Summary Corporate Finance
(6th edition)
Berk and DeMarzo
Finance for Pre-Master
Eindhoven, November 24, 2025
, Finance
Pre-Master
Contents
1 Chapter 3: Financial Decision Making and the Law of One Price 3
1.1 Valuing Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Interest Rates and the Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Present Value and the NPV Decision Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Arbitrage and the Law of One Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Chapter 4: The Time Value of Money 4
2.1 Perpetuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Growing Perpetuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 Growing Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.5 Payments and Loan Amortization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.6 Applications and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Chapter 5: Interest Rates 5
3.1 Interest Rate Quotes and Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Determinants of Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3 Risk and Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.4 Opportunity Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4 Chapter 6: Bond Cash Flows, Prices and Yields 7
4.1 Zero-Coupon Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2 Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3 Dynamic Behavior of Bond Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.4 Expected Return of Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.5 Corporate Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.6 Extra: Forward Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5 Chapter 9: Valuing Stocks 12
5.1 The Dividend Discount Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.2 Applying the Dividend-Discount Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.3 Total Payout and Free Cash Flow Valuation Models . . . . . . . . . . . . . . . . . . . . . 13
5.4 Valuation Based on Comparable Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.5 Information, Competition, and Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6 Chapter 10: Capital Markets and the Pricing of Risk 16
6.1 Common Measures of Risk and Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.2 Diversification in Stock Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.3 Risk and Return Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.4 Summary Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7 Chapter 11: Optimal Portfolio Choice and the CAPM 19
7.1 The Expected Return of a Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.2 The Volatility of a Two-Stock Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.3 The Volatility of Large Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7.4 Risk Vs. Return: Choosing an Efficient Portfolio . . . . . . . . . . . . . . . . . . . . . . . 20
7.5 Risk-Free Saving, Borrowing, and the Efficient Portfolio . . . . . . . . . . . . . . . . . . . 21
7.6 The Efficient Portfolio and Required Returns . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.7 The Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8 Chapter 12: Estimating the Cost of Capital 24
8.1 The Equity Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8.2 Market Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8.3 Beta Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
8.4 The Debt Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
8.5 Project Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
8.6 Final Thoughts on CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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9 Chapter 14: Capital Structure in a Perfect Market 28
9.1 Equity Vs. Debt Financing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
9.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value . . . . . . . . . . . . . . . . . . 29
9.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital . . . . . . . . . . . . . . . . 30
9.4 Capital Structure Fallacies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
10 Chapter 15: Debt and Taxes 33
10.1 The Interest Tax Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
10.2 Valuing the Interest Tax Shield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
10.3 Recapitalizing to Capture the Tax Shield . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
10.4 Personal Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
10.5 Optimal Capital Structure with Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
11 Chapter 16: Financial Distress, Managerial Incentives, and Information 38
11.1 Default and Bankruptcy in a Perfect Market . . . . . . . . . . . . . . . . . . . . . . . . . 38
11.2 The Cost of Bankruptcy and Financial Distress . . . . . . . . . . . . . . . . . . . . . . . . 38
11.3 Optimal Capital Structure: The Tradeoff Theory . . . . . . . . . . . . . . . . . . . . . . . 39
11.4 Exploiting Debt Holders: The Agency Costs of Leverage . . . . . . . . . . . . . . . . . . . 40
11.5 Motivating Managers: The Agency Benefits of Leverage . . . . . . . . . . . . . . . . . . . 40
11.6 Agency Costs and the Tradeoff Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
11.7 Asymmetric Information and Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . 41
12 Chapter 17: Payout Policy 42
12.1 Distributions to Shareholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
12.2 Comparison of Dividends and Share Repurchases . . . . . . . . . . . . . . . . . . . . . . . 43
12.3 The Tax Disadvantage of Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
12.4 Dividend Capture and Tax Clientles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
12.5 Payout Versus Retention of Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
12.6 Stock Dividends, Splits, and Spin-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
12.7 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
13 Chapter 18: Capital Budgeting and Valuation with Leverage 49
13.1 Overview of Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
13.2 The Weighted Average Cost of Capital Method . . . . . . . . . . . . . . . . . . . . . . . . 49
13.3 The Adjusted Present Value Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
13.4 The Flow-to-Equity Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
13.5 APV with Other Leverage Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
13.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
14 Chapter 23: Raising Equity Capital 53
14.1 Equity Financing for Private Companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
14.2 The Initial Public Offering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
14.3 IPO Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
14.4 The Seasoned Equity Offering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
15 Chapter 24: Debt Financing 59
15.1 Corporate Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
15.2 Other Types of Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
15.3 Bond Covenants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
15.4 Repayment Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
A Basic Terms 63
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1 | Chapter 3: Financial Decision Making and the Law of One Price
1.1 | Valuing Decisions
A financial manager’s goal is to make decisions that increase firm value by ensuring benefits exceed
costs. To compare them consistently, all must be expressed in cash today. Other disciplines (marketing,
accounting, economics, etc.) provide inputs, but finance evaluates them using market prices.
