How the numbers work: running a business

ROI Guide

The ROI Formula

ROI = (Current Value - Original Investment) / Original Investment × 100
Or:
ROI = (Gain from Investment - Cost of Investment) / Cost of Investment × 100

Simple Example

You invest $10,000 in shares
After 2 years, your investment is worth $12,500
ROI = ($12,500 - $10,000) / $10,000 × 100
ROI = $2,500 / $10,000 × 100

ROI = 25%

Annualized ROI

Investment: $10,000 → $12,500 over 2 years
Total ROI: 25% (as calculated above)
Annualized ROI = [(12,500/10,000)^(1/2)] - 1 × 100
= [1.25^0.5] - 1 × 100
= 1.118 - 1 × 100

= 11.8% per year

Common Applications

Buy shares: $5,000
Sell shares: $6,200
ROI = 24%

Common Applications

Purchase price + costs: $500,000
Sell after 5 years: $650,000
ROI = 30%

Common Applications

Machine cost: $100,000
Profit generated over 3 years: $140,000
ROI = 40%

Common Applications

Campaign cost: $20,000
Additional revenue generated: $75,000
Profit: $55,000
ROI = 275%

Example 2: Rental Property Investment

Property price: $650,000
Legal fees: $3,000
Building inspection: $500
Initial repairs: $15,000
Total investment: $668,500

Example 2: Rental Property Investment

Rental income: $520/week × 52 × 5 = $135,200
Expenses (rates, insurance, maintenance): $45,000
Net rental income: $90,200
Property value: $780,000
Selling costs (agent, legal): $25,000
Net sale proceeds: $755,000

Example 2: Rental Property Investment

Total return = $755,000 + $90,200 - $668,500
= $176,700
ROI = $176,700 / $668,500 × 100
Annualized: 4.8% per year

ROI = 26.4% (over 5 years)

Example 3: Business Equipment

Machine cost: $12,000
Installation: $800
Training: $500
Total: $13,300

Example 3: Business Equipment

Additional coffee sales: $45,000/year
Coffee costs: $18,000/year
Maintenance: $1,200/year
Net profit per year: $25,800
3-year profit: $77,400

Example 3: Business Equipment

ROI = $77,400 / $13,300 × 100
Annualized: 88.5% per year

ROI = 582%

Example 4: Marketing Campaign

Ad spend: $5,000
Creative design: $800
Total cost: $5,800

Example 4: Marketing Campaign

Revenue from campaign: $28,500
Cost of goods sold: $11,400 (40% margin)
Gross profit: $17,100
Campaign cost: $5,800
Net profit: $11,300

Negative ROI (Losses)

Investment: $20,000
Current value: $14,000
Loss: $6,000
ROI = -$6,000 / $20,000 × 100

ROI = -30%

🌍 Real-World ROI Examples

Investment: $100,000 for 10% equity
Company valuation: $1,000,000
Time: 5 years

🌍 Real-World ROI Examples

Company sold for: $8,000,000
Your 10% share: $800,000
ROI = ($800,000 - $100,000) / $100,000 × 100
Annualized: 51.6% per year

ROI = 700%

🌍 Real-World ROI Examples

Company IPO valuation: $3,500,000
Your 10% stake worth: $350,000
ROI = 250%
Annualized: 28.5% per year

🌍 Real-World ROI Examples

Company bankrupt, assets sold
Recovery: $5,000 (creditors paid first)
ROI = -95%

🌍 Real-World ROI Examples

Solar panels + installation: $15,000
Government rebate: -$2,000
Net investment: $13,000

🌍 Real-World ROI Examples

Electricity bill reduction: $1,850/year
Feed-in tariff (sell excess): $280/year
Total annual benefit: $2,130
Maintenance cost: $100/year
Net annual savings: $2,030

🌍 Real-World ROI Examples

Total savings: $2,030 × 10 = $20,300
ROI = ($20,300 - $13,000) / $13,000 × 100
Annualized: 4.6% per year
Payback period: $13,000 / $2,030 = 6.4 years

ROI = 56.2%

Training course costs: $50,000
Lost productivity (time away): $25,000
Total investment: $75,000

Productivity increase: $45,000
Error reduction savings: $18,000
Faster project completion: $22,000
Total benefit: $85,000

Year 1 benefit: $85,000
Year 2 benefit: $75,000 (slight decline)
Year 3 benefit: $65,000
Total 3-year benefit: $225,000
ROI = ($225,000 - $75,000) / $75,000 × 100
Annualized: 44.2% per year

ROI = 200%

Contribute $300/month + employer match $150
Total contribution: $450/month × 12 × 35 = $189,000
Average return: 7% per year (growth fund)
Final value at 65: $738,500
Gain: $549,500
ROI = $549,500 / $189,000 × 100

ROI = 291%

Save $450/month × 84 months = $37,800
Use as 10% deposit on $380,000 property
Property value after 28 years: $950,000
Mortgage paid off, own outright
ROI = ($950,000 - $37,800) / $37,800 × 100

ROI = 2,413%

WACC Explained

The WACC Formula

WACC = (E/V × Re) + (D/V × Rd × (1 - Tc))
Where:
E = Market value of equity
D = Market value of debt
V = E + D (total market value)
Re = Cost of equity
Rd = Cost of debt
Tc = Corporate tax rate

Simple Example

Equity: $6 million (60% of capital)
Debt: $4 million (40% of capital)
Cost of equity (Re): 12%
Cost of debt (Rd): 6%
Tax rate: 28%
WACC = (0.60 × 12%) + (0.40 × 6% × (1 - 0.28))
WACC = 7.2% + 1.73%

WACC = 8.93%

Components of WACC

Re = Rf + β × (Rm - Rf)
Rf = Risk-free rate (government bonds)
β = Beta (stock volatility vs market)
Rm = Expected market return
(Rm - Rf) = Market risk premium

Components of WACC

NZ government bond rate: 4.5%
Company beta: 1.2
Market return: 10%
Re = 4.5% + 1.2 × (10% - 4.5%)
Re = 4.5% + 6.6%

Re = 11.1%

Components of WACC

Total interest expense: $300,000
Total debt: $5,000,000
Rd = $300,000 / $5,000,000

Rd = 6.0%

Components of WACC

Pre-tax cost of debt: 6.0%
Tax rate: 28%
After-tax cost = 6.0% × (1 - 0.28)

After-tax cost = 4.32%

Example 1: NZ Manufacturing Company

Equity:
Shares outstanding: 10 million
Current share price: $8.50
Market value of equity (E): 10M × $8.50 = $85 million
Debt:
Bank loans: $30 million
Bonds outstanding: $20 million (at par)
Market value of debt (D): $50 million
Total value (V):
V = $85M + $50M = $135 million

Example 1: NZ Manufacturing Company

Weight of equity (E/V) = $85M / $135M = 63.0%
Weight of debt (D/V) = $50M / $135M = 37.0%

Example 1: NZ Manufacturing Company

Risk-free rate (NZ 10-year govt bonds): 4.2%
Market return (NZX50 expected): 9.5%
Company beta: 1.15
Re = Rf + β × (Rm - Rf)
Re = 4.2% + 1.15 × (9.5% - 4.2%)
Re = 4.2% + 6.10%

