BusinessMath Quarterly Series
8 min read
Part 5 of 12-Week BusinessMath Series
Business decisions often require assumptions about the future. What if the interest rate rises? What if our sales volume drops? What price maximizes profit?
Excel’s “What-If Analysis” tools answer these questions by systematically varying inputs and calculating outputs. But building these analyses in code often requires writing custom loops, managing nested arrays, and formatting results manually.
BusinessMath allows you to explore scenarios programmatically—to test assumptions, find break-even points, and identify optimal strategies—without the complexity of manual iteration.
BusinessMath provides Data Tables that work just like Excel’s sensitivity analysis tools, but with Swift’s type safety and composability.
How much will monthly payments change if interest rates rise?
import BusinessMath
// Loan parameters
let principal = 300_000.0
let loanTerm = 360 // 30 years monthly
// Test different interest rates
let rates = Array(stride(from: 0.03, through: 0.07, by: 0.005))
// Create data table
let paymentTable = DataTable.oneVariable(
inputs: rates,
calculate: { annualRate in
let monthlyRate = annualRate / 12.0
return payment(
presentValue: principal,
rate: monthlyRate,
periods: loanTerm,
futureValue: 0,
type: .ordinary
)
}
)
print("Mortgage Payment Sensitivity Analysis")
print("======================================")
print("Loan Amount: \(principal.currency())")
print("Term: 30 years\n")
for (rate, monthlyPayment) in paymentTable {
let totalPaid = monthlyPayment * Double(loanTerm)
let totalInterest = totalPaid - principal
print("\(round(rate * 1000)/10)%\t\t\(monthlyPayment.currency())\t\t\(totalInterest.currency())")
}
Output:
Mortgage Payment Sensitivity Analysis
======================================
Loan Amount: $300,000.00
Term: 30 years
3.0% $1,264.81 $155,332.36
3.5% $1,347.13 $184,968.26
4.0% $1,432.25 $215,608.52
4.5% $1,520.06 $247,220.13
5.0% $1,610.46 $279,767.35
5.5% $1,703.37 $313,212.12
6.0% $1,798.65 $347,514.57
6.5% $1,896.20 $382,633.47
7.0% $1,995.91 $418,526.69
The insight: A 1% rate increase (4% → 5%) adds $178/month and $64,000 in total interest over 30 years!
At what sales volume does a business become profitable?
// Business parameters
let fixedCosts = 50_000.0
let variableCostPerUnit = 15.0
let pricePerUnit = 25.0
// Test different sales volumes
let volumes = Array(stride(from: 1000.0, through: 10000.0, by: 1000.0))
let profitTable = DataTable.oneVariable(
inputs: volumes,
calculate: { volume in
let revenue = pricePerUnit * volume
let totalCosts = fixedCosts + (variableCostPerUnit * volume)
return revenue - totalCosts
}
)
print("\nBreak-Even Analysis")
print("Fixed Costs: \(fixedCosts.currency())")
print("Contribution Margin: \((pricePerUnit - variableCostPerUnit).currency())/unit\n")
for (volume, profit) in profitTable {
let status = profit >= 0 ? "✓" : "✗"
print("\(volume.number()) units\t\(profit.currency()) \(status)")
}
// Calculate exact break-even
let breakEvenVolume = fixedCosts / (pricePerUnit - variableCostPerUnit)
print("\nBreak-Even Volume: \(breakEvenVolume.number()) units")
Output:
Break-Even Analysis
Fixed Costs: $50,000.00
Contribution Margin: $10.00/unit
1,000 units ($40,000.00) ✗
2,000 units ($30,000.00) ✗
3,000 units ($20,000.00) ✗
4,000 units ($10,000.00) ✗
5,000 units $0.00 ✓
6,000 units $10,000.00 ✓
7,000 units $20,000.00 ✓
8,000 units $30,000.00 ✓
9,000 units $40,000.00 ✓
10,000 units $50,000.00 ✓
Break-Even Volume: 5,000 units
What price and volume combination maximizes profit?