Competitive Market: A market in which a good can be bought and sold at the same price; value is
independent of individual preferences.
Valuation Principle: The value of an asset is determined by its competitive market price. A decision
increases firm value when benefits (at market prices) exceed costs.
1.2 | Interest Rates and the Time Value of Money
Time value of money: Money today is worth more than money in the future.
Risk-Free Rate (rf ): Interest rate for borrowing or lending without risk, with factor (1 + rf ).
Present Value (PV): P V = (1+r)
cn
n
Future Value (FV): F V = c0 (1 + r)n
Discount Factor: DF = 1+r1
, today’s price of $1 in one year. The risk-free rate rf is its discount rate.
Discounting = converting future cash flows to present value.
1.3 | Present Value and the NPV Decision Rule
Net Present Value: N P V = P V (Benefits) − P V (Costs)
NPV Rule: Accept projects with N P V > 0; choose the highest NPV.
1.4 | Arbitrage and the Law of One Price
Law of One Price: Identical goods/securities must trade for the same price in competitive markets (no
arbitrage).
Arbitrage Opportunity: Risk-free profit without investment, occurring if (i) prices differ across markets
or (ii) an asset’s price ̸= PV of its cash flows.
Page 3
(6th edition)
Berk and DeMarzo
Finance for Pre-Master
Eindhoven, November 24, 2025
, Finance
Pre-Master
Contents
1 Chapter 3: Financial Decision Making and the Law of One Price 3
1.1 Valuing Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Interest Rates and the Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Present Value and the NPV Decision Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Arbitrage and the Law of One Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Chapter 4: The Time Value of Money 4
2.1 Perpetuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Growing Perpetuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 Growing Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.5 Payments and Loan Amortization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.6 Applications and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Chapter 5: Interest Rates 5
3.1 Interest Rate Quotes and Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Determinants of Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3 Risk and Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.4 Opportunity Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4 Chapter 6: Bond Cash Flows, Prices and Yields 7
4.1 Zero-Coupon Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2 Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3 Dynamic Behavior of Bond Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.4 Expected Return of Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.5 Corporate Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.6 Extra: Forward Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5 Chapter 9: Valuing Stocks 12
5.1 The Dividend Discount Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.2 Applying the Dividend-Discount Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.3 Total Payout and Free Cash Flow Valuation Models . . . . . . . . . . . . . . . . . . . . . 13
5.4 Valuation Based on Comparable Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.5 Information, Competition, and Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . 15
6 Chapter 10: Capital Markets and the Pricing of Risk 16
6.1 Common Measures of Risk and Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.2 Diversification in Stock Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.3 Risk and Return Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.4 Summary Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7 Chapter 11: Optimal Portfolio Choice and the CAPM 19
7.1 The Expected Return of a Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.2 The Volatility of a Two-Stock Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.3 The Volatility of Large Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7.4 Risk Vs. Return: Choosing an Efficient Portfolio . . . . . . . . . . . . . . . . . . . . . . . 20
7.5 Risk-Free Saving, Borrowing, and the Efficient Portfolio . . . . . . . . . . . . . . . . . . . 21
7.6 The Efficient Portfolio and Required Returns . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.7 The Capital Asset Pricing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8 Chapter 12: Estimating the Cost of Capital 24
8.1 The Equity Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8.2 Market Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8.3 Beta Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
8.4 The Debt Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
8.5 Project Cost of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
8.6 Final Thoughts on CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Page 1
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Pre-Master
9 Chapter 14: Capital Structure in a Perfect Market 28
9.1 Equity Vs. Debt Financing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
