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Page 1: The Time Value of Money

Introduction to Time Value of Money

• Understanding the time value of money is crucial as it forms the basis for financial decision-making.

• Key focus of this chapter includes:

  • Valuing Bonds

  • Valuing Stocks

  • Net Present Value and Investment Criteria

  • Discounted Cash Flow Analysis

• Learning Objectives:

  • LO1: Calculate future value of money invested at a given interest rate.

  • LO2: Calculate the present value of future payments.

  • LO3: Find present and future values of cash payment streams.

  • LO4: Determine interest rates implied by present or future values.

  • LO5: Differentiate between real and nominal cash flows and interest rates.

  • LO6: Compare interest rates over different time intervals.

• Real-life implications such as loans and investments frame how we view the time value of money.

Practical Implications

• The example of an auto dealership highlights the misconception about interest rates.

• Effective annual interest rates versus monthly payments on loans.

• Companies invest in tangible assets (factories) and intangible assets (patents) expecting returns.

Page 2: Financial Decisions and Cash Flow Comparison

Financial Decisions

• Realization of salary against current expenditures, such as tuition.

• Borrowing for education and its long-term repayment plans becomes essential.

Cash Flow Comparisons

• The significance of comparing cash payments across different times.

• Financial considerations explore future salary against current tuition costs.

• Importance of calculations related to present and future values.

• Understanding of inflation and interest rates in financial terms.

Page 3: Principles of Investment

Growth of Investments

• Funds invested at a specific interest rate will grow.

• Investment return versus initial outlay is examined through examples.

• Example: An initial $100 investment earning 6% interest.

Page 4: Compounding Interest

Understanding Compounding

• Compounding interest leads to growing investment value resulting in future worth.

• Illustrations utilize a simple $100 investment to showcase the compounding approach and growth over multiple years.

Page 5: Mechanics of Compound Interest

Details on Calculation

• Year by year breakdown of balance growth due to interest compounding.

• Formula: Future Value (FV) = Initial Investment × (1 + r)^t

• Definitions of simple versus compound interest.

Page 6: Factors Influencing Growth

Interest Rates and Their Effects

• Effect of varying interest rates on investment returns.

• Comparison of different growth rates over the same period.

• Visualization through tables of projected investment growth.

Page 7: Future Value Calculation Formula

FV Calculation Formula

• The future value calculation formula (PV × (1 + r)^t).

• Introduction of financial calculator usage for effective calculations.

Page 8: Future Value Factors Table

Visual Aid for FV Factors

• Table outlines future value factors based on various periods and interest rates.

Page 9: Examples using Future Value Factors

Practical Application

• Engaging numerical examples using future value factors for quick calculations and longer term prospects without lengthy calculations.

Page 10: Future Value with Monthly Compounding

Monthly Compounding Explained

• Breakdown of investments made with monthly rather than yearly periods.

Page 11: Present Values Defined

Concept of Present Value (PV)

• Explanation of why present value is crucial when equating future payment worth.

• Basic present value formula (PV = FV / (1 + r)^t).

Page 12: Calculating the Present Value

Process of Calculation

• Detailed steps demonstrating present value calculation through numerical examples.

Page 13: Continuous Cash Flow Concepts

Cash Flow Streams

• Understanding how cash flow includes both present and future considerations, utilizing appropriate discount mechanisms for accuracy.

Page 14: Discount Factors

Discount Factor Application

• Introduction to discount factors and their relevance in present value calculations.

Page 15: Implementing Discount Factors

Practical Applications

• Ensures clarity on cash flow management allowing comparison to become easy between cash flows at different points.

Page 16: Price Comparison Impact

Financial Planning

• Advising on strategizing for major expenditures based on present value calculations, utilizing discount factors.

Page 17: Loan Example - Puerto Rico

Real-World Context

• Application of calculating present value to understand borrowing costs for informational purposes.

Page 18: Cost Analysis via Present Value

Loan Payment Comparison

• Example comparing different payment options in an installment plan. Detailed explainer comparing total costs ahead of decision-making without ignoring timelines.

Page 19: Evaluation of Best Options

Cost considerations derived through present value of installment payments versus upfront payments.

Page 20: Interest Rate Discovery

Implied Interest Rates

• Methodology to uncover market interest rates through loan observations.

Page 21: Interest Rate Calculation Techniques

Techniques Explained

• Breakdown of possible routes toward finding implied interest rates through proper mathematical formulation.

