7.1 Now versus Later Concepts
3 min read•june 18, 2024
Money's value changes over time due to factors like , , and . This concept forms the basis of financial decision-making, with quantifying the . Higher rates indicate greater time value.
and are key concepts in time value calculations. represents money's worth at a future date, while present value is the current worth of future money. These calculations are crucial for evaluating investments and financial planning.
Time Value of Money
Effects of time on money value
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- Money has a time value due to:
- involves the potential earnings lost by not investing money available now (savings account, stocks)
- Inflation erodes the purchasing power of money over time as prices increase (consumer goods, services)
- Risk and make future cash flows less certain than present cash flows (economic conditions, market volatility)
- rates quantify the time value of money
- Higher interest rates indicate a greater time value of money (10% vs 2% annual return)
- The relationship between time and money value forms the foundation of financial decision-making ( choices, budgeting)
Future value vs present value
- Future value (FV) represents the value of a sum of money at a specific future date
- Calculated by applying to a present sum over a given time period (5 years, 10 years)
- Formula:
- = Present value (initial investment)
- = Interest rate per period (annual, quarterly)
- = Number of periods (years, months)
- affects the growth rate of investments (daily, monthly, annually)
- Present value (PV) represents the current value of a future sum of money
- Calculated by a future sum at a given interest rate over a specific time period
- Formula:
- Key differences between future value and present value:
- Direction of time
- Future value projects a present sum forward in time (growth)
- Present value discounts a future sum back to the present (shrinkage)
- Effect of interest rates
- Higher interest rates lead to higher future values and lower present values (compounding, discounting)
- Direction of time
Significance of lump sum cash flows
- are single, one-time payments or receipts
- Examples include investments (real estate purchase), loans (mortgage), and asset purchases or sales (business acquisition)
- Lump sum cash flows serve as building blocks for more complex financial calculations
- and are series of equal, periodic lump sum cash flows (monthly rent, annual dividends)
- The timing of lump sum cash flows is crucial in determining their value
- Cash flows occurring at different times must be adjusted for the time value of money to be comparable (net present value analysis)
- Lump sum cash flows are used in various financial applications:
- decisions compare the present value of future cash flows to the initial investment (project viability)
- determines the periodic payments required to pay off a lump sum loan (car financing, student loans)
- Retirement planning estimates the future value of current lump sum investments (401(k) contributions, IRA deposits)
Interest rates and investment evaluation
- is the stated rate on financial instruments, not accounting for compounding or inflation
- represents the true annual cost of borrowing or return on investment, considering compounding
- Net present value (NPV) is used to evaluate investments by comparing the present value of all cash inflows to the present value of all cash outflows
- is the discount rate that makes the NPV of all cash flows equal to zero
- The shows the relationship between interest rates and time to maturity for debt securities
Key Terms to Review (31)
Annuities: An annuity is a series of equal payments made at regular intervals, such as monthly or annually, over a specified period of time. Annuities are commonly used for retirement planning and income generation, and they are an important concept in the context of the timing of cash flows and the comparison of present and future values.
Capital Budgeting: Capital budgeting is the process of evaluating and selecting long-term investments or projects that are expected to generate returns for a business over multiple years. It involves analyzing the costs, risks, and potential benefits of various investment options to determine the most advantageous use of a company's limited financial resources.
Compound Interest: Compound interest is the interest earned on interest, where the interest accumulated on the principal balance of an investment or loan is added to the principal, and the resulting sum then earns additional interest. This process of earning interest on interest creates exponential growth over time, making compound interest a powerful concept in finance.
Compounding Frequency: Compounding frequency refers to the rate at which interest is calculated and added to the principal amount in an investment or loan. It determines how quickly the value of an investment or the balance of a loan grows over time due to the effects of compound interest.
Core inflation index: The core inflation index measures the change in prices of goods and services, excluding food and energy. It provides a clearer view of long-term inflation trends by omitting the more volatile categories.
Discounting: Discounting is the process of determining the present value of a future cash flow or payment. It involves adjusting the value of a future amount to account for the time value of money, reflecting the idea that money has a higher value in the present than in the future due to factors such as inflation and opportunity cost.
Effective Annual Rate: The effective annual rate (EAR) is the actual annual interest rate earned or paid on an investment or loan, taking into account the effects of compounding. It represents the true annual cost or yield of a financial instrument, accounting for the frequency of compounding periods within a year.
Effective annual rate (EAR): Effective Annual Rate (EAR) is the actual interest rate an investor earns or pays in a year after accounting for compounding. It provides a true reflection of the annual cost of borrowing or the annual return on investment.