Re = 10.3%

Example 1: NZ Manufacturing Company

Total annual interest: $3.2 million
Total debt: $50 million
Rd = $3.2M / $50M

Rd = 6.4%

Example 1: NZ Manufacturing Company

Corporate tax rate: 28%
After-tax cost of debt = 6.4% × (1 - 0.28)

After-tax Rd = 4.61%

Example 1: NZ Manufacturing Company

WACC = (E/V × Re) + (D/V × Rd × (1 - Tc))
WACC = (0.630 × 10.3%) + (0.370 × 4.61%)
WACC = 6.49% + 1.71%

WACC = 8.20%

Example 2: Comparing Capital Structures

Note: Higher debt increases both cost of debt (6% → 7%) and cost of equity (11% → 12.5%) due to increased financial risk
But tax shield benefit outweighs the risk increase
WACC decreases from 9.00% to 8.77%

Lower WACC = Higher company value

Example 3: Project Evaluation Using WACC

NPV = -$5.0M + $800K/1.082 + $1.2M/1.082² + ... + $1.5M/1.082⁵
NPV = -$5.0M + $739K + $1,025K + $1,190K + $1,100K + $1,016K
NPV = -$5.0M + $5.07M

NPV = $70,000 (Positive!)

Example 3: Project Evaluation Using WACC

IRR = 8.5%
IRR (8.5%) > WACC (8.2%)

Decision: ACCEPT PROJECT

Example 4: Valuing a Company Using WACC

Sum of PVs = $11.0M + $11.8M + $12.4M + $12.7M + $13.0M + $162.5M
Enterprise Value = $223.4M
Less: Net Debt = $40M

Equity Value = $183.4M

🌍 Real-World WACC Examples

Market cap (equity): $2,400M
Debt outstanding: $1,600M
Total value: $4,000M
Equity weight: 60%
Debt weight: 40%

🌍 Real-World WACC Examples

Cost of Equity (CAPM):
Risk-free rate: 4.0%
Beta: 0.75 (utilities are stable, low beta)
Market premium: 5.5%
Re = 4.0% + 0.75 × 5.5% = 8.1%
Cost of Debt:
Average interest rate: 5.2%
After-tax (28%): 5.2% × 0.72 = 3.74%

🌍 Real-World WACC Examples

WACC = (0.60 × 8.1%) + (0.40 × 3.74%)
WACC = 4.86% + 1.50%

WACC = 6.36%

🌍 Real-World WACC Examples

Grid upgrade cost: $250M
Expected return: 7.5%
7.5% > 6.36% WACC

Approve project (creates value)

🌍 Real-World WACC Examples

Recent funding round valuation: $80M
Equity: $80M (investors + founders)
Debt: $5M (equipment financing)
Equity weight: 94.1%
Debt weight: 5.9%

🌍 Real-World WACC Examples

Cost of Equity:
Risk-free: 4.0%
Beta: 1.8 (high volatility, high growth)
Market premium: 6.0%
Re = 4.0% + 1.8 × 6.0% = 14.8%
Cost of Debt:
Interest rate: 9.5% (risky borrower)
After-tax: 9.5% × 0.72 = 6.84%

WACC = (0.941 × 14.8%) + (0.059 × 6.84%)
WACC = 13.93% + 0.40%

WACC = 14.33%

Market cap: $350M
Bank debt: $120M
Bonds: $80M
Total debt: $200M
Equity weight: 63.6%
Debt weight: 36.4%

WACC = (0.636 × 11.74%) + (0.364 × 4.90%)
WACC = 7.47% + 1.78%

WACC = 9.25%

WACC reduction: 8.88% → 8.52% (36 basis points)
On $200M enterprise value:
Annual savings: $200M × 0.36% = $720,000
Company value increase: ~$8-10M

Price Elasticity of Demand Guide

The PED Formula

PED = (% Change in Quantity Demanded) / (% Change in Price)
Using Midpoint Method (more accurate):
PED = [(Q2 - Q1) / ((Q2 + Q1)/2)] / [(P2 - P1) / ((P2 + P1)/2)]
Where:
Q1 = Original quantity demanded
Q2 = New quantity demanded
P1 = Original price
P2 = New price

Simple Example

% Change in Quantity = (160 - 200) / ((160 + 200)/2) = -40 / 180 = -22.2%
% Change in Price = (5 - 4) / ((5 + 4)/2) = 1 / 4.5 = 22.2%
PED = -22.2% / 22.2% = -1.0

PED = 1.0 (using absolute value)

Why PED Matters for Business

Current: $50 price × 1,000 units = $50,000 revenue
Raise price 10% to $55
Demand falls 20% (PED of 2.0) to 800 units
New revenue: $55 × 800 = $44,000
Result: Lost $6,000! Wrong move.

Why PED Matters for Business

Current: $50 price × 1,000 units = $50,000 revenue
Raise price 10% to $55
Demand falls only 5% (PED of 0.5) to 950 units
New revenue: $55 × 950 = $52,250
Result: Gained $2,250! Good move.

Example 1: Coffee Shop Price Change

Original price (P1): $4.50
New price (P2): $5.00
Original quantity (Q1): 300 cups/day
New quantity (Q2): 270 cups/day

Example 1: Coffee Shop Price Change

% ΔQ = (Q2 - Q1) / ((Q2 + Q1)/2) × 100
% ΔQ = (270 - 300) / ((270 + 300)/2) × 100
% ΔQ = -30 / 285 × 100
% ΔQ = -10.53%

Example 1: Coffee Shop Price Change

% ΔP = (P2 - P1) / ((P2 + P1)/2) × 100
% ΔP = (5.00 - 4.50) / ((5.00 + 4.50)/2) × 100
% ΔP = 0.50 / 4.75 × 100
% ΔP = 10.53%

Example 1: Coffee Shop Price Change

PED = |% ΔQ / % ΔP|
PED = |-10.53% / 10.53%|

PED = 1.0

Example 1: Coffee Shop Price Change

Old revenue: $4.50 × 300 = $1,350/day
New revenue: $5.00 × 270 = $1,350/day
Change: $0 (unit elastic means revenue unchanged)

Example 2: Electronics Store Sale

Original price: $1,200
Sale price: $900
Original sales: 20 units/month
Sale period sales: 45 units/month

Example 2: Electronics Store Sale

% ΔQ = (45 - 20) / ((45 + 20)/2) × 100 = 76.92%
% ΔP = (900 - 1200) / ((900 + 1200)/2) × 100 = -28.57%
PED = |76.92% / -28.57%|

PED = 2.69 (Elastic)

Example 2: Electronics Store Sale

Old revenue: $1,200 × 20 = $24,000
Sale revenue: $900 × 45 = $40,500
Increase: $16,500 (+68.75%)

Example 3: Petrol Price Increase

Price rises from $2.20 to $2.50 per litre
Weekly sales drop from 50,000L to 48,000L

Example 3: Petrol Price Increase

% ΔQ = (48,000 - 50,000) / 49,000 × 100 = -4.08%
% ΔP = (2.50 - 2.20) / 2.35 × 100 = 12.77%
PED = |-4.08% / 12.77%|

PED = 0.32 (Inelastic)

Example 3: Petrol Price Increase

Old revenue: $2.20 × 50,000 = $110,000
New revenue: $2.50 × 48,000 = $120,000
Increase: $10,000 (+9.1%)

