 1.40% + 9.75% = 11.15%.

On your calculator
  1. 0.25×8×0.7+(0.75×13)= 11.15
  1. 0.25ENTER8×0.7×0.75ENTER13×+ 11.15

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

After-tax cost of debt Memorize
rd (1−t)r_d\,(1 - t)
Quick example

A company borrows at 6% and pays tax at 25%. Its after-tax cost of debt is 6% × 0.75 = 4.5%.

On your calculator
  1. 6×0.75= 4.5
  1. 6ENTER0.75× 4.5

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

Market-value weight of debt Use it
wd=DD+Ew_d = \frac{D}{D + E}
Quick example

Debt of 120 and equity with a market value of 280. w_d = 120 ÷ (120 + 280) = 30%, so w_e = 70%.

On your calculator
  1. 120÷(120+280)= 0.3
  1. 120ENTER120ENTER280+÷ 0.3

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

Factors affecting capital structure and the cost of capital

Operating leverage Memorize
Operating leverage=Fixed costsTotal costs\text{Operating leverage} = \frac{\text{Fixed costs}}{\text{Total costs}}
Quick example

Fixed costs of 80 and variable costs of 120. Operating leverage = 80 ÷ (80 + 120) = 40%.

On your calculator
  1. 80÷(80+120)= 0.4
  1. 80ENTER80ENTER120+÷ 0.4

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

Interest coverage Memorize
Interest coverage=EBITInterest expense\text{Interest coverage} = \frac{\text{EBIT}}{\text{Interest expense}}
Quick example

Earnings before interest and taxes (EBIT) of 150 and interest expense of 25. Interest coverage = 150 ÷ 25 = 6.0×.

On your calculator
  1. 150÷25= 6
  1. 150ENTER25÷ 6

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

Modigliani–Miller propositions with and without taxes

MM Proposition I without taxes Memorize
VL=VUV_L = V_U
Quick example

An all-equity firm worth 800 issues debt of 300 and buys back shares. With no taxes, the levered firm is still worth 800.

MM Proposition II without taxes Memorize
re=r0+(r0−rd) DEr_e = r_0 + (r_0 - r_d)\,\frac{D}{E}
Quick example

Unlevered cost of capital 12%, cost of debt 6%, D/E = 0.5. r_e = 12% + (12% − 6%) × 0.5 = 15%. WACC stays at 12%.

On your calculator
  1. 12−6×0.5+12= 15
  1. 12ENTER6−0.5×12+ 15

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

MM Proposition I with taxes Memorize
VL=VU+tDV_L = V_U + tD
Quick example

Unlevered value 900, permanent debt 250, tax rate 30%. V_L = 900 + 0.30 × 250 = 975.

On your calculator
  1. 0.3×250+900= 975
  1. 0.3ENTER250×900+ 975

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

MM Proposition II with taxes Memorize
re=r0+(r0−rd)(1−t) DEr_e = r_0 + (r_0 - r_d)(1 - t)\,\frac{D}{E}
Quick example

r_0 = 12%, r_d = 6%, t = 30%, D/E = 0.5. r_e = 12% + 6% × 0.70 × 0.5 = 14.1%. WACC falls as D/E rises.

On your calculator
  1. 12−6×0.7×0.5+12= 14.1
  1. 12ENTER6−0.7×0.5×12+ 14.1

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

Optimal and target capital structure, pecking order and agency costs

Static trade-off theory Memorize
VL=VU+tD−PV(costs of financial distress)V_L = V_U + tD - PV(\text{costs of financial distress})
Quick example

V_U = 400, t = 25%, D = 120, PV of distress costs = 8. V_L = 400 + 0.25 × 120 − 8 = 422.

On your calculator
  1. 0.25×120+400−8= 422
  1. 0.25ENTER120×400+8− 422

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

Debt weight from D/E Memorize
wd=D/E1+D/Ew_d = \frac{D/E}{1 + D/E}
Quick example

A target D/E of 0.6 gives w_d = 0.6 ÷ 1.6 = 37.5%.

On your calculator
  1. 0.6÷(1+0.6)= 0.375
  1. 0.6ENTER1ENTER0.6+÷ 0.375

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

Equity weight from D/E Memorize
we=11+D/Ew_e = \frac{1}{1 + D/E}
Quick example

A target D/E of 0.6 gives w_e = 1 ÷ 1.6 = 62.5%.

On your calculator
  1. 1÷(1+0.6)= 0.625
  1. 1ENTER1ENTER0.6+÷ 0.625

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

Module 7 Business Models

What a business model describes: who, what, where, how much and how

Payback on customer acquisition cost Know the idea
T=KP−cT = \frac{K}{P - c}
Quick example

A subscription sells for 20 a month with variable costs of 8. Winning each customer costs 156. Payback = 156 ÷ (20 − 8) = 13 months.

On your calculator
  1. 156÷(20−8)= 13
  1. 156ENTER20ENTER8−÷ 13

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

Pricing and revenue models

Net price Use it
N=L (1−δ)N = L\,(1 - \delta)
Quick example

List price 250 and total discounts and promotions of 12% of list. Net price = 250 × (1 − 0.12) = 220.

On your calculator
  1. 250×(1−0.12)= 220
  1. 250ENTER1ENTER0.12−× 220

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

Conventional business models, variations and innovation

Bank spread income Use it
I=L (r−f)I = L\,(r - f)
Quick example

A bank has 1,200 of loans earning 5.8%, funded at 3.9%. Spread income = 1,200 × (0.058 − 0.039) = 22.8.

On your calculator
  1. 1200×(0.058−0.039)= 22.8
  1. 0.058ENTER0.039−1200× 22.8

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

Franchisor royalty income Use it
R=N×S×ρR = N \times S \times \rho
Quick example

80 franchisees each have sales of 0.9 and pay a 6% royalty. Royalty income = 80 × 0.9 × 0.06 = 4.32.

On your calculator
  1. 80×0.9×0.06= 4.32
  1. 80ENTER0.9×0.06× 4.32

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

Network effects and platform business models

Possible connections in a one-sided network Know the idea
C=n (n−1)2C = \frac{n\,(n - 1)}{2}
Quick example

15 users, any two of whom can connect: 15 × 14 ÷ 2 = 105 possible connections.

On your calculator
  1. 15×14÷2= 105
  1. 15ENTER14×2÷ 105

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

Possible connections on a two-sided platform Know the idea
X=B×SX = B \times S
Quick example

120 buyers and 80 sellers: only buyer-seller pairs count, so 120 × 80 = 9,600 possible connections.

On your calculator
  1. 120×80= 9600
  1. 120ENTER80× 9600

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

Analyst Dojo Plus

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