Future value: Future value is the amount of money an investment will grow to over a period of time at a given interest rate. It reflects the value of a current asset at a future date based on expected growth.
Future Value: Future value (FV) is the value of an asset or cash flow at a future date, based on a given rate of growth or interest rate. It represents the amount a sum of money will grow to over a certain period of time when compounded at a specific interest rate.
Inflation: Inflation is a sustained increase in the general price level of goods and services in an economy over time. It is a key macroeconomic concept that has far-reaching implications on the time value of money, business cycles, and personal financial decisions.
Interest: Interest is the cost of borrowing money, typically expressed as a percentage of the principal amount. It can also be seen as the return on investment for money that is lent or invested over time.
Interest Rates: Interest rates refer to the cost of borrowing money or the return on saving and investing. They are a fundamental concept in finance that impact both personal and business decisions related to the time value of money.
Internal Rate of Return (IRR): The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. It is a widely used metric in finance to evaluate the profitability and viability of potential investments or projects.
Investment: Investment is the allocation of resources, typically money, with the expectation of generating an income or profit. It involves committing capital to an asset with hopes that its value will increase over time.
Loan amortization: Loan amortization is the process of gradually paying off a loan through scheduled, pre-determined payments that include both principal and interest. The payment amounts are designed to fully repay the loan by the end of its term.
Loan Amortization: Loan amortization is the process of gradually paying off a loan over time through a series of scheduled, equal payments. It involves the systematic reduction of the loan balance by allocating each payment towards both the principal and interest components of the loan.
Lump Sum Cash Flows: Lump sum cash flows refer to a single, one-time payment or receipt of cash, as opposed to a series of smaller, recurring cash flows. This concept is important in the context of time value of money and evaluating the present value of future cash flows.
Nominal interest rate: Nominal interest rate is the percentage increase in money that the borrower pays to the lender, not accounting for inflation. It represents the rate quoted on loans and investments.
Nominal Interest Rate: The nominal interest rate is the stated or advertised rate of interest on a loan or investment, without accounting for the effects of inflation. It represents the pure time value of money and serves as a benchmark for comparing the cost of borrowing or the return on savings across different financial instruments.
Opportunity cost: Opportunity cost is the value of the next best alternative that is forgone when making a decision. It represents the benefits you could have received by taking an alternative action.
Opportunity Cost: Opportunity cost is the value of the next best alternative that must be forgone in order to pursue a certain action or decision. It represents the trade-offs involved in allocating limited resources to one use instead of another.
Perpetuities: A perpetuity is an annuity or other stream of payments that continues forever. It represents a financial obligation that has no end date, making it a valuable tool in long-term financial planning and investment strategies. Perpetuities are closely tied to the concepts of time value of money and discounting future cash flows.
Present Value: Present value is a fundamental concept in finance that refers to the current worth of a future sum of money or stream of cash flows, discounted at an appropriate rate of interest. It is a crucial tool for evaluating the time value of money and making informed financial decisions across various topics in finance.
Real interest rates: Real interest rates are the rates of interest an investor expects to receive after allowing for inflation. It is calculated by subtracting the inflation rate from the nominal interest rate.
Risk: Risk refers to the potential for an event or action to have an adverse impact on an individual, organization, or system. It involves the possibility of a negative outcome or undesirable consequence occurring, which can have financial, operational, or reputational implications.
Time Value of Money: The time value of money is a fundamental concept in finance that recognizes the difference in value between a sum of money available today and the same sum available at a future point in time. It is based on the principle that money available at the present time is worth more than the identical sum in the future due to its potential to earn interest or be invested to generate a return.
Time value of money (TVM): Time Value of Money (TVM) is the concept that money available now is worth more than the same amount in the future due to its potential earning capacity. This principle underlines why receiving money today is preferable to receiving it later.
Uncertainty: Uncertainty refers to the lack of complete information or predictability about a situation or outcome. It is a state of being unsure or indefinite, where the future is unknown or the likelihood of events occurring is unclear.
Yield curve: The yield curve is a graphical representation of the interest rates on debt for a range of maturities. It shows the relationship between short-term and long-term bond yields issued by the same entity.
Yield Curve: The yield curve is a graphical representation of the relationship between the yield (or interest rate) and the maturity of a set of similar debt instruments, typically government bonds. It provides a visual depiction of the term structure of interest rates, reflecting the market's expectations about future interest rates and economic conditions.