Study sheet: Free Cash Flow and Time Value

📋 Course Outline

1. Finance, Risk, and Uncertainty
2. Equity, Debt, and Required Return
3. Managers and Investors’ Perspectives
4. Financial Analysis and Stakeholder Trust
5. Balance Sheets and Income Statements
6. Accrual Accounting and Cash Flow
7. Working Capital and Cash Needs
8. Debt and Invested Capital
9. Book Value and Market Value
10. Earnings Quality and Free Cash Flow
11. Free Cash Flow and Investment Needs
12. Margins and Operating Performance
13. Return on Invested Capital
14. Time Value and Opportunity Cost
15. Cash Flow Streams and Valuation
16. Net Present Value and Value Creation
17. Internal Rate of Return
18. Payback Period and Its Limits

📖 1. Finance, Risk, and Uncertainty

🔑 Key Concepts & Definitions

• Finance : The study of how individuals, businesses, and organizations raise, allocate, and use scarce monetary resources over time while managing risks and detecting opportunities.

★ Must-know

📌 Risk refers to uncertain outcomes that can be assessed, whereas uncertainty describes outcomes that are not reliably predictable.

📌 Diversification reduces exposure by avoiding concentration in a single investment, summarized by the rule “never put all your eggs in one basket.”

Further detail

• Financial decision making requires assessing expected returns, evaluating investment opportunities, analyzing risk, and allocating assets.

💡 Memory Hook

Risk can be priced; uncertainty cannot be predicted with confidence.

📖 2. Equity, Debt, and Required Return

🔑 Key Concepts & Definitions

• Opportunity Cost of Capital : The return an investor forgoes on the best available alternative investment with equivalent risk and term, representing the required return.

★ Must-know

📌 An equity holder receives potential dividends and share-price appreciation, has voting and control rights, and is paid last in liquidation, whereas a debt holder generally receives predetermined income, has no decision power, and is paid before equity holders.

• Appropriate benchmarks include:
  • A time trend
  • Competitors and industry peers
  • The target
  • An alternative opportunity with the same level of risk

Further detail

📌 A private company has ownership concentrated among identified owners, whereas a public company offers ownership shares to a broader investing public through a stock-market listing.

📌 Required return is an estimate used for a decision today and is not the realized return earned in the future.

💡 Memory Hook

Equity shares upside and control; debt receives fixed claims and seniority.

📖 3. Managers and Investors’ Perspectives

★ Must-know

• Higher risk should lead investors to require higher return as compensation, but taking more risk does not guarantee a higher realized return.

• Historical evidence shows a statistical correlation between high risk and high return, but past performance does not guarantee future results.

• Correlation does not establish causation, so observing that two variables move together is insufficient to conclude that one causes the other.

• Shareholders own part of a company’s equity rather than directly owning the company’s assets, and dividend payments are made at the company’s discretion.

Further detail

• The course identifies these value drivers:

  • Attracting and satisfying clients
  • After-sale services and user experience
  • Reputation and trust
  • High quality
  • Innovation and adaptability to new needs
  • Employee knowledge and expertise

• The company’s perspective treats the estimated equity cost of capital as the return required by shareholders to compensate for the risk associated with the company. — Berk J. and DeMarzo P., Corporate Finance

💡 Memory Hook

Investor risk → required return → company cost of capital.

📖 4. Financial Analysis and Stakeholder Trust

🔑 Key Concepts & Definitions

• Financial Analysis : The evaluation of whether a company is financially healthy enough to retain stakeholder trust and attract investors by interpreting financial reports and their data.

★ Must-know

• The three typical stakeholder perspectives are:
  • Equity-oriented stakeholders
  • Debt-capital-oriented stakeholders
  • Compensation-oriented stakeholders

📌 A rigorous financial analysis must combine and cross-analyze multiple indicators because there is no single indicator of good financial health.

• 🔄 A financial analysis follows these main stages:
  1. Assess the sector and accounting policies
  2. Analyze growth
  3. Analyze profitability
  4. Analyze risk
  5. Communicate conclusions and recommendations

Further detail

• In the long run, a company can survive only if it creates value for shareholders, meets commitments to stakeholders, generates wealth, invests, finances its investments, earns a sufficient return, and manages illiquidity risk.

💡 Memory Hook

A financial health checkup uses several indicators rather than one symptom.

📖 5. Balance Sheets and Income Statements

🔑 Key Concepts & Definitions

• Balance Sheet : A snapshot of a firm’s financial position at a given point in time, listing its assets and the liabilities and shareholders’ equity that finance them.
• Income Statement : An income statement reports revenues and expenses over a period of time to measure the company’s accounting wealth creation and resulting earnings.

★ Must-know

📐 Formula — The balance sheet must satisfy $\text{Total Assets} = \text{Liabilities} + \text{Shareholders' Equity}$.

