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Principles of Economics

C | Present Discounted Value

Principles of EconomicsC | Present Discounted Value
  1. Preface
  2. 1 Welcome to Economics!
    1. Introduction
    2. 1.1 What Is Economics, and Why Is It Important?
    3. 1.2 Microeconomics and Macroeconomics
    4. 1.3 How Economists Use Theories and Models to Understand Economic Issues
    5. 1.4 How Economies Can Be Organized: An Overview of Economic Systems
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
  3. 2 Choice in a World of Scarcity
    1. Introduction to Choice in a World of Scarcity
    2. 2.1 How Individuals Make Choices Based on Their Budget Constraint
    3. 2.2 The Production Possibilities Frontier and Social Choices
    4. 2.3 Confronting Objections to the Economic Approach
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  4. 3 Demand and Supply
    1. Introduction to Demand and Supply
    2. 3.1 Demand, Supply, and Equilibrium in Markets for Goods and Services
    3. 3.2 Shifts in Demand and Supply for Goods and Services
    4. 3.3 Changes in Equilibrium Price and Quantity: The Four-Step Process
    5. 3.4 Price Ceilings and Price Floors
    6. 3.5 Demand, Supply, and Efficiency
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  5. 4 Labor and Financial Markets
    1. Introduction to Labor and Financial Markets
    2. 4.1 Demand and Supply at Work in Labor Markets
    3. 4.2 Demand and Supply in Financial Markets
    4. 4.3 The Market System as an Efficient Mechanism for Information
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  6. 5 Elasticity
    1. Introduction to Elasticity
    2. 5.1 Price Elasticity of Demand and Price Elasticity of Supply
    3. 5.2 Polar Cases of Elasticity and Constant Elasticity
    4. 5.3 Elasticity and Pricing
    5. 5.4 Elasticity in Areas Other Than Price
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  7. 6 Consumer Choices
    1. Introduction to Consumer Choices
    2. 6.1 Consumption Choices
    3. 6.2 How Changes in Income and Prices Affect Consumption Choices
    4. 6.3 Labor-Leisure Choices
    5. 6.4 Intertemporal Choices in Financial Capital Markets
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  8. 7 Cost and Industry Structure
    1. Introduction to Cost and Industry Structure
    2. 7.1 Explicit and Implicit Costs, and Accounting and Economic Profit
    3. 7.2 The Structure of Costs in the Short Run
    4. 7.3 The Structure of Costs in the Long Run
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  9. 8 Perfect Competition
    1. Introduction to Perfect Competition
    2. 8.1 Perfect Competition and Why It Matters
    3. 8.2 How Perfectly Competitive Firms Make Output Decisions
    4. 8.3 Entry and Exit Decisions in the Long Run
    5. 8.4 Efficiency in Perfectly Competitive Markets
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  10. 9 Monopoly
    1. Introduction to a Monopoly
    2. 9.1 How Monopolies Form: Barriers to Entry
    3. 9.2 How a Profit-Maximizing Monopoly Chooses Output and Price
    4. Key Terms
    5. Key Concepts and Summary
    6. Self-Check Questions
    7. Review Questions
    8. Critical Thinking Questions
    9. Problems
  11. 10 Monopolistic Competition and Oligopoly
    1. Introduction to Monopolistic Competition and Oligopoly
    2. 10.1 Monopolistic Competition
    3. 10.2 Oligopoly
    4. Key Terms
    5. Key Concepts and Summary
    6. Self-Check Questions
    7. Review Questions
    8. Critical Thinking Questions
    9. Problems
  12. 11 Monopoly and Antitrust Policy
    1. Introduction to Monopoly and Antitrust Policy
    2. 11.1 Corporate Mergers
    3. 11.2 Regulating Anticompetitive Behavior
    4. 11.3 Regulating Natural Monopolies
    5. 11.4 The Great Deregulation Experiment
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  13. 12 Environmental Protection and Negative Externalities
    1. Introduction to Environmental Protection and Negative Externalities
    2. 12.1 The Economics of Pollution
    3. 12.2 Command-and-Control Regulation
    4. 12.3 Market-Oriented Environmental Tools
    5. 12.4 The Benefits and Costs of U.S. Environmental Laws
    6. 12.5 International Environmental Issues
    7. 12.6 The Tradeoff between Economic Output and Environmental Protection
    8. Key Terms
    9. Key Concepts and Summary
    10. Self-Check Questions
    11. Review Questions
    12. Critical Thinking Questions
    13. Problems
  14. 13 Positive Externalities and Public Goods
    1. Introduction to Positive Externalities and Public Goods
    2. 13.1 Why the Private Sector Under Invests in Innovation
