corporate-finance-basics

# Corporate Finance Basics

Finance is the discipline of allocating capital over time under uncertainty. Every business decision that commits resources has a financial structure: a cost, a benefit, a timing, and a risk. This skill catalogs the core techniques a manager or founder uses to evaluate investments, raise capital, and read financial statements — enough to make sound decisions without pretending to be a CFO.

**Agent affinity:** drucker (capital allocation and effectiveness), mintzberg (reading financials in context)

**Concept IDs:** bus-debt-vs-equity, bus-cost-benefit-analysis, bus-break-even-analysis, bus-investment-appraisal

## The Finance Toolbox at a Glance

| # | Technique | Best for | Key signal |
|---|---|---|---|
| 1 | Time value of money | Comparing cash flows across time | Decision involves money now vs later |
| 2 | Net present value (NPV) | Evaluating investments | Must pick among projects with different timing |
| 3 | Internal rate of return (IRR) | Ranking projects | Need a single summary number |
| 4 | Payback period | Quick screening | Liquidity matters more than total return |
| 5 | Break-even analysis | Sizing a new product | Need to know the volume required to not lose money |
| 6 | Cost-benefit analysis | Structured decision | Costs and benefits span categories and time |
| 7 | Debt vs equity | Structuring capital | Must decide whether to borrow or sell ownership |
| 8 | Working capital | Managing the operating cycle | Cash is tight despite profits |
| 9 | Reading the three statements | Understanding any business | Need a diagnosis from financials |
| 10 | Cost of capital (WACC) | Discount rate selection | Need to know what return justifies an investment |

## Technique 1 — Time Value of Money

**Core principle.** A dollar today is worth more than a dollar tomorrow, because the dollar today can be invested to earn a return, or simply because future dollars are less certain. The conversion is done with a discount rate $r$.

**Formulas.**

- **Future value:** $FV = PV \cdot (1 + r)^n$ where $PV$ is present value, $r$ is the periodic rate, $n$ is the number of periods.
- **Present value:** $PV = FV / (1 + r)^n$

**Worked example.** At $r = 8$ percent annual, $1000 received five years from now is worth $1000 / 1.08^5 = 1000 / 1.4693 \approx 680.58$ today. The opposite direction: $1000 invested today at 8 percent grows to $1469.33 in five years.

**When it matters.** Any decision where cash flows occur at different times must be time-adjusted. Comparing "save $500/year for 10 years" against "pay $3000 up-front" without discounting gives the wrong answer.

## Technique 2 — Net Present Value (NPV)

**Pattern:** Sum the discounted cash flows of a project, including the initial investment as a negative at time zero. If NPV is positive, the project creates value at the chosen discount rate. If NPV is negative, it destroys value.

**Formula.**

$$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$$

**Worked example.** A project requires $100K today and produces $40K/year for 3 years. At $r = 10$ percent:

$$NPV = -100 + \frac{40}{1.1} + \frac{40}{1.1^2} + \frac{40}{1.1^3} = -100 + 36.36 + 33.06 + 30.05 = -0.53$$

Slightly negative. The project is not quite worth doing at a 10 percent cost of capital. At 8 percent the same project has NPV of +3.08 and is worth doing. The choice of discount rate is load-bearing.

**Decision rule.** Accept any project with positive NPV at the firm's cost of capital. Rank competing projects by NPV.

## Technique 3 — Internal Rate of Return (IRR)

**Pattern:** The IRR is the discount rate that makes NPV equal to zero. It summarizes the project's return as a single annualized rate, comparable across projects.

**Decision rule.** Accept projects with IRR above the cost of capital. Reject below.

**Limitations.** IRR has three failure modes that NPV does not:

1. **Non-unique IRRs** — projects with non-conventional cash flows (e.g., negative cash flow in the middle) can have multiple valid IRRs.
2. **Scale blindness** — a 50 percent IRR on a $10K investment is worse than a 15 percent IRR on a $10M investment for most firms, but IRR ranks the smaller project higher.
3. **Reinvestment assumption** — IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself, which is usually not achievable.

**Rule of thumb.** Use NPV for the decision; report IRR as a summary for communication.

## Technique 4 — Payback Period

**Pattern:** The time required for cumulative cash inflows to equal the initial investment. A $100K investment producing $25K/year has a 4-year payback.

**Strength.** Simple, intuitive, and a reasonable proxy for liquidity risk — how long is capital locked up?

**Weakness.** Ignores time value of money and ignores cash flows after the payback threshold. A project with a 3-year payback and then zero return is ranked the same as one with a 3-year payback and then another decade of return.

**When to use.** As a screening filter before NPV. Payback is fast to compute and rules out obvious losers. Any project passing the payback screen still needs a full NPV before commitment.

## Technique 5 — Break-even Analysis

**Pattern:** Find the volume at which total revenue equals total cost. Below break-even, the firm loses money; above, it profits. The formula separates fixed costs (independent of volume) from variable costs (proportional to volume).

**Formula.** $Q_{BE} = \frac{FC}{P - VC}$ where $Q_{BE}$ is break-even quantity, $FC$ is fixed costs, $P$ is price per unit, $VC$ is variable cost per unit, and $(P - VC)$ is the contribution margin.

**Worked example.** A product has $200K annual fixed cost, sells for $50, and costs $30 variable per unit. Break-even is $200{,}000 / (50 - 30) = 10{,}000$ units. If forecast demand is 8,000, the product loses money even at full execution. If forecast is 15,000, it produces a profit of $(15{,}000 - 10{,}000) \times 20 = 100{,}000$.

**Strategic use.** Break-even exposes whether a product