• The main balance-sheet categories presented are:
  • Long-lived assets
  • Inventories
  • Accounts receivable
  • Cash and marketable securities
  • Shareholders’ equity
  • Long-term debt
  • Short-term debt
  • Accounts payable

📌 Operating expenses are consumed in the operating cycle and reduce wealth, whereas investments in fixed assets are used without being directly destroyed and are recorded as capital expenditure rather than an immediate operating expense.

📌 Net income typically does not equal the cash earned by the firm because accrual accounting records revenues when sales are made and matches related costs to the revenue period, even when cash has not moved.

Further detail

📌 The balance-sheet date can affect interpretation because seasonal businesses may show very different inventories and cash balances at different times of the year; for example, 80% of LEGO’s annual sales occur between September and December.

💡 Memory Hook

The balance sheet is a snapshot; the income statement records performance over time.

📖 6. Accrual Accounting and Cash Flow

🔑 Key Concepts & Definitions

• Cash Flow Statement : assesses a company’s ability to generate cash and shows how cash is allocated through operating, investing, and financing activities

★ Must-know

📌 Net income typically does not equal the cash earned by a firm because of non-cash items, accruals, and uses of cash that are not recorded on the income statement.

📌 Accrual accounting recognizes revenue when a sale is made rather than when cash is received, and matches costs with the revenues they generate regardless of the timing of cash outflows.

• The three components are:
  • cash flows from operations
  • cash flows from investments
  • cash flows from financing

Further detail

• Depreciation is not an actual cash expense but recognizes that fixed assets wear out and become less valuable over time.

💡 Memory Hook

Net income measures accounting wealth, whereas cash flow measures actual cash movement.

📖 7. Working Capital and Cash Needs

🔑 Key Concepts & Definitions

• Working Capital Needs : the short-term cash required to operate the business and reflect the time lag between operating cash outflows and inflows

★ Must-know

📐 Formula — Working capital needs are calculated as $\mathrm{WCN} = \mathrm{Inventory} + \mathrm{Accounts\ receivable} - \mathrm{Accounts\ payable}$.

• JIT’s working capital needs increased from €2.6 million in Year 1 to €3.3 million in Year 2, requiring €700,000 to finance the increase.

📌 Any reduction in working capital needs generates a positive cash flow, provided that the firm’s proper functioning is not altered.

Further detail

• Working capital needs depend on:
  • sales
  • the length and nature of the operating cycle
  • supplier credit terms
  • the average collection period
  • inventory turnover

💡 Memory Hook

Cash inflows delayed behind operating outflows → working capital needs consume cash.

📖 8. Debt and Invested Capital

★ Must-know

📐 Formula — Net financial debt equals long-term and short-term financial debt minus cash and short-term investments: $\mathrm{Net\ financial\ debt} = \mathrm{Financial\ debt} - \mathrm{Cash\ and\ short\text{-}term\ investments}$.

📐 Formula — Capital employed equals fixed assets plus working capital and also equals shareholders’ equity plus net financial debt: $\mathrm{Capital\ employed} = \mathrm{Fixed\ assets} + \mathrm{Working\ capital} = \mathrm{Shareholders’\ equity} + \mathrm{Net\ financial\ debt}$.

• Analyzing financial debt helps assess:
  • default risk
  • management autonomy
  • financial distress and reputation
  • cost of capital

Further detail

• JIT’s capital employed was €124.0 million in Year 2 and €83.5 million in Year 1.

💡 Memory Hook

Fixed assets + working capital → capital employed = equity + net financial debt.

📖 9. Book Value and Market Value

★ Must-know

📌 Book value of equity is an accounting measure based partly on historical asset costs, whereas market value reflects investors’ expectations about future performance.

📐 Formula — Market capitalization equals the market price per share multiplied by the number of shares outstanding: $\mathrm{Market\ capitalization} = \mathrm{Market\ price\ per\ share} \times \mathrm{Shares\ outstanding}$.

📐 Formula — The market-to-book ratio equals the market value of equity divided by the book value of equity: $\mathrm{Market\text{-}to\text{-}book\ ratio} = \frac{\mathrm{Market\ value\ of\ equity}}{\mathrm{Book\ value\ of\ equity}}$.

Further detail

• With 3.6 million shares trading at €14 per share, JIT’s market capitalization was €50.4 million, compared with a book value of equity of €32 million.

• JIT’s market-to-book ratio was approximately 1.5, meaning investors were willing to pay one and a half times the book value of its shares.

💡 Memory Hook

Book value records historical accounting values, whereas market value reflects investors’ expectations.

📖 10. Earnings Quality and Free Cash Flow

★ Must-know

📌 A positive net income does not necessarily indicate good future performance because non-cash items, accruals, extraordinary items, and non-recurring items can distort earnings quality.

