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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.