Testing Price Changes Safely

1. Select two similar customer groups
2. Keep price same for Group A (control)
3. Change price for Group B (test)
4. Compare demand changes
5. Calculate PED from results

Testing Price Changes Safely

1. Make small price change (5-10%)
2. Monitor demand for 2-4 weeks
3. Calculate PED
4. If profitable, continue; if not, revert

🌍 Real-World Price Elasticity Examples

Old price: $14.99/month
New price: $16.99/month (13.3% increase)
Subscribers before: 850,000
Subscribers after: 810,000

🌍 Real-World Price Elasticity Examples

% ΔQ = (810k - 850k) / 830k × 100 = -4.82%
% ΔP = (16.99 - 14.99) / 15.99 × 100 = 12.51%
PED = |-4.82% / 12.51%|

PED = 0.39 (Inelastic)

🌍 Real-World Price Elasticity Examples

Price increase: $180 → $220 (22% increase)
Weekly bookings drop: 1,200 → 1,140 (5% decrease)
PED = 5% / 22% = 0.23 (Very inelastic)

Price increase: $150 → $190 (26.7% increase)
Weekly bookings drop: 800 → 600 (25% decrease)
PED = 25% / 26.7% = 0.94 (Nearly unit elastic)

Price: $5.50 → $6.50
Daily sales: 200 → 140 loaves
% ΔQ = -30%, % ΔP = 18.2%
PED = 1.65 (Elastic)

Price: $2.00 → $2.30
Daily sales: 1,000 → 950 loaves
% ΔQ = -5.1%, % ΔP = 14.3%
PED = 0.36 (Inelastic)

Price drop: $65 → $49/month
Memberships increase: 400 → 580
% ΔQ = +45%, % ΔP = -24.6%
PED = 1.83 (Elastic)
Revenue: $26,000 → $28,420 (+9.3%)

Price increase: $65 → $75/month
Memberships decrease: 400 → 360
% ΔQ = -10%, % ΔP = 14.3%
PED = 0.70 (Inelastic but close to 1)
Revenue: $26,000 → $27,000 (+3.8%)

Cashflow Management Guide - NZ Personal Finance

What is Cashflow?

Net Cashflow = Total Cash Received - Total Cash Paid Out
Measured over a specific period (week, month, quarter, year)

What is Cashflow?

This month: Income $5,000, Expenses $4,200
Net cashflow: $5,000 - $4,200 = +$800 (positive)
Next month: Income $5,000, Expenses $5,800 (rates due!)
Net cashflow: $5,000 - $5,800 = -$800 (negative)

Why Cashflow ≠ Income

Person A: Income $90,000/year
After tax: $67,275 ($5,606/month)
Expenses: $5,800/month
Monthly cashflow: -$194 (negative!)
Annual cashflow: -$2,325
Result: Good income, but going backwards $2,325/year

Why Cashflow ≠ Income

Person B: Income $55,000/year
After tax: $44,355 ($3,696/month)
Expenses: $3,200/month
Monthly cashflow: +$496 (positive!)
Annual cashflow: +$5,952
Result: Lower income, but saving $5,952/year

The Timing Mismatch Problem

Income: $2,500 every fortnight (26 pays/year)
Rent: $550/week
Other expenses: $350/week
Total weekly outflow: $900
Week 1: +$2,500 in, -$900 out = +$1,600
Week 2: $0 in, -$900 out = -$900
Week 3: +$2,500 in, -$900 out = +$1,600
Week 4: $0 in, -$900 out = -$900

Cashflow vs Profit (Business Context)

Invoice customer: $10,000
Customer pays in 60 days (profit now, cash later)
Meanwhile: rent due, materials to buy, staff to pay
Profit: $10,000 - $6,000 costs = $4,000 (profitable!)
Cashflow: $0 in, $6,000 out = -$6,000 (broke!)

Method 1: Simple Weekly Cashflow Tracker

Salary (after tax): $2,400 fortnightly
Convert to weekly: $2,400 ÷ 2 = $1,200/week average
Partner's income: $800/week
Government support (if any): $150/week
Other income: $50/week
Total weekly income: $2,200

Total income: $2,200/week
Fixed expenses: $673/week
Variable expenses: $735/week
Total expenses: $1,408/week
Net cashflow: $2,200 - $1,408 = +$792/week
Annual surplus: $792 × 52 = $41,184

Common NZ Cashflow Pressure Points

Average NZ rates: $3,000-$4,500/year
Due: July or spread over quarterly instalments
Cashflow impact: $3,500 hit in one month
Solution: Save $292/month year-round

Common NZ Cashflow Pressure Points

Car insurance: $1,200 (renewal March)
House insurance: $1,800 (renewal March)
Contents insurance: $600 (renewal March)
Total hit: $3,600 in one month!
Solution: Save $300/month or stagger renewal dates

Common NZ Cashflow Pressure Points

Per child (state school):
Start of year: Uniform $150, stationery $80, fees $200 = $430
Mid-year: Activities $150, camp $180 = $330
2 kids: $1,520 annual impact
Solution: Save $130/month year-round

Common NZ Cashflow Pressure Points

Annual rego: $150-$200
WOF: $60-$80
Plus repairs if WOF fails: $200-$800
Unexpected: tyres $600, battery $200
Solution: Vehicle maintenance fund $80/month

Common NZ Cashflow Pressure Points

Summer power: $150/month
Winter power: $350/month
Difference: $200/month extra June-August
3-month hit: $600 extra
Solution: Average billing or save $50/month summer

Common NZ Cashflow Pressure Points

Gifts: $800
Food/entertaining: $500
Travel: $1,000
Total: $2,300
Solution: Save $190/month from January

🌍 Real-World NZ Cashflow Scenarios

Rent: $550/week = $2,383/month
Power: $180
Internet: $85
Phone: $45
Groceries: $600
Transport (bus): $150
Insurance (monthly allocation): $140
Subscriptions: $35
Eating out: $250
Entertainment: $150
Personal care: $80
Clothing: $100
Miscellaneous: $120
Total: $4,318/month

🌍 Real-World NZ Cashflow Scenarios

Income: $4,866
Expenses: $4,318
Net cashflow: +$548/month
Annual surplus: $6,576

Rent: $2,800
Car payment: $520
Insurance: $320
Internet/phone: $150
ACC levy: $250
Tax (set aside 30%): $3,000 average
Fixed total: $7,040/month

Groceries: $800
Petrol: $400
Power: $250
Other: $500
Variable total: $1,950/month

Income received: $0 (payment lag)
Expenses due: $8,990
Shortfall: -$8,990
Without buffer: Would need credit card/overdraft

2023: $7,859 - $7,200 = +$659/month surplus
Saving: $7,908/year
2024: $7,859 - $8,350 = -$491/month deficit!
Going backwards: -$5,892/year
Swing: $13,800/year worse off

Cut expenses: $620/month
Increased income: $700/month
Total improvement: $1,320/month
New cashflow: -$491 + $1,320 = +$829/month
Back to positive, saving $9,948/year

Profit: $93,000
Income tax (33%): $30,690
ACC levy: $1,800
Available for living: $60,510
Monthly average: $5,043

CAPM Guide - Capital Asset Pricing Model

The CAPM Formula

Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)
or more simply:
Expected Return = Risk-Free Rate + Beta × Market Risk Premium