    3. 13.2 How Governments Can Encourage Innovation
    4. 13.3 Public Goods
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  15. 14 Poverty and Economic Inequality
    1. Introduction to Poverty and Economic Inequality
    2. 14.1 Drawing the Poverty Line
    3. 14.2 The Poverty Trap
    4. 14.3 The Safety Net
    5. 14.4 Income Inequality: Measurement and Causes
    6. 14.5 Government Policies to Reduce Income Inequality
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  16. 15 Issues in Labor Markets: Unions, Discrimination, Immigration
    1. Introduction to Issues in Labor Markets: Unions, Discrimination, Immigration
    2. 15.1 Unions
    3. 15.2 Employment Discrimination
    4. 15.3 Immigration
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
  17. 16 Information, Risk, and Insurance
    1. Introduction to Information, Risk, and Insurance
    2. 16.1 The Problem of Imperfect Information and Asymmetric Information
    3. 16.2 Insurance and Imperfect Information
    4. Key Terms
    5. Key Concepts and Summary
    6. Self-Check Questions
    7. Review Questions
    8. Critical Thinking Questions
    9. Problems
  18. 17 Financial Markets
    1. Introduction to Financial Markets
    2. 17.1 How Businesses Raise Financial Capital
    3. 17.2 How Households Supply Financial Capital
    4. 17.3 How to Accumulate Personal Wealth
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  19. 18 Public Economy
    1. Introduction to Public Economy
    2. 18.1 Voter Participation and Costs of Elections
    3. 18.2 Special Interest Politics
    4. 18.3 Flaws in the Democratic System of Government
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  20. 19 The Macroeconomic Perspective
    1. Introduction to the Macroeconomic Perspective
    2. 19.1 Measuring the Size of the Economy: Gross Domestic Product
    3. 19.2 Adjusting Nominal Values to Real Values
    4. 19.3 Tracking Real GDP over Time
    5. 19.4 Comparing GDP among Countries
    6. 19.5 How Well GDP Measures the Well-Being of Society
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  21. 20 Economic Growth
    1. Introduction to Economic Growth
    2. 20.1 The Relatively Recent Arrival of Economic Growth
    3. 20.2 Labor Productivity and Economic Growth
    4. 20.3 Components of Economic Growth
    5. 20.4 Economic Convergence
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  22. 21 Unemployment
    1. Introduction to Unemployment
    2. 21.1 How the Unemployment Rate is Defined and Computed
    3. 21.2 Patterns of Unemployment
    4. 21.3 What Causes Changes in Unemployment over the Short Run
    5. 21.4 What Causes Changes in Unemployment over the Long Run
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  23. 22 Inflation
    1. Introduction to Inflation
    2. 22.1 Tracking Inflation
    3. 22.2 How Changes in the Cost of Living are Measured
    4. 22.3 How the U.S. and Other Countries Experience Inflation
    5. 22.4 The Confusion Over Inflation
    6. 22.5 Indexing and Its Limitations
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  24. 23 The International Trade and Capital Flows
    1. Introduction to the International Trade and Capital Flows
    2. 23.1 Measuring Trade Balances
    3. 23.2 Trade Balances in Historical and International Context
    4. 23.3 Trade Balances and Flows of Financial Capital
    5. 23.4 The National Saving and Investment Identity
    6. 23.5 The Pros and Cons of Trade Deficits and Surpluses
    7. 23.6 The Difference between Level of Trade and the Trade Balance
    8. Key Terms
    9. Key Concepts and Summary
    10. Self-Check Questions
    11. Review Questions
    12. Critical Thinking Questions
    13. Problems
  25. 24 The Aggregate Demand/Aggregate Supply Model
    1. Introduction to the Aggregate Demand/Aggregate Supply Model
    2. 24.1 Macroeconomic Perspectives on Demand and Supply
    3. 24.2 Building a Model of Aggregate Demand and Aggregate Supply
    4. 24.3 Shifts in Aggregate Supply
    5. 24.4 Shifts in Aggregate Demand
    6. 24.5 How the AD/AS Model Incorporates Growth, Unemployment, and Inflation
    7. 24.6 Keynes’ Law and Say’s Law in the AD/AS Model
    8. Key Terms
    9. Key Concepts and Summary
    10. Self-Check Questions
    11. Review Questions
    12. Critical Thinking Questions
    13. Problems
  26. 25 The Keynesian Perspective
    1. Introduction to the Keynesian Perspective
    2. 25.1 Aggregate Demand in Keynesian Analysis
    3. 25.2 The Building Blocks of Keynesian Analysis
    4. 25.3 The Phillips Curve
    5. 25.4 The Keynesian Perspective on Market Forces