// Fixed business parameters
let monthlyFixedCosts = 100_000.0
let variableCostPerUnit = 30.0
// Scenarios to test
let pricePoints = [40.0, 45.0, 50.0, 55.0, 60.0]
let volumeScenarios = [2000.0, 2500.0, 3000.0, 3500.0, 4000.0]
// Create two-variable profit matrix
let profitMatrix = DataTable.twoVariable(
rowInputs: pricePoints,
columnInputs: volumeScenarios,
calculate: { price, volume in
let revenue = price * volume
let totalCosts = monthlyFixedCosts + (variableCostPerUnit * volume)
return revenue - totalCosts
}
)
// Print formatted results
print("\nPricing Strategy Matrix (Monthly Profit)")
// Option 1: Use built-in formatter (simpler, basic formatting)
// let formatted = DataTable.formatTwoVariable(
// profitMatrix,
// rowInputs: pricePoints,
// columnInputs: volumeScenarios
// )
// print(formatted)
// Option 2: Custom formatting with currency (shown below)
var header = "Price "
for volume in volumeScenarios {
header += "\(Int(volume))".paddingLeft(toLength: 14)
}
print(header)
print(String(repeating: "=", count: 70))
for (rowIndex, price) in pricePoints.enumerated() {
var rowString = "\(price.currency()) "
for colIndex in 0.. maxProfit {
maxProfit = profit
optimalPrice = price
optimalVolume = volume
}
}
}
print("\nOptimal Strategy:")
print("Price: \(optimalPrice.currency()), Volume: \(optimalVolume.number(0)) units")
print("Maximum Monthly Profit: \(maxProfit.currency())")
Output:
Pricing Strategy Matrix (Monthly Profit)
Price 2000 2500 3000 3500 4000
======================================================================
$40 ($80,000) ($75,000) ($70,000) ($65,000) ($60,000)
$45 ($70,000) ($62,500) ($55,000) ($47,500) ($40,000)
$50 ($60,000) ($50,000) ($40,000) ($30,000) ($20,000)
$55 ($50,000) ($37,500) ($25,000) ($12,500) $0
$60 ($40,000) ($25,000) ($10,000) $5,000 $20,000
Optimal Strategy:
Price: $60.00, Volume: 4,000 units
Maximum Monthly Profit: $20,000.00
The insight: Higher prices with higher volumes yield maximum profit, but you need to validate whether demand supports both.
Data tables are generic over both input and output types:
public struct DataTable {
// One-variable table: [Input] → [Output]
static func oneVariable(
inputs: [Input],
calculate: (Input) -> Output
) -> DataTable
// Two-variable table: [Input₁] × [Input₂] → [[Output]]
static func twoVariable(
rowInputs: [Input],
columnInputs: [Input],
calculate: (Input, Input) -> Output
) -> [[Output]]
}
This works with any numeric type (Double, Float) and preserves type information through the calculation.
Export results for spreadsheet analysis:
let csv = DataTable.toCSV(
paymentTable,
inputHeader: "Interest Rate",
outputHeader: "Monthly Payment"
)
// Write to file
try csv.write(toFile: "loan_payments.csv", atomically: true, encoding: .utf8)
import BusinessMath
// Loan parameters
let principal = 300_000.0
let loanTerm = 360 // 30 years monthly
// Test different interest rates
let rates = Array(stride(from: 0.03, through: 0.07, by: 0.005))
// Create data table
let paymentTable = DataTable.oneVariable(
inputs: rates,
calculate: { annualRate in
let monthlyRate = annualRate / 12.0
return payment(
presentValue: principal,
rate: monthlyRate,
periods: loanTerm,
futureValue: 0,
type: .ordinary
)
}
)
print("Mortgage Payment Sensitivity Analysis")
print("======================================")
print("Loan Amount: \(principal.currency())")
print("Term: 30 years\n")
for (rate, monthlyPayment) in paymentTable {
let totalPaid = monthlyPayment * Double(loanTerm)
let totalInterest = totalPaid - principal
print("\(rate.percent(1))\t\t\(monthlyPayment.currency())\t\t\(totalInterest.currency())")
}
// Business parameters
let fixedCosts_mortgagePayment = 50_000.0
let variableCostPerUnit_mortgagePayment = 15.0