Component 4: Market Risk Premium

Market Risk Premium = Market Return - Risk-Free Rate
Example: 10% - 4% = 6% market risk premium

Simple Example

Risk-free rate (NZ government bonds): 4%
Market return (NZX 50 historical average): 9%
Beta of the tech stock: 1.3
CAPM Calculation:
Expected Return = 4% + 1.3 × (9% - 4%)
Expected Return = 4% + 1.3 × 5%
Expected Return = 4% + 6.5%

Expected Return = 10.5%

Example 1: Basic CAPM Calculation

Risk-free rate (NZ 10-year bonds): 4.2%
Expected market return (NZX 50): 8.5%
Fisher & Paykel beta: 0.85

Example 1: Basic CAPM Calculation

Market Risk Premium = Market Return - Risk-Free Rate
= 8.5% - 4.2%

= 4.3%

Example 1: Basic CAPM Calculation

Expected Return = Risk-Free Rate + Beta × Market Risk Premium
= 4.2% + 0.85 × 4.3%
= 4.2% + 3.66%

= 7.86%

Example 2: High-Beta Tech Stock

Risk-free rate: 3.5%
Market return: 10%
Tech stock beta: 1.8

Example 2: High-Beta Tech Stock

Expected Return = 3.5% + 1.8 × (10% - 3.5%)
= 3.5% + 1.8 × 6.5%
= 3.5% + 11.7%

= 15.2%

Example 3: Defensive Stock (Low Beta)

Risk-free rate: 4%
Market return: 9%
Utility company beta: 0.6

Example 3: Defensive Stock (Low Beta)

Expected Return = 4% + 0.6 × (9% - 4%)
= 4% + 0.6 × 5%
= 4% + 3%

= 7%

Using CAPM for Investment Decisions

Stock Beta: 1.2
CAPM Expected Return: 4% + 1.2(9% - 4%) = 10%
Stock's Actual Forecast Return: 12%

Decision: Consider buying (12% > 10%)

🌍 Real-World Examples

NZ 10-year government bond yield (risk-free rate): 4.5%
NZX 50 historical return (market return): 8.8%
Market risk premium: 8.8% - 4.5% = 4.3%

🌍 Real-World Examples

Beta: 0.9
Analyst forecast return: 7.5%
CAPM Expected Return:
= 4.5% + 0.9 × 4.3%
= 4.5% + 3.87%

= 8.37%

🌍 Real-World Examples

Beta: 1.6
Analyst forecast return: 12%
CAPM Expected Return:
= 4.5% + 1.6 × 4.3%
= 4.5% + 6.88%

= 11.38%

Risk-free rate: 4%
Market return: 10%
Market risk premium: 6%

30% Defensive Stocks (8.2% return) = $15,000
50% Market Index Fund (10% return) = $25,000
20% Growth Stocks (12.4% return) = $10,000

(0.30 × 8.2%) + (0.50 × 10%) + (0.20 × 12.4%)
= 2.46% + 5% + 2.48%

= 9.94%

(0.30 × 0.7) + (0.50 × 1.0) + (0.20 × 1.4)
= 0.21 + 0.50 + 0.28

= 0.99

Company: Manufacturing Ltd
Industry beta: 1.1
Risk-free rate (NZ 10-year bonds): 4.3%
Expected market return (NZX 50): 9.2%

Cost of Equity = 4.3% + 1.1 × (9.2% - 4.3%)
= 4.3% + 1.1 × 4.9%
= 4.3% + 5.39%

= 9.69%

Return on investment: $250,000 / $2,000,000 = 12.5%
Cost of equity (hurdle rate): 9.69%
12.5% > 9.69%

Decision: Proceed with expansion

Profit Margin Guide

The Basic Formula

Profit Margin % = (Selling Price - Cost Price) / Selling Price × 100
Or:
Profit Margin % = Profit / Revenue × 100

Simple Example

Buy product for: $60
Sell product for: $100
Profit: $40
Profit Margin = ($100 - $60) / $100 × 100
= $40 / $100 × 100

Profit Margin = 40%

Types of Profit Margins

Revenue: $1,000,000
COGS (Cost of Goods Sold): $400,000
Gross Profit: $600,000 (60% gross margin)
Operating Expenses: $350,000
Operating Profit: $250,000 (25% operating margin)
Interest & Tax: $100,000
Net Profit: $150,000 (15% net margin)

Profit Margin vs Markup

Cost: $50, Selling Price: $100, Profit: $50
Margin = $50 / $100 = 50%
Markup = $50 / $50 = 100%
Same $50 profit, different percentages!

Basic Calculation Example

Wholesale cost: $40
Retail price: $79.99
Profit = $79.99 - $40 = $39.99
Margin % = $39.99 / $79.99 × 100

Margin = 50%

Working Backwards: Find Selling Price

Margin = (Price - Cost) / Price
0.60 = (Price - $30) / Price
0.60 × Price = Price - $30
$30 = Price - 0.60 × Price
$30 = 0.40 × Price
Price = $30 / 0.40

Price = $75

Working Backwards: Find Selling Price

Selling Price = Cost / (1 - Desired Margin %)
= $30 / (1 - 0.60)
= $30 / 0.40 = $75

Margin Improvement Strategies

Revenue: $100,000
Profit: $40,000

Margin Improvement Strategies

New price: $110, Volume: 950 units
Revenue: $104,500
Cost: $60 × 950 = $57,000
Profit: $47,500
Margin: 45.5%
Profit increase: $7,500 (18.75%)

Margin Improvement Strategies

Price: $100, New cost: $54, Volume: 1,000
Revenue: $100,000
Cost: $54,000
Profit: $46,000
Margin: 46%
Profit increase: $6,000 (15%)

Margin Improvement Strategies

Premium: $340,000 (50% margin) = $170,000 profit
Standard: $500,000 (35% margin) = $175,000 profit
Budget: $160,000 (15% margin) = $24,000 profit
Total profit: $369,000
Overall margin: 36.9%
Profit increase: $14,000 (3.9%)

Volume vs Margin Trade-off

Price: $150, Cost: $60, Volume: 500
Margin: 60%
Revenue: $75,000
Profit: $45,000

Volume vs Margin Trade-off

Price: $90, Cost: $60, Volume: 1,500
Margin: 33%
Revenue: $135,000
Profit: $45,000

Breakeven Analysis

Contribution margin per unit = $50 - $20 = $30
Breakeven units = Fixed costs / Contribution margin
= $50,000 / $30

= 1,667 units to break even

🌍 Real-World Profit Margin Examples

Selling price: $5.00
Coffee beans: $0.40
Milk: $0.35
Cup/lid: $0.25
Total cost: $1.00
Gross margin: 80%

🌍 Real-World Profit Margin Examples

Selling price: $12.00
Ingredients: $4.50
Packaging: $0.50
Total cost: $5.00
Gross margin: 58%

🌍 Real-World Profit Margin Examples

Gross profit: $1,757
Labor (2 staff × 8hr × $25): $400
Rent (daily): $200
Utilities, other: $100
Net profit: $1,057
Net margin: 43%

Revenue per customer: $99
Hosting costs: $5
Support (allocated): $4
COGS: $9
Gross margin: 91%

Gross margin: 25%
Net margin: 2%
Annual revenue: $500M
Net profit: $10M
Strategy: High volume, low margins