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
  27. 26 The Neoclassical Perspective
    1. Introduction to the Neoclassical Perspective
    2. 26.1 The Building Blocks of Neoclassical Analysis
    3. 26.2 The Policy Implications of the Neoclassical Perspective
    4. 26.3 Balancing Keynesian and Neoclassical Models
    5. Key Terms
    6. Key Concepts and Summary
    7. Self-Check Questions
    8. Review Questions
    9. Critical Thinking Questions
    10. Problems
  28. 27 Money and Banking
    1. Introduction to Money and Banking
    2. 27.1 Defining Money by Its Functions
    3. 27.2 Measuring Money: Currency, M1, and M2
    4. 27.3 The Role of Banks
    5. 27.4 How Banks Create Money
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  29. 28 Monetary Policy and Bank Regulation
    1. Introduction to Monetary Policy and Bank Regulation
    2. 28.1 The Federal Reserve Banking System and Central Banks
    3. 28.2 Bank Regulation
    4. 28.3 How a Central Bank Executes Monetary Policy
    5. 28.4 Monetary Policy and Economic Outcomes
    6. 28.5 Pitfalls for Monetary Policy
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  30. 29 Exchange Rates and International Capital Flows
    1. Introduction to Exchange Rates and International Capital Flows
    2. 29.1 How the Foreign Exchange Market Works
    3. 29.2 Demand and Supply Shifts in Foreign Exchange Markets
    4. 29.3 Macroeconomic Effects of Exchange Rates
    5. 29.4 Exchange Rate Policies
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  31. 30 Government Budgets and Fiscal Policy
    1. Introduction to Government Budgets and Fiscal Policy
    2. 30.1 Government Spending
    3. 30.2 Taxation
    4. 30.3 Federal Deficits and the National Debt
    5. 30.4 Using Fiscal Policy to Fight Recession, Unemployment, and Inflation
    6. 30.5 Automatic Stabilizers
    7. 30.6 Practical Problems with Discretionary Fiscal Policy
    8. 30.7 The Question of a Balanced Budget
    9. Key Terms
    10. Key Concepts and Summary
    11. Self-Check Questions
    12. Review Questions
    13. Critical Thinking Questions
    14. Problems
  32. 31 The Impacts of Government Borrowing
    1. Introduction to the Impacts of Government Borrowing
    2. 31.1 How Government Borrowing Affects Investment and the Trade Balance
    3. 31.2 Fiscal Policy, Investment, and Economic Growth
    4. 31.3 How Government Borrowing Affects Private Saving
    5. 31.4 Fiscal Policy and the Trade Balance
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  33. 32 Macroeconomic Policy Around the World
    1. Introduction to Macroeconomic Policy around the World
    2. 32.1 The Diversity of Countries and Economies across the World
    3. 32.2 Improving Countries’ Standards of Living
    4. 32.3 Causes of Unemployment around the World
    5. 32.4 Causes of Inflation in Various Countries and Regions
    6. 32.5 Balance of Trade Concerns
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  34. 33 International Trade
    1. Introduction to International Trade
    2. 33.1 Absolute and Comparative Advantage
    3. 33.2 What Happens When a Country Has an Absolute Advantage in All Goods
    4. 33.3 Intra-industry Trade between Similar Economies
    5. 33.4 The Benefits of Reducing Barriers to International Trade
    6. Key Terms
    7. Key Concepts and Summary
    8. Self-Check Questions
    9. Review Questions
    10. Critical Thinking Questions
    11. Problems
  35. 34 Globalization and Protectionism
    1. Introduction to Globalization and Protectionism
    2. 34.1 Protectionism: An Indirect Subsidy from Consumers to Producers
    3. 34.2 International Trade and Its Effects on Jobs, Wages, and Working Conditions
    4. 34.3 Arguments in Support of Restricting Imports
    5. 34.4 How Trade Policy Is Enacted: Globally, Regionally, and Nationally
    6. 34.5 The Tradeoffs of Trade Policy
    7. Key Terms
    8. Key Concepts and Summary
    9. Self-Check Questions
    10. Review Questions
    11. Critical Thinking Questions
    12. Problems
  36. A | The Use of Mathematics in Principles of Economics
  37. B | Indifference Curves
  38. C | Present Discounted Value
  39. The Expenditure-Output Model
  40. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
    18. Chapter 18
    19. Chapter 19
    20. Chapter 20
    21. Chapter 21
    22. Chapter 22
    23. Chapter 23
    24. Chapter 24
    25. Chapter 25
    26. Chapter 26
    27. Chapter 27
    28. Chapter 28
    29. Chapter 29
    30. Chapter 30
    31. Chapter 31
    32. Chapter 32
    33. Chapter 33
    34. Chapter 34
  41. References
  42. Index