let pricePerUnit_mortgagePayment = 25.0
// Test different sales volumes
let volumes = Array(stride(from: 1000.0, through: 10000.0, by: 1000.0))
let profitTable = DataTable.oneVariable(
inputs: volumes,
calculate: { volume in
let revenue = pricePerUnit_mortgagePayment * volume
let totalCosts = fixedCosts_mortgagePayment + (variableCostPerUnit_mortgagePayment * volume)
return revenue - totalCosts
}
)
print("\nBreak-Even Analysis")
print("Fixed Costs: \(fixedCosts_mortgagePayment.currency())")
print("Contribution Margin: \((pricePerUnit_mortgagePayment - variableCostPerUnit_mortgagePayment).currency())/unit\n")
for (volume, profit) in profitTable {
let status = profit >= 0 ? "✓" : "✗"
print("\(volume.number(0).paddingLeft(toLength: 6)) units\t\(profit.currency()) \(status)")
}
// Calculate exact break-even
let breakEvenVolume = fixedCosts_mortgagePayment / (pricePerUnit_mortgagePayment - variableCostPerUnit_mortgagePayment)
print("\nBreak-Even Volume: \(breakEvenVolume.number(0)) units")
// Fixed business parameters
let monthlyFixedCosts = 100_000.0
let variableCostPerUnit = 30.0
// Scenarios to test
let pricePoints = [40.0, 45.0, 50.0, 55.0, 60.0]
let volumeScenarios = [2000.0, 2500.0, 3000.0, 3500.0, 4000.0]
// Create two-variable profit matrix
let profitMatrix = DataTable.twoVariable(
rowInputs: pricePoints,
columnInputs: volumeScenarios,
calculate: { price, volume in
let revenue = price * volume
let totalCosts = monthlyFixedCosts + (variableCostPerUnit * volume)
return revenue - totalCosts
}
)
// Print formatted results
print("\nPricing Strategy Matrix (Monthly Profit)")
// Option 1: Use built-in formatter (simpler, basic formatting)
// let formatted = DataTable.formatTwoVariable(
// profitMatrix,
// rowInputs: pricePoints,
// columnInputs: volumeScenarios
// )
// print(formatted)
// Option 2: Custom formatting with currency (shown below)
var header = "Price".padding(toLength: 10, withPad: " ", startingAt: 0)
for volume in volumeScenarios {
header += "\(Int(volume))".paddingLeft(toLength: 12)
}
print(header)
print(String(repeating: "=", count: 70))
for (rowIndex, price) in pricePoints.enumerated() {
var rowString = "\(price.currency(0).padding(toLength: 10, withPad: " ", startingAt: 0))"
for colIndex in 0.. maxProfit {
maxProfit = profit
optimalPrice = price
optimalVolume = volume
}
}
}
print("\nOptimal Strategy:")
print("Price: \(optimalPrice.currency()), Volume: \(optimalVolume.number(0)) units")
print("Maximum Monthly Profit: \(maxProfit.currency())")
→ Full API Reference: BusinessMath Docs – 2.1 Data Table Analysis
Modifications to try:
A CFO analyzing capital equipment purchases needs to understand sensitivity to key assumptions:
Data tables answer all these questions with 10-20 lines of code instead of complex spreadsheets.
When we first implemented data tables, we assumed users would want highly customized formatting. So we built a complex system with format strings, alignment options, and custom renderers.
It was too complicated.
The refactor was brutal: we deleted 300 lines of formatting code and replaced it with two simple functions: toCSV() and formatTwoVariable(). Users could export to CSV for Excel, or get basic console output. That’s it.
The lesson: Don’t over-engineer formatting. Users either want raw data (CSV) or basic display (console). Everything in between is complexity they don’t need.
Related Methodology: Coding Standards That Scale (Week 5)
Coming up next: Documentation as Design (Tuesday) - How writing docs before code reveals API flaws early.
This week: We’ll explore financial ratios (Wednesday) and risk analytics (Friday) to complete the Analysis Tools topic.
Series Progress:
Tagged with: businessmath, swift, data-tables, sensitivity-analysis, what-if