Gross margin: 65%
Net margin: 18%
Annual revenue: $5M
Net profit: $900k
Strategy: Low volume, high margins

Price Elasticity of Supply Guide

The PES Formula (Midpoint Method)

PES = (% Change in Quantity Supplied) / (% Change in Price)
Using midpoint method:
PES = [(Q2 - Q1) / ((Q2 + Q1)/2)] / [(P2 - P1) / ((P2 + P1)/2)]

Simple Example

% Change Quantity = (11,500 - 10,000) / 10,750 = 14.0%
% Change Price = (240 - 200) / 220 = 18.2%
PES = 14.0% / 18.2%

PES = 0.77 (Inelastic)

Example 1: Coffee Shop Staffing

Wage: $22/hour → $25/hour
Workers willing to work: 12 → 16
% Change Quantity = (16 - 12) / 14 = 28.6%
% Change Price = (25 - 22) / 23.5 = 12.8%
PES = 28.6% / 12.8%

PES = 2.23 (Elastic)

Example 2: Commercial Property Development

Office rent: $500 → $650 per m²/year
Available space: 100,000 → 102,000 m²
PES = 0.12 (Highly inelastic)
Can't build new buildings in 6 months

Example 2: Commercial Property Development

Same rent increase
Available space: 100,000 → 125,000 m²
PES = 1.45 (Elastic)
New buildings completed, supply responds

Example 3: Agricultural Production

Milk price: $0.50 → $0.70 per litre
Weekly supply: 1M → 1.1M litres
% Change Quantity = (1.1 - 1.0) / 1.05 = 9.5%
% Change Price = (0.70 - 0.50) / 0.60 = 33.3%
PES = 9.5% / 33.3%

PES = 0.29 (Inelastic)

Market Equilibrium Impact

Demand ↑ 20%
Price rises only 8%
Quantity increases 16%
Result: Modest price increase, big quantity increase

Market Equilibrium Impact

Demand ↑ 20%
Price rises 18%
Quantity increases only 5%
Result: Large price spike, small quantity increase

Tax Burden and Elasticity

Example: Tax on professional sports tickets
Supply: Fixed (stadium capacity) PES = 0.1
Demand: Flexible (entertainment options) PED = 2.0
Result: Sellers bear 95% of tax
Can't increase supply, must absorb tax

Tax Burden and Elasticity

Example: Tax on gasoline
Supply: Flexible (refineries adjust) PES = 1.5
Demand: Inflexible (must drive) PED = 0.3
Result: Buyers bear 80% of tax
Suppliers pass costs to consumers

🌍 Real-World Supply Elasticity Examples

Price: $2 → $8 per mask (300% increase)
Global supply: 50M → 60M per day (20% increase)
PES = 20% / 300% = 0.07
Nearly perfectly inelastic

🌍 Real-World Supply Elasticity Examples

Price stabilized: $3 per mask
Supply: 200M per day (300% increase from baseline)
PES = 1.5 (now elastic)
Factories converted, new producers entered

🌍 Real-World Supply Elasticity Examples

Average price: $800k → $1.2M (50% increase)
Dwellings: 500,000 → 510,000 (2% increase)
PES = 0.04 (extremely inelastic)

🌍 Real-World Supply Elasticity Examples

Average fare: $20
Drivers active: 500

🌍 Real-World Supply Elasticity Examples

Surge fare: $50 (150% increase)
Drivers active: 1,200 (140% increase)
PES = 140% / 150% = 0.93

Developer salary: $100k → $130k (30% increase)
Team size: 50 → 52 developers (4% increase)
PES = 0.13 (very inelastic)
Reason: Can only hire immediately available talent

Same salary increase
Team size: 50 → 65 developers (30% increase)
PES = 1.0 (unit elastic)
Reason: Recruited nationally, trained juniors

Same salary level maintained
Team size: 50 → 85 developers (70% increase)
PES = 2.33 (elastic)
Reason: Offshore teams, coding bootcamp graduates, automation tools

Gross Margin Guide

The Gross Margin Formula

Gross Margin % = ((Revenue - COGS) / Revenue) × 100
Or:
Gross Margin % = (Gross Profit / Revenue) × 100

Simple Example

You sell a product for: $100
Cost to make/buy it (COGS): $40
Gross Profit = $100 - $40 = $60
Gross Margin = ($60 / $100) × 100

= 60%

Gross Margin vs Net Profit Margin

Revenue: $1,000,000
COGS: $400,000
Gross Profit: $600,000 (60% gross margin)
Operating Expenses: $450,000
Interest: $20,000
Taxes: $39,000
Net Income: $91,000 (9.1% net profit margin)

Detailed Calculation Examples

Project revenue: $50,000
Designer hours: 200 at $35/hour = $7,000
Developer hours: 150 at $45/hour = $6,750
Stock photos/fonts: $500
Total COGS: $14,250
Gross Profit = $50,000 - $14,250 = $35,750
Gross Margin = ($35,750 / $50,000) × 100

= 71.5%

Four Ways to Improve Gross Margin

Selling price: $50
COGS: $30
Gross margin: 40%

Four Ways to Improve Gross Margin

New selling price: $55
COGS: $30 (unchanged)
New gross profit: $25
New gross margin: 45.5%

Four Ways to Improve Gross Margin

Selling price: $50
Old COGS: $30
New COGS after negotiation: $27 (10% reduction)
Old gross margin: 40%
New gross margin: 46%

Four Ways to Improve Gross Margin

Product A: $100,000 revenue, 15% margin
Product B: $80,000 revenue, 55% margin
Overall margin: 32.8%
Drop Product A, focus on Product B:
Revenue decreases 44% BUT
Gross margin jumps to 55%
Can grow Product B to offset revenue loss

The Margin-Volume Trade-Off

Price: $100
COGS: $30
Gross margin: 70%
Units sold: 1,000
Total gross profit: $70,000

The Margin-Volume Trade-Off

Price: $70 (30% discount)
COGS: $30
Gross margin: 57%
Units sold: 2,000 (doubled)
Total gross profit: $80,000

🌍 Real-World Gross Margin Examples

Flat whites sold: 150 × $4.20 profit = $630
Muffins sold: 45 × $3.30 profit = $148.50
Sandwiches sold: 60 × $5.50 profit = $330
Smoothies sold: 30 × $5.00 profit = $150
Total daily gross profit: $1,258.50

🌍 Real-World Gross Margin Examples

Selling price: $120
COGS (product + shipping): $45
Gross profit per unit: $75
Gross margin: 62.5%
Expected monthly sales: 200 units
Monthly gross profit: $15,000

Selling price: $89
COGS: $45
Gross profit per unit: $44
Gross margin: 49.4%
Expected monthly sales: 400 units
Monthly gross profit: $17,600

Selling price: $500
Current COGS breakdown:
- Raw materials: $180
- Direct labor: $90
- Packaging: $30
Total COGS: $300
Gross margin: 40%
Monthly production: 500 units
Monthly gross profit: $100,000

Selling price: $500 (unchanged)
New COGS: $265
New gross margin: 47%
Monthly gross profit: $117,500
Improvement: $17,500/month extra profit

Project fee: $100,000
Consultant hours: 800 at $50/hour = $40,000
Gross margin: 60%

Project fee: $100,000 (can't easily raise due to contracts)
Consultant rate increased to $60/hour (20% raise)
Same 800 hours = $48,000 COGS
New gross margin: 52%
Margin compression: 8 percentage points!