Page 22: Financial Calculator Use Cases

Calculator Overview

• Overview of input required for calculation via calculators alleviates complexities of manual processes.

Page 23: Assessing Investment Growth

Dual Cash Flow Assessment

• Structured breakdown detailing anticipated growth through various investment scenarios

Page 24: Multiple Cash Flows in Investments

Understanding Investments beyond Single Payments

• Explanation on how to assess multiple inflows over time systematically.

Page 25: Streamlining through Excel

Spreadsheet Usage and Explanation

• Benefits of spreadsheets noted in financial calculations and how to operate essential financial functions to retrieve results.

Page 26: Overview of Future Payment Coverage

Future Investments and Cash Flow

• Final examples highlight larger scopes of financial decision-making in relation to multiple cash payments.

Page 27: Analyzing Payment Options

Streamlined Cash Payments

• Importance of time value explored through installment payment structure comparisons.

Page 28: Valuing Perpetuities

Understanding Perpetuities

• Theoretical underpinnings of perpetuities and how present values are established over time.

Page 29: Further Analysis of Multi-Period Payments

Payment Valuation Extensity

• Insights into delayed perpetuities and their value systems, eloquent understanding vital.

Page 30: Realizing Annuities

Annuity Valuation Principle

• Break approaches of annuity valuation with illustrated technical approaches to ensure clarity.

Page 31: Example with Payments

Assessment Methodologies & Documentation

• Important connections between cash flow understanding, equating payments through systematic valuation show implications on finance broadly.

Page 32: General Annuity Values

Annuity Definitions

• Further affirmation of how an annuity is valued, providing simple yet effective equations to derive numerically accurate results.

Page 33: Inflation Considerations

Time Value Mechanics & Inflation

• The financial discussion wraps around the continuous effect inflation has on investment growth and cash flow considerations manifestation.

Page 34: Inflation Measurement & CPI

Consumer Index Insights

• Connections drawn around inflation readings through consumer price index facilitating direct implications on investments.

Page 35: Real Cost Analysis

Communication Example

• Insights into expenses of goods emphasizes the practical implications of cost adjustments across time periods and inflation.

Page 36: Salary Growth & Real Dollar Value

Salary Implications on Expenditures

• Commentary on behavioral patterns of consumerism amidst inflationary environments to ensure lasting measures on cash utilization.

Page 37: Real vs. Nominal Rates

Interest Rate Definition Clarity

• Accessing differences between genuine monetary growth implications through real versus nominal discussions highlights importance for comprehensive decision making.

Page 38: Understanding Inflation Adjustments

Practicality of Money Utilization

• How money must be conceptualized in seasonal versus annuality must always reflect real buying power dynamics.

Page 39: Effective Annual Interest Rate Calculations

Interest Comparisons

• Discusses necessity for clear formulations in deriving effective annual rates derived from simple periodic inputs establishing the efficient return mechanism.

Page 40: Establishing Monthly Rates

Establishing Consistency

• Discusses the consistent methods necessary for treating simple percentage rates into effective calculations across timing themes.

Page 41: Semi-annual Compounding Rates

Canadian Mortgage Insights

• Evaluation of unique issues carried through in assessing denominated mortgage products on consumer opportunities.

Page 42: General Overview of APR Calculations

Determining Perspectives

• Highlighting practical methodologies unique to variable treatments will emphasize definite professional needs for efficiency in financial matters.

Page 43: Compounding Frequency Importance

Frequency Factor Impact

• Ties direct effects from attention to inflationary experiences adjusted against multiple compounding techniques brings light to savings growth methodology ultimately.

Page 44: Continuous Compounding

Theoretical Calculations

• Expands understanding further towards continuous compounding explores more theoretical frameworks established around growth perspectives necessary for advanced financial knowledge.

Page 45: Illustrating Mortgages

Practical Application for Consumers

• Methodologies creating understanding to real-life impacts of financial calculations that ultimately lead back into everyday scenarios.

Page 46: Amortization Understanding

Interest Payment Structure Overview

• Highlights fundamental characteristics of understanding mortgage products' timing and scope as relates back to wider financial frameworks.

Page 47: Summary Points

Summary of Fundamental Concepts

• Key terms and learning frameworks ensuring clarity around the core principles of finance-based decisions established through effective engagement in cash flow management.