• EBITDA measures wealth generated by the core business and is not altered by investment policy, depreciation methods, financial debt, taxes, or non-recurring items.

📌 When free cash flow is positive, operating cash generation covers operating and investment needs and may be used to pay dividends or reduce debt; when it is negative, additional financial resources must be raised.

Further detail

• JIT’s free cash flow was negative €38.5 million because cash from operating activities was €1.3 million and capital expenditures were €39.8 million.

💡 Memory Hook

Non-cash and non-recurring items distort earnings → cash flow analysis tests earnings quality.

📖 11. Free Cash Flow and Investment Needs

★ Must-know

📌 Free Cash Flow greater than zero means that cash generated by the firm’s activities covers its operating and investment needs and may be used to pay dividends or reduce debt.

📌 Free Cash Flow less than zero means that additional financial resources must be raised to cover the company’s capital requirements.

Further detail

📐 Formula — Free Cash Flow equals cash from operating activities plus cash from investing activities: $FCF = 1.3 - 39.8 = -38.5$ in the JIT example, in € millions.

• Free cash flows reflect the financial strength or “muscles” of a company, so spending money does not necessarily make a company poorer and receiving money does not necessarily make it richer.

💡 Memory Hook

Positive free cash flow funds needs; negative free cash flow requires additional financing.

📖 12. Margins and Operating Performance

★ Must-know

📌 A margin measures profit relative to net revenue, whereas a return measures profit relative to invested capital.

📐 Formula — The margin ratio is calculated as profit divided by net revenue: $Margin = \frac{Profit}{Net\ Revenue}$.

📌 Margin ratios scale each income-statement item as a percentage of revenue, indicate the firm’s ability to generate profit after expenses, and help compare operating performance across firms and over time.

📌 Margins should be compared with an appropriate benchmark through time-trend analysis, comparison with competitors and industry peers, or comparison with the company’s target.

Further detail

• JIT’s Year 2 margins were:
  • 52.0% gross margin
  • 6.2% EBITDA margin
  • 5.6% EBIT margin
  • 1.6% pretax margin
  • 1.1% net margin

💡 Memory Hook

Margin is profit per 100 of revenue; return is profit per 100 invested.

📖 13. Return on Invested Capital

🔑 Key Concepts & Definitions

• Return on Equity : measures the owners’ accounting return on their investments in a company

★ Must-know

📐 Formula — Return on Invested Capital, also called Return on Capital Employed, is calculated as EBIT divided by invested capital: $ROIC = \frac{EBIT}{Capital\ Invested} = \frac{EBIT}{Fixed\ Assets + Working\ Capital}$.

📐 Formula — Return on Equity is calculated as net income divided by shareholders’ equity: $ROE = \frac{Net\ Income}{Equity}$.

Further detail

• In the JIT example, Year 2 capital employed was €124.3 million, EBIT was €10.4 million, and ROIC was 8.4%.

• JIT’s ROE was 6.2% in Year 2 and 6.1% in Year 1.

📌 ROE can be misleading because book value may be meaningless, a one-period return may be insufficient, and financial leverage can heavily influence it.

💡 Memory Hook

Investment requires funding → profitability creates wealth for capital providers.

📖 14. Time Value and Opportunity Cost

★ Must-know

📌 Only cash-flow values at the same point in time can be compared or combined.

📐 Formula — To move a cash flow forward in time, compound it using $FV = PV(1+r)^N$.

📐 Formula — To move a cash flow backward in time, discount it using $PV = \frac{FV}{(1+r)^N}$.

Further detail

• A risk-free interest rate is the rate at which money can be borrowed or lent without risk and is represented by the safest government bond available.

• Investing €10,000 at 3% for one year produces €10,300, so the time value of money is €300.

💡 Memory Hook

Compare at one date → compound forward → discount backward → use the required return.

📖 15. Cash Flow Streams and Valuation

🔑 Key Concepts & Definitions

• Constant Perpetuity : a stream of equal cash flows paid at regular intervals forever with no fixed maturity date

★ Must-know

📐 Formula — The present value of a stream of cash flows is the sum of each cash flow discounted to the present: $PV = \sum_{t=0}^{T}\frac{C_t}{(1+r)^t}$.

Further detail

• A €30,000 annual perpetuity discounted at 8% requires €375,000 today when the first payment occurs in one year.

• Cash-flow streams can be classified as:

  • constant perpetuities
  • growing perpetuities
  • constant annuities
  • growing annuities

• In the Euromillion example, receiving €15 million today is more valuable at an 8% interest rate than receiving 30 annual payments of €1 million, even though the upfront option pays half the total nominal amount.

💡 Memory Hook

Perpetuities last forever; annuities have a fixed maturity date.