As explained in Financial Markets, the prices of stocks and bonds depend on future events. The price of a bond depends on the future payments that the bond is expected to make, including both payments of interest and the repayment of the face value of the bond. The price of a stock depends on the expected future profits earned by the firm. The concept of a present discounted value (PDV), which is defined as the amount you should be willing to pay in the present for a stream of expected future payments, can be used to calculate appropriate prices for stocks and bonds. To place a present discounted value on a future payment, think about what amount of money you would need to have in the present to equal a certain amount in the future. This calculation will require an interest rate. For example, if the interest rate is 10%, then a payment of $110 a year from now will have a present discounted value of $100—that is, you could take $100 in the present and have $110 in the future. We will first shows how to apply the idea of present discounted value to a stock and then we will show how to apply it to a bond.

Applying Present Discounted Value to a Stock

Consider the case of Babble, Inc., a company that offers speaking lessons. For the sake of simplicity, say that the founder of Babble is 63 years old and plans to retire in two years, at which point the company will be disbanded. The company is selling 200 shares of stock and profits are expected to be $15 million right away, in the present, $20 million one year from now, and $25 million two years from now. All profits will be paid out as dividends to shareholders as they occur. Given this information, what will an investor pay for a share of stock in this company?

A financial investor, thinking about what future payments are worth in the present, will need to choose an interest rate. This interest rate will reflect the rate of return on other available financial investment opportunities, which is the opportunity cost of investing financial capital, and also a risk premium (that is, using a higher interest rate than the rates available elsewhere if this investment appears especially risky). In this example, say that the financial investor decides that appropriate interest rate to value these future payments is 15%.

Table C1 shows how to calculate the present discounted value of the future profits. For each time period, when a benefit is going to be received, apply the formula:

Present discounted value = Future value received years in the future(1 + Interest rate)numbers of years tPresent discounted value = Future value received years in the future(1 + Interest rate)numbers of years t
Payments from Firm Present Value
$15 million in present $15 million
$20 million in one year $20 million/(1 + 0.15)1 = $17.4 million
$25 million in two years $25 million/(1 + 0.15)2 = $18.9 million
Total $51.3 million
Table C1 Calculating Present Discounted Value of a Stock

Next, add up all the present values for the different time periods to get a final answer. The present value calculations ask what the amount in the future is worth in the present, given the 15% interest rate. Notice that a different PDV calculation needs to be done separately for amounts received at different times. Then, divide the PDV of total profits by the number of shares, 200 in this case: 51.3 million/200 = 0.2565 million. The price per share should be about $256,500 per share.