IRR Guide

The IRR Concept

NPV = 0
Or expanded:
Initial Investment = Present Value of Future Cash Flows

Simple Example

Year 0: -$10,000 (investment)
Year 1: +$4,000
Year 2: +$5,000
Year 3: +$4,000
IRR = 13.7%

Example: Equipment Purchase

NPV = -$150,000 + $30,000/1.10 + $35,000/1.10² + ... + $85,000/1.10⁵
NPV = -$150,000 + $27,273 + $28,926 + $33,808 + $40,980 + $52,775
NPV = $33,762 (positive, so IRR > 10%)

Example: Equipment Purchase

NPV = -$150,000 + $30,000/1.18 + $35,000/1.18² + ... + $85,000/1.18⁵
NPV = -$1,458 (slightly negative, so IRR < 18%)

Using Excel (Much Easier)

In Excel, list cash flows in column A (A1 to A6)
A1: -150000
A2: 30000
A3: 35000
A4: 45000
A5: 60000
A6: 85000
In cell B1, enter: =IRR(A1:A6)

Result: 17.02%

🌍 Real-World IRR Applications

Initial investment: $400,000 (buildout, equipment, inventory)
Year 1 net cash flow: $60,000
Year 2: $85,000 (growing reputation)
Year 3: $110,000
Year 4: $125,000
Year 5: $140,000
Residual value Year 5: $200,000 (sell or refinance)

🌍 Real-World IRR Applications

Year 0: -$400,000
Year 1-4: Cash flows as above
Year 5: $140,000 + $200,000 = $340,000
IRR = 21.3%

🌍 Real-World IRR Applications

Owner's hurdle rate: 18% (reflects risk and opportunity cost)
IRR of 21.3% exceeds 18%

Decision: Proceed with expansion

🌍 Real-World IRR Applications

Purchase price: $550,000
Down payment (20%): $110,000
Annual net rental income (after mortgage): $8,500
Hold for 10 years
Expected appreciation: 3% annually
Selling price Year 10: $739,000
Less loan balance: -$310,000
Less selling costs (6%): -$44,000
Net proceeds: $385,000

🌍 Real-World IRR Applications

Year 0: -$110,000 (down payment)
Years 1-10: $8,500 annually
Year 10 additional: $385,000 (sale proceeds)
Total Year 10: $393,500
IRR = 11.8%

Purchase price: $50M
Equity invested: $15M (30%)
Debt: $35M (70%)
Hold period: 5 years

EBITDA: $12M
Exit multiple: 7x EBITDA
Enterprise value: $84M
Less debt: -$28M (paid down from $35M)
Equity value: $56M

Year 0: -$15M
Year 1-5: Annual cash flows as above
Year 5 exit: $56M + $3M cash flow = $59M
IRR = 32.1%

Investment: $10,000
Year 1 return: $13,000
IRR = 30%
NPV at 10% = $1,818

Investment: $100,000
Year 1: $30,000
Year 2: $50,000
Year 3: $60,000
IRR = 18%
NPV at 10% = $18,882

EBITDA Guide

The EBITDA Formula

EBITDA = Revenue - COGS - Operating Expenses (excluding D&A)
Or starting from net income:
EBITDA = Net Income + Interest + Taxes + Depreciation + Amortization

Simple Example

Revenue: $1,000,000
Cost of Goods Sold: $400,000
Gross Profit: $600,000
Operating Expenses (cash):
Rent: $60,000
Salaries: $280,000
Utilities: $20,000
Other: $40,000
Cash Operating Expenses: $400,000
Non-Cash Expenses (added back for EBITDA):
Depreciation: $35,000
Amortization: $15,000
EBITDA = $600,000 - $400,000

EBITDA = $200,000

Method 1: Top-Down from Revenue

Revenue: $5,000,000
Cost of Goods Sold: $2,000,000
Gross Profit: $3,000,000

Method 1: Top-Down from Revenue

EBITDA = Gross Profit - Cash Operating Expenses
EBITDA = $3,000,000 - $2,000,000

EBITDA = $1,000,000

Method 2: Bottom-Up from Net Income

Net Income: $450,000
Add back: Income Tax ($150,000)
Add back: Interest Expense ($100,000)
Add back: Depreciation ($250,000)
Add back: Amortization ($50,000)
EBITDA = $450,000 + $150,000 + $100,000 + $250,000 + $50,000

EBITDA = $1,000,000

EBITDA Margin

EBITDA Margin = (EBITDA / Revenue) × 100
For ManufactureCo:
EBITDA Margin = ($1,000,000 / $5,000,000) × 100

= 20%

Adjusted EBITDA

EBITDA: $1,000,000
Add back: Restructuring costs ($80,000 one-time)
Add back: Legal settlement ($50,000 unusual)
Add back: Loss on asset sale ($20,000)
Adjusted EBITDA: $1,150,000

🌍 Real-World EBITDA Applications

Revenue: $800,000,000
COGS: $320,000,000
Operating Expenses (cash): $240,000,000
Depreciation: $120,000,000 (huge network infrastructure)
Amortization: $20,000,000 (spectrum licenses)
Interest: $30,000,000
Taxes: $21,000,000

🌍 Real-World EBITDA Applications

Industry EBITDA multiple for telecom: 8x
Enterprise Value = $240M × 8

= $1,920,000,000 (≈$1.92 billion)

🌍 Real-World EBITDA Applications

Revenue: $12,000,000
Food costs (COGS): $3,600,000 (30%)
Labor: $4,200,000
Rent: $1,800,000
Other operating: $900,000
Depreciation: $360,000 (equipment, furniture)
Interest: $180,000
EBITDA = $12M - $3.6M - $4.2M - $1.8M - $0.9M

EBITDA = $1,500,000

Annual Interest Payments: $180,000
Interest Coverage = EBITDA / Interest
= $1,500,000 / $180,000

= 8.3x coverage (very healthy)

EBITDA: $4,000,000
Purchase Price: 6x EBITDA = $24,000,000
Down Payment (equity): $6,000,000
Debt Financing: $18,000,000
Interest Rate: 6% = $1,080,000/year

EBITDA: $4,000,000
Interest Coverage = $4,000,000 / $1,080,000

= 3.7x (healthy coverage)

Improve EBITDA to $6M over 5 years (50% growth)
Exit at 6x EBITDA = $36M
Repay debt: -$12M (paid down $6M over 5 years)
Net proceeds: $24M
Initial equity: $6M
Return: 4x equity in 5 years (≈32% IRR)

EBIT Guide - Earnings Before Interest and Tax

The EBIT Formula

EBIT = Revenue - Cost of Goods Sold - Operating Expenses
Or alternatively:
EBIT = Net Income + Interest + Taxes

Simple Example

Revenue: $500,000
Cost of Goods Sold (COGS): $200,000
Gross Profit: $300,000
Operating Expenses:
Rent: $30,000
Salaries: $120,000
Utilities: $10,000
Supplies: $5,000
Vehicle: $8,000
Total Operating Expenses: $173,000
EBIT = $300,000 - $173,000