9.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value . . . . . . . . . . . . . . . . . . 29
9.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital . . . . . . . . . . . . . . . . 30
9.4 Capital Structure Fallacies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
10 Chapter 15: Debt and Taxes 33
10.1 The Interest Tax Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
10.2 Valuing the Interest Tax Shield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
10.3 Recapitalizing to Capture the Tax Shield . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
10.4 Personal Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
10.5 Optimal Capital Structure with Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
11 Chapter 16: Financial Distress, Managerial Incentives, and Information 38
11.1 Default and Bankruptcy in a Perfect Market . . . . . . . . . . . . . . . . . . . . . . . . . 38
11.2 The Cost of Bankruptcy and Financial Distress . . . . . . . . . . . . . . . . . . . . . . . . 38
11.3 Optimal Capital Structure: The Tradeoff Theory . . . . . . . . . . . . . . . . . . . . . . . 39
11.4 Exploiting Debt Holders: The Agency Costs of Leverage . . . . . . . . . . . . . . . . . . . 40
11.5 Motivating Managers: The Agency Benefits of Leverage . . . . . . . . . . . . . . . . . . . 40
11.6 Agency Costs and the Tradeoff Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
11.7 Asymmetric Information and Capital Structure . . . . . . . . . . . . . . . . . . . . . . . . 41
12 Chapter 17: Payout Policy 42
12.1 Distributions to Shareholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
12.2 Comparison of Dividends and Share Repurchases . . . . . . . . . . . . . . . . . . . . . . . 43
12.3 The Tax Disadvantage of Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
12.4 Dividend Capture and Tax Clientles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
12.5 Payout Versus Retention of Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
12.6 Stock Dividends, Splits, and Spin-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
12.7 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
13 Chapter 18: Capital Budgeting and Valuation with Leverage 49
13.1 Overview of Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
13.2 The Weighted Average Cost of Capital Method . . . . . . . . . . . . . . . . . . . . . . . . 49
13.3 The Adjusted Present Value Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
13.4 The Flow-to-Equity Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
13.5 APV with Other Leverage Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
13.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
14 Chapter 23: Raising Equity Capital 53
14.1 Equity Financing for Private Companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
14.2 The Initial Public Offering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
14.3 IPO Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
14.4 The Seasoned Equity Offering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
15 Chapter 24: Debt Financing 59
15.1 Corporate Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
15.2 Other Types of Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
15.3 Bond Covenants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
15.4 Repayment Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
A Basic Terms 63
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, Finance
Pre-Master
1 | Chapter 3: Financial Decision Making and the Law of One Price
1.1 | Valuing Decisions
A financial manager’s goal is to make decisions that increase firm value by ensuring benefits exceed
costs. To compare them consistently, all must be expressed in cash today. Other disciplines (marketing,
accounting, economics, etc.) provide inputs, but finance evaluates them using market prices.
Competitive Market: A market in which a good can be bought and sold at the same price; value is
independent of individual preferences.
Valuation Principle: The value of an asset is determined by its competitive market price. A decision
increases firm value when benefits (at market prices) exceed costs.
1.2 | Interest Rates and the Time Value of Money
Time value of money: Money today is worth more than money in the future.
Risk-Free Rate (rf ): Interest rate for borrowing or lending without risk, with factor (1 + rf ).
Present Value (PV): P V = (1+r)
cn
n
Future Value (FV): F V = c0 (1 + r)n
Discount Factor: DF = 1+r1
, today’s price of $1 in one year. The risk-free rate rf is its discount rate.
Discounting = converting future cash flows to present value.
1.3 | Present Value and the NPV Decision Rule
Net Present Value: N P V = P V (Benefits) − P V (Costs)
NPV Rule: Accept projects with N P V > 0; choose the highest NPV.
1.4 | Arbitrage and the Law of One Price
Law of One Price: Identical goods/securities must trade for the same price in competitive markets (no
arbitrage).
Arbitrage Opportunity: Risk-free profit without investment, occurring if (i) prices differ across markets
or (ii) an asset’s price ̸= PV of its cash flows.
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