Of course, in the real world expected profits are a best guess, not a hard piece of data. Deciding which interest rate to apply for discounting to the present can be tricky. One needs to take into account both potential capital gains from the future sale of the stock and also dividends that might be paid. Differences of opinion on these issues are exactly why some financial investors want to buy a stock that other people want to sell: they are more optimistic about its future prospects. Conceptually, however, it all comes down to what you are willing to pay in the present for a stream of benefits to be received in the future.

Applying Present Discounted Value to a Bond

A similar calculation works in the case of bonds. Financial Markets explains that if the interest rate falls after a bond is issued, so that the investor has locked in a higher rate, then that bond will sell for more than its face value. Conversely, if the interest rate rises after a bond is issued, then the investor is locked into a lower rate, and the bond will sell for less than its face value. The present value calculation sharpens this intuition.

Think about a simple two-year bond. It was issued for $3,000 at an interest rate of 8%. Thus, after the first year, the bond pays interest of 240 (which is 3,000 × 8%). At the end of the second year, the bond pays $240 in interest, plus the $3,000 in principle. Calculate how much this bond is worth in the present if the discount rate is 8%. Then, recalculate if interest rates rise and the applicable discount rate is 11%. To carry out these calculations, look at the stream of payments being received from the bond in the future and figure out what they are worth in present discounted value terms. The calculations applying the present value formula are shown in Table C2.

Stream of Payments (for the 8% interest rate) Present Value (for the 8% interest rate) Stream of Payments (for the 11% interest rate) Present Value (for the 11% interest rate)
$240 payment after one year $240/(1 + 0.08)1 = $222.20 $240 payment after one year $240/(1 + 0.11)1 = $216.20
$3,240 payment after second year $3,240/(1 + 0.08)2 = $2,777.80 $3,240 payment after second year $3,240/(1 + 0.11)2 = $2,629.60
Total $3,000 Total $2,845.80
Table C2 Computing the Present Discounted Value of a Bond

The first calculation shows that the present value of a $3,000 bond, issued at 8%, is just $3,000. After all, that is how much money the borrower is receiving. The calculation confirms that the present value is the same for the lender. The bond is moving money around in time, from those willing to save in the present to those who want to borrow in the present, but the present value of what is received by the borrower is identical to the present value of what will be repaid to the lender.

The second calculation shows what happens if the interest rate rises from 8% to 11%. The actual dollar payments in the first column, as determined by the 8% interest rate, do not change. However, the present value of those payments, now discounted at a higher interest rate, is lower. Even though the future dollar payments that the bond is receiving have not changed, a person who tries to sell the bond will find that the investment’s value has fallen.

Again, real-world calculations are often more complex, in part because, not only the interest rate prevailing in the market, but also the riskiness of whether the borrower will repay the loan, will change. In any case, the price of a bond is always the present value of a stream of future expected payments.

Other Applications

Present discounted value is a widely used analytical tool outside the world of finance. Every time a business thinks about making a physical capital investment, it must compare a set of present costs of making that investment to the present discounted value of future benefits. When government thinks about a proposal to, for example, add safety features to a highway, it must compare costs incurred in the present to benefits received in the future. Some academic disputes over environmental policies, like how much to reduce carbon dioxide emissions because of the risk that they will lead to a warming of global temperatures several decades in the future, turn on how one compares present costs of pollution control with long-run future benefits. Someone who wins the lottery and is scheduled to receive a string of payments over 30 years might be interested in knowing what the present discounted value is of those payments. Whenever a string of costs and benefits stretches from the present into different times in the future, present discounted value becomes an indispensable tool of analysis.

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