EBIT = $127,000

Detailed EBIT Calculation Example

Sales revenue: $800,000
Returns and discounts: ($20,000)
Net Revenue: $780,000

Detailed EBIT Calculation Example

Inventory purchases: $320,000
Freight and shipping: $15,000
Total COGS: $335,000

Detailed EBIT Calculation Example

EBIT = Gross Profit - Operating Expenses
EBIT = $445,000 - $348,000

EBIT = $97,000

EBIT Margin

EBIT Margin = (EBIT / Revenue) × 100
For RetailCo:
EBIT Margin = ($97,000 / $780,000) × 100

= 12.4%

Using EBIT for Decision Making

Current EBIT: $97,000
Estimated new location EBIT: $45,000
Combined EBIT: $142,000
Improvement: +46% increase in operating profit

🌍 Real-World EBIT Applications

Revenue: $2,000,000
COGS: $400,000
Operating Expenses: $1,100,000
EBIT: $500,000
Interest Expense: $150,000 (lots of debt)
Tax: $105,000
Net Income: $245,000

🌍 Real-World EBIT Applications

Revenue: $1,800,000
COGS: $350,000
Operating Expenses: $1,000,000
EBIT: $450,000
Interest Expense: $20,000 (minimal debt)
Tax: $129,000
Net Income: $301,000

Revenue (consulting fees): $1,200,000
COGS: $0 (service business, no physical products)
Gross Profit: $1,200,000
Operating Expenses:
Employee salaries: $680,000
Office rent: $85,000
Technology/software: $45,000
Travel: $75,000
Marketing: $40,000
Other expenses: $35,000
Total Operating Expenses: $960,000
EBIT = $1,200,000 - $960,000

EBIT = $240,000

Revenue: $180,000
COGS: $95,000
Gross Profit: $85,000
Operating Expenses: $145,000
EBIT = $85,000 - $145,000

EBIT = -$60,000 (loss)

To reach break-even EBIT ($0):
Need to increase gross profit by $60,000
At current 47% gross margin ($85k/$180k)
Would need revenue of ~$310,000
Or reduce operating expenses to $85,000

NPV Guide - Net Present Value

The NPV Formula

NPV = Σ [CFt / (1 + r)^t] - Initial Investment
Where:
CFt = Cash flow in period t
r = Discount rate
t = Time period

Simple Example

Initial investment: $10,000
Year 1 cash flow: $4,000
Year 2 cash flow: $5,000
Year 3 cash flow: $4,000
Discount rate: 10%
PV Year 1: $4,000 / 1.10 = $3,636
PV Year 2: $5,000 / 1.10² = $4,132
PV Year 3: $4,000 / 1.10³ = $3,005
Total PV of inflows: $10,773
NPV = $10,773 - $10,000

NPV = $773

Example: Manufacturing Equipment

Year 1: $30,000 / (1.10)¹ = $27,273
Year 2: $35,000 / (1.10)² = $28,926
Year 3: $45,000 / (1.10)³ = $33,808
Year 4: $60,000 / (1.10)⁴ = $40,981
Year 5: $85,000 / (1.10)⁵ = $52,779

Uneven Cash Flow Example

Year 0: -$200,000
Year 1: -$50,000 / 1.15 = -$43,478
Year 2: $40,000 / 1.15² = $30,246
Year 3: $120,000 / 1.15³ = $78,945
Year 4: $180,000 / 1.15⁴ = $102,941
Year 5: $200,000 / 1.15⁵ = $99,432
Sum of PVs: $68,086

NPV = $68,086

🌍 Real-World NPV Examples

Initial fit-out: $350,000
Equipment: $150,000
Initial inventory: $50,000
Total: $550,000

🌍 Real-World NPV Examples

PV of 10 years cash flows: $685,240
Initial investment: $550,000

NPV = $135,240

🌍 Real-World NPV Examples

System cost: $18,000
Government rebate: -$3,000
Net investment: $15,000

🌍 Real-World NPV Examples

Electricity bill reduction: $2,100/year
Maintenance: -$100/year
Net annual benefit: $2,000
System life: 25 years

🌍 Real-World NPV Examples

PV of 25 years × $2,000 at 5%: $28,199
Initial cost: $15,000

NPV = $13,199

Property price: $600,000
Down payment (30%): $180,000
Renovation: $20,000
Total cash invested: $200,000

Years 1-10: $8,000/year positive
Year 10 sale: $780,000 (30% appreciation)
Less remaining mortgage: -$320,000
Net proceeds Year 10: $460,000

PV of annual $8k: $45,181
PV of Year 10 proceeds: $148,135
Total PV: $193,316
Initial investment: $200,000

NPV = -$6,684

Asset Turnover Ratio Guide

Simple Example

ABC Retail Store
Annual net sales: $500,000
Assets at start of year: $200,000
Assets at end of year: $250,000
Step 1: Calculate Average Assets
($200,000 + $250,000) ÷ 2 = $225,000
Step 2: Calculate Ratio
$500,000 ÷ $225,000 = 2.22
This means ABC generates $2.22 in sales for every $1 of assets.

Asset Turnover Ratio: 2.22x

High Asset Turnover Ratio

Example: High Ratio (4.0x)
Online retailer with minimal physical assets
Sales: $2,000,000
Average assets: $500,000

Ratio: 4.0x - Very efficient, low asset intensity

Low Asset Turnover Ratio

Example: Low Ratio (0.3x)
Electric utility company
Sales: $300,000,000
Average assets: $1,000,000,000

Ratio: 0.3x - Normal for utilities (massive infrastructure)

🔢 Real-World Examples

Annual sales: $450,000
Beginning assets: $150,000
Ending assets: $170,000
Average assets: ($150,000 + $170,000) ÷ 2 = $160,000

Asset Turnover: $450,000 ÷ $160,000 = 2.81x

🔢 Real-World Examples

Annual sales: $800,000
Beginning assets: $600,000 (expensive roasting equipment)
Ending assets: $650,000
Average assets: ($600,000 + $650,000) ÷ 2 = $625,000

Asset Turnover: $800,000 ÷ $625,000 = 1.28x

Annual sales: $600,000
Total assets: $250,000

Asset Turnover: 2.4x

Projected total sales: $1,100,000 (not quite double)
Projected total assets: $520,000 (new store + inventory)

Projected Turnover: 2.12x

Annual sales: $2,000,000
Average assets: $1,600,000
Large inventory: $400,000
Equipment utilization: 60%

Asset Turnover: 1.25x

Annual sales: $2,200,000 (10% increase)
Average assets: $1,400,000 (reduced!)
Lean inventory: $200,000 (50% reduction)
Equipment utilization: 85%

Asset Turnover: 1.57x

CAGR Explained

Simple Example

Step 1: Divide ending by beginning
$16,000 ÷ $10,000 = 1.6
Step 2: Raise to power of (1 ÷ years)
1.6 ^ (1 ÷ 5) = 1.6 ^ 0.2 = 1.0986
Step 3: Subtract 1
1.0986 - 1 = 0.0986
Step 4: Convert to percentage

0.0986 × 100 = 9.86% CAGR

Step-by-Step Calculation

Given:
Beginning Value: $25,000
Ending Value: $34,500
Number of Years: 3
Formula:
CAGR = ($34,500 ÷ $25,000)^(1÷3) - 1
Step 1:
$34,500 ÷ $25,000 = 1.38
Step 2:
1.38 ^ (1÷3) = 1.38 ^ 0.333 = 1.1135
Step 3:
1.1135 - 1 = 0.1135