📖 16. Net Present Value and Value Creation

🔑 Key Concepts & Definitions

• Net Present Value : the difference between the present value of its benefits and the present value of its costs
• Opportunity Cost of Capital : the best available expected return in the market on an investment with comparable risk and term

★ Must-know

📐 Formula — The net present value is calculated as $NPV = PV(\text{Benefits}) - PV(\text{Costs})$ or as the present value of all project cash flows.

📌 A project with NPV greater than zero could create value because its expected return exceeds the required return, whereas a project with NPV less than zero does not create value under the stated assumptions.

📌 When choosing among alternative plans, the decision-maker should select the alternative with the highest NPV.

Further detail

• For a project costing €100,000 today and generating €107,000 in one year at a 10% required return, the NPV is −€2,727, so the project is not value-creating despite its positive 7% return.

💡 Memory Hook

Required return below project return → positive NPV → value creation

📖 17. Internal Rate of Return

🔑 Key Concepts & Definitions

• Internal Rate of Return : the compound annual average rate of return of a project

★ Must-know

📐 Formula — The internal rate of return is the discount rate that makes the net present value of all project cash flows equal to zero, so it solves $NPV = 0$.

📌 An investment is generally accepted when its IRR exceeds the required return, because its return then covers the opportunity cost of capital.

Further detail

• If an investment of $1,000 produces $2,000 in six years, its IRR is 12.25% per year.

• For savings and loans, the IRR is also called the effective interest rate, and the same method is used to calculate a bond’s yield to maturity.

💡 Memory Hook

IRR measures project return, while the required return measures its financing hurdle

📖 18. Payback Period and Its Limits

🔑 Key Concepts & Definitions

• Payback Period : the amount of time required to recover the initial investment
• Capital Budgeting : the process used to analyze alternative investments and decide which ones to accept
• Free Cash Flow : The cash remaining after revenues have covered commitments to employees, suppliers, creditors, the state, and investment needs in working capital and capital expenditures.

★ Must-know

📌 Under the payback rule, a project is accepted if its payback period is less than a prespecified length of time and rejected otherwise.

• The payback rule ignores the project’s cost of capital and the time value of money.

• Free cash flow is calculated as revenues minus costs of goods sold, depreciation, and income tax, plus depreciation, minus the change in net working capital and capital expenditures.

📌 In capital budgeting, forecasted earnings are not forecasted cash flows because net income excludes or includes items differently from cash, including depreciation, accruals, and capital expenditures.

• 🔄 Capital budgeting follows three stages:
  1. Forecasting incremental earnings
  2. Determining free cash flows
  3. Deciding whether to invest using NPV, IRR, and the payback period

📌 The NPV rule evaluates whether a project creates value, the IRR rule compares the project’s return with the cost of capital, and the payback period measures the time required to recover the initial investment.

📌 Income statements report revenues, expenses, and net income, but forecasted earnings are not forecasted cash flows.

• A company with positive net income can run out of cash because net income does not necessarily equal the amount of cash the firm has earned.

• Net income differs from cash because of:

  • Non-cash items such as amortization and depreciation
  • Accruals such as unrealized revenues
  • Uses of cash not reported on the income statement such as capital expenditures

• 🔄 Cash flows are extracted from accounting statements by:

  1. Eliminating non-cash items
  2. Deducting changes in working capital
  3. Accounting for investment activities

📐 Formula — Free cash flow is calculated as sales minus operating costs and depreciation, yielding EBIT; after subtracting income tax and adding back depreciation and amortization, increases in working capital needs and capital expenditures are deducted: $FCF = EBIT - Income\ tax + Depreciation\ and\ amortization - \Delta NWC - Capital\ Expenditure.$

📌 Unlevered net income is used in capital budgeting because interest expense is typically excluded, allowing the project to be judged on its capacity to generate wealth rather than on how it is financed.

Further detail

• The payback rule: ignores cash flows after the required payback period, uses an arbitrary cutoff, is biased against long-term projects

💡 Memory Hook

Payback asks when cash is recovered, whereas NPV asks whether value is created

📊 Synthesis Tables

Equity Versus Debt

Dimension	Equity	Debt
Control	Voting and decision-making powers	Normally no decision power except in default
Income	Uncertain dividends and share-price appreciation	Predetermined fixed income
Liquidation	Paid last	Paid before equity holders
Risk	Bears business risk	Primarily exposed to default risk

Financial Statement Measures

Measure	What it captures	Main limitation
Net income	Accounting earnings after expenses, taxes, and non-recurring items	May include non-cash items and accruals
Cash flow	Cash generated and allocated through operations, investment, and financing	Does not itself measure accounting profitability
Free cash flow	Cash from operations plus cash from investing	Negative values require additional financing