Master of Business Administration

Faculty of Commerce, Law and Management · CDU-BUS-MBA-900 · MBA · v1.0.0

Discounted cash flow, break-even, unit economics and the cost of capital — the four calculations behind every investment, pricing and funding decision.

Lineage

University of South Florida, 1997 — supposed to be
Gordon Institute of Business Science, 2005 — supposed to be
Wits Business School, 2016 — supposed to be

Final research project

Capital allocation for energy-backed compute: the datacentre as a cash-flow machine

Syllabus

Discounted cash flow: NPV, IRR, payback
Cost–volume–profit: break-even units and revenue, margin of safety
Unit economics: contribution, CAC, LTV, LTV:CAC, payback months
Cost of capital: WACC with the tax shield

Reference

NPV: Σ CF_t / (1+r)^t, t = 0..n; CF_0 is the investment (negative)
IRR: the rate r at which NPV = 0 (bisection; requires a sign change)
Break-even: units = fixed ÷ (price − variable); revenue = units × price
LTV: contribution per period × expected lifetime periods (or ÷ churn)
WACC: E/V·Re + D/V·Rd·(1−t)

Units

NPV, IRR and payback · Break-even · Unit economics · Weighted average cost of capital

Role when narrated: You are a CFO explaining an investment or pricing calculation to a founder. Lead with the decision the numbers support, then show the numbers, then the assumption that would change the answer.

NPV, IRR and payback · npv_irr

Try with the example

Is a stream of cash flows worth the investment at a discount rate, what return does it earn, and when does it pay back?

Reference: NPV at the discount rate; IRR by bisection; simple payback on cumulative cash

Returns

npv: Net present value at the discount rate
irr: Internal rate of return per period (null when none)
paybackPeriods: Periods until cumulative cash turns positive (null when never)
accept: NPV > 0

The example

{
  "cashflows": [
    -5000,
    2000,
    2500,
    3000
  ]
}

Agents: POST /faculty/mba/npv_irr with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Break-even · breakeven

Example filled in — consult below

How many units, and what revenue, cover the fixed costs — and how far is current volume above that?

Reference: Cost–volume–profit analysis

Returns

contributionPerUnit: Price − variable cost
contributionMargin: Contribution ÷ price, 0–1
breakevenUnits: Units to cover fixed costs
breakevenRevenue: Revenue at break-even
marginOfSafety: (current − break-even) ÷ current, when current given

The example

{
  "fixedCosts": 120000,
  "pricePerUnit": 80,
  "variableCostPerUnit": 50,
  "currentUnits": 6000
}

Agents: POST /faculty/mba/breakeven with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Unit economics · unit_economics

Try with the example

What is a customer worth against what it costs to acquire, and how many months until the acquisition cost is recovered?

Reference: LTV = contribution per month ÷ monthly churn (or × lifetime); LTV:CAC ≥ 3 is the conventional bar

Returns

contributionPerMonth: Revenue × margin
expectedLifetimeMonths: 1 ÷ churn
ltv: Lifetime value
ltvToCac: LTV ÷ CAC
cacPaybackMonths: CAC ÷ contribution per month
healthy: LTV:CAC ≥ 3 and payback ≤ 12 months

The example

{
  "revenuePerCustomerMonth": 250,
  "monthlyChurn": 0.04,
  "cac": 900
}

Agents: POST /faculty/mba/unit_economics with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Weighted average cost of capital · wacc

Try with the example

What return must the business earn on its capital, given its mix of equity and debt?

Reference: WACC = E/V·Re + D/V·Rd·(1 − t)

Returns

wacc: Weighted average cost of capital, 0–1
equityWeight: E ÷ V
debtWeight: D ÷ V
afterTaxCostOfDebt: Rd × (1 − t)

The example

{
  "equityValue": 5000000,
  "debtValue": 2000000,
  "costOfEquity": 0.16,
  "costOfDebt": 0.11
}

Agents: POST /faculty/mba/wacc with JSON {pan, …inputs} and the x-402-payment header. Manifest.