CAGR = 11.35% per year

Step-by-Step Calculation

Given:
Beginning Value (2019): $500,000
Ending Value (2024): $1,200,000
Number of Years: 5
Calculation:
CAGR = ($1,200,000 ÷ $500,000)^(1÷5) - 1
= 2.4 ^ 0.2 - 1
= 1.1914 - 1

CAGR = 19.14% per year

Working Backwards: Using CAGR to Forecast

Future Value = $50,000 × (1 + 0.07)^20
= $50,000 × (1.07)^20
= $50,000 × 3.8697

= $193,485

🌍 Real-World CAGR Examples

Beginning Value (2018): $40,000
Ending Value (2025): $68,500
Time Period: 7 years
CAGR = ($68,500 ÷ $40,000)^(1÷7) - 1
= 1.7125 ^ 0.1429 - 1
= 1.0789 - 1

= 7.89% CAGR

Year 1 (2021): $150,000
Year 2 (2022): $320,000
Year 3 (2023): $580,000
Year 4 (2024): $950,000
Year 5 (2025): $1,400,000

Beginning: $150,000
Ending: $1,400,000
Years: 4 (from 2021 to 2025)
CAGR = ($1,400,000 ÷ $150,000)^(1÷4) - 1
= 9.333 ^ 0.25 - 1

= 74.4% CAGR

Purchased 2015: $650,000
Current Value 2025: $1,050,000
Time: 10 years
CAGR = ($1,050,000 ÷ $650,000)^(1÷10) - 1

= 4.93% CAGR

Purchased 2018: $420,000
Current Value 2025: $580,000
Time: 7 years
CAGR = ($580,000 ÷ $420,000)^(1÷7) - 1

= 4.68% CAGR

Employee Share Schemes Tax

How the Benefit Is Measured

Market value of the shares on the share scheme taxing date
minus any amount you paid for the shares or rights

= your taxable ESS benefit (employment income)

🔢 Worked Examples

Step 1: value the benefit
400 shares × $25.00 = $10,000 market value
Less amount paid: $0
ESS benefit: $10,000
Step 2: find the marginal rate
Salary $95,000 is in the 33% band ($78,101 to $180,000)
Benefit $10,000 stacks on top: $95,000 to $105,000, still under $180,000
So all $10,000 is taxed at 33%
Step 3: the tax

$10,000 × 33% = $3,300 of income tax

🔢 Worked Examples

Step 1: what he paid
$8.00 × (1 − 0.15) = $6.80 per share
1,000 × $6.80 = $6,800 paid
Step 2: the benefit (the discount)
Market value: 1,000 × $8.00 = $8,000
Benefit: $8,000 − $6,800 = $1,200
Step 3: the tax
Income $70,000 is in the 30% band; $70,000 + $1,200 = $71,200, still under $78,100

$1,200 × 30% = $360 of income tax

If the value were fixed at grant (2026)
Price then $10.00: 500 × $10.00 = $5,000 (but this is NOT the benefit)
The benefit is measured on the taxing date (2029)
Price then $18.00: 500 × $18.00 = $9,000 market value
Less amount paid: $0

ESS benefit: $9,000, taxed in the year the restrictions lift

Total ESS benefit for the year
RSUs: $10,000
Discount: $2,000
Total: $12,000
Tax at the marginal rate
Salary $85,000 + $12,000 = $97,000, all within the 33% band
$12,000 × 33% = $3,960

Set aside about $3,960 for the year-end bill

Budgeting on an Irregular Income

Two Numbers to Work Out

Add up your essential costs for a typical month
Average your income over the last several months
Set your personal wage at or below that average
Make sure the wage covers at least your essential costs

In a Lean Month

Good month: top up buffer, then fund goals and tax
Lean month: draw the same wage, buffer fills the gap
Long lean stretch: trim wants temporarily
Always keep tax money separate and untouched

Business Structure Basics

Sole Trader

Business profit is added to your personal income
Taxed at your personal marginal rates
You carry the debts personally
Lowest cost and paperwork of the three

A Simple Decision Path

1. Note the risk level of your work
2. Estimate your likely profit and tax position
3. Decide if you need partners or investors
4. Start as a sole trader if simple, or incorporate if risk or scale warrants
5. Get accounting and legal advice before deciding

Agency Agreements in NZ: Before You Sign

⏰ Your Cancellation Rights

Change of mind: cancel in writing by 5pm on the first working day after you are given your copy
Unsolicited approach: five working days to cancel, and it does not have to be in writing
Longer than 90 days: either party may cancel any time after day 90, in writing

How the numbers work: running a business

The ROI Formula

Simple Example

Annualized ROI

Common Applications

Common Applications

Common Applications

Common Applications

Example 1: Share Investment

Example 1: Share Investment

Example 1: Share Investment

Example 2: Rental Property Investment

Example 2: Rental Property Investment

Example 2: Rental Property Investment

Example 3: Business Equipment

Example 3: Business Equipment

Example 3: Business Equipment

Example 4: Marketing Campaign

Example 4: Marketing Campaign

Negative ROI (Losses)

🌍 Real-World ROI Examples

🌍 Real-World ROI Examples

🌍 Real-World ROI Examples

🌍 Real-World ROI Examples

🌍 Real-World ROI Examples

🌍 Real-World ROI Examples

🌍 Real-World ROI Examples

The WACC Formula

Simple Example

Components of WACC

Components of WACC

Components of WACC

Components of WACC

Example 1: NZ Manufacturing Company

Example 1: NZ Manufacturing Company

Example 1: NZ Manufacturing Company

Example 1: NZ Manufacturing Company

Example 1: NZ Manufacturing Company

Example 1: NZ Manufacturing Company

Example 2: Comparing Capital Structures

Example 3: Project Evaluation Using WACC

Example 3: Project Evaluation Using WACC

Example 4: Valuing a Company Using WACC

🌍 Real-World WACC Examples

🌍 Real-World WACC Examples

🌍 Real-World WACC Examples

🌍 Real-World WACC Examples

🌍 Real-World WACC Examples

🌍 Real-World WACC Examples

The PED Formula

Simple Example

Why PED Matters for Business

Why PED Matters for Business

Example 1: Coffee Shop Price Change

Example 1: Coffee Shop Price Change

Example 1: Coffee Shop Price Change

Example 1: Coffee Shop Price Change

Example 1: Coffee Shop Price Change

Example 2: Electronics Store Sale

Example 2: Electronics Store Sale

Example 2: Electronics Store Sale

Example 3: Petrol Price Increase

Example 3: Petrol Price Increase

Example 3: Petrol Price Increase

Testing Price Changes Safely

Testing Price Changes Safely

🌍 Real-World Price Elasticity Examples

🌍 Real-World Price Elasticity Examples

🌍 Real-World Price Elasticity Examples

What is Cashflow?

What is Cashflow?

Why Cashflow ≠ Income

Why Cashflow ≠ Income

The Timing Mismatch Problem

Cashflow vs Profit (Business Context)

Method 1: Simple Weekly Cashflow Tracker

Common NZ Cashflow Pressure Points

Common NZ Cashflow Pressure Points

Common NZ Cashflow Pressure Points

Common NZ Cashflow Pressure Points