intermediate lesson • 25 min
Time Value of Money: Comparing Money Across Time
What You Will Learn
By the end of this lesson, you should be able to: explain why the timing of a cash flow matters; distinguish present value from future value; use a timeline to organize dates, periods, and amounts; apply the basic future-value and present-value formulas; explain how compounding and inflation affect the interpretation of money over time; and recognize that a discount rate depends on the valuation context and assumptions.
Evidence & citations14 sources
Time value of money is the principle that the value of a cash flow depends on when it is received or paid. (supported)
Present value is the value today of a future cash flow after discounting it using an assumed rate and time period. Future value is the value at a specified later date of money held or invested today after applying an assumed rate of return. (supported with limitations)
A timeline can organize the dates, periods, and amounts of cash flows before a TVM calculation is performed. (supported)
With periodic compounding at a constant rate, future value can be calculated as FV = PV × (1 + r)^n, where r is the rate per period and n is the number of periods. (supported)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
Inflation can reduce the purchasing power of a fixed amount of money over time, so nominal dollar amounts and real purchasing power are distinct concepts. (supported)
A discount rate is used to convert a future cash flow into a present value; the appropriate rate depends on the valuation context and assumptions. (supported)
The Simple Idea
A dollar today and a dollar later are not automatically equivalent. Money held today may earn a return, while inflation may reduce what a fixed amount can buy over time. Time value of money gives us a way to compare cash flows that occur on different dates by translating them to a common date.
Evidence & citations4 sources
Time value of money is the principle that the value of a cash flow depends on when it is received or paid. (supported)
Inflation can reduce the purchasing power of a fixed amount of money over time, so nominal dollar amounts and real purchasing power are distinct concepts. (supported)
Present Value and Future Value
Present value, or PV, is the value today of a future cash flow after applying an assumed rate and time period. Future value, or FV, is the value at a later date of money held or invested today after applying an assumed rate of return. These are two directions of the same comparison: moving money forward uses compounding, while moving it backward uses discounting.
Evidence & citations4 sources
Present value is the value today of a future cash flow after discounting it using an assumed rate and time period. Future value is the value at a specified later date of money held or invested today after applying an assumed rate of return. (supported with limitations)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
The Core Formulas
With periodic compounding at a constant rate, future value is calculated as FV = PV × (1 + r)^n. Here, r is the rate per period and n is the number of periods. To calculate the present value of one future cash flow under the same assumptions, use PV = FV ÷ (1 + r)^n. The rate and the number of periods must use matching units: for example, a rate per period should be paired with the corresponding number of periods.
Evidence & citations4 sources
With periodic compounding at a constant rate, future value can be calculated as FV = PV × (1 + r)^n, where r is the rate per period and n is the number of periods. (supported)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
A Step-by-Step Method
First, identify the cash flow, its amount, and the date when it occurs. Second, draw a timeline showing the relevant dates and periods. Third, decide whether you are moving the amount forward to find future value or backward to find present value. Fourth, identify the rate per period and the number of periods. Finally, apply the matching formula and state the assumptions. For example, if PV is 1,000, r is 5% per period, and n is 2 periods, FV = 1,000 × (1.05)^2 = 1,102.50. Reversing the direction, a future cash flow of 1,000 has PV = 1,000 ÷ (1.05)^2, approximately 907.03.
Evidence & citations6 sources
A timeline can organize the dates, periods, and amounts of cash flows before a TVM calculation is performed. (supported)
With periodic compounding at a constant rate, future value can be calculated as FV = PV × (1 + r)^n, where r is the rate per period and n is the number of periods. (supported)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
Comparing Two Payment Dates
Suppose a person is comparing two cash flows: 1,000 received today and 1,000 received two periods from now. To compare them using a 5% rate per period, the later amount can be discounted: PV = 1,000 ÷ (1.05)^2, approximately 907.03. Under these stated assumptions, the later 1,000 is equivalent to about 907.03 today. This calculation does not by itself establish which choice is preferable; it only translates the amounts to the same date.
Evidence & citations7 sources
Time value of money is the principle that the value of a cash flow depends on when it is received or paid. (supported)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
A discount rate is used to convert a future cash flow into a present value; the appropriate rate depends on the valuation context and assumptions. (supported)
Key Terms
- Cash flow
- money received or paid at a particular time. Present value: the value today of a future cash flow after discounting. Future value: the value at a later date of money held or invested today after applying an assumed rate. Compounding: adding previously earned interest to the balance so later interest is calculated on that larger balance. Discount rate: a rate used to convert a future cash flow into present value; its suitability depends on the valuation context and assumptions. Nominal amount: a stated dollar amount. Real purchasing power: what that amount can buy after considering changes such as inflation.
Evidence & citations11 sources
Time value of money is the principle that the value of a cash flow depends on when it is received or paid. (supported)
Present value is the value today of a future cash flow after discounting it using an assumed rate and time period. Future value is the value at a specified later date of money held or invested today after applying an assumed rate of return. (supported with limitations)
Compounding means that previously earned interest is included in the balance on which later interest is calculated. (supported)
A discount rate is used to convert a future cash flow into a present value; the appropriate rate depends on the valuation context and assumptions. (supported)
Inflation can reduce the purchasing power of a fixed amount of money over time, so nominal dollar amounts and real purchasing power are distinct concepts. (supported)
Important Assumptions and Limitations
A time-value calculation is only as meaningful as its assumptions. The rate must match the period used in the formula, and the selected discount rate should fit the valuation context and the cash flows being discounted. A nominal dollar result is not automatically a statement about purchasing power: inflation can reduce the purchasing power of a fixed amount over time, so nominal amounts and real purchasing power are distinct. The formulas shown also describe a single cash flow under periodic compounding at a constant rate; different cash-flow patterns or assumptions require corresponding methods.
Evidence & citations9 sources
With periodic compounding at a constant rate, future value can be calculated as FV = PV × (1 + r)^n, where r is the rate per period and n is the number of periods. (supported)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
A discount rate is used to convert a future cash flow into a present value; the appropriate rate depends on the valuation context and assumptions. (supported)
Inflation can reduce the purchasing power of a fixed amount of money over time, so nominal dollar amounts and real purchasing power are distinct concepts. (supported)
Common Misconceptions
Misconception 1: “Future value and present value are different kinds of money.” They are different measures of the same cash flow translated to different dates. Misconception 2: “Compounding means applying interest only to the original amount.” Compounding includes previously earned interest in the balance used for later interest calculations. Misconception 3: “A discount rate is universally correct.” The appropriate rate depends on the valuation context and assumptions. Misconception 4: “A larger future dollar amount always means greater purchasing power.” Inflation can reduce what a fixed amount buys, so nominal dollars and real purchasing power must be distinguished.
Evidence & citations9 sources
Present value is the value today of a future cash flow after discounting it using an assumed rate and time period. Future value is the value at a specified later date of money held or invested today after applying an assumed rate of return. (supported with limitations)
Compounding means that previously earned interest is included in the balance on which later interest is calculated. (supported)
A discount rate is used to convert a future cash flow into a present value; the appropriate rate depends on the valuation context and assumptions. (supported)
Inflation can reduce the purchasing power of a fixed amount of money over time, so nominal dollar amounts and real purchasing power are distinct concepts. (supported)
Key Takeaways
Time value of money is the principle that the value of a cash flow depends on when it is received or paid. Future value moves today's money forward through compounding: FV = PV × (1 + r)^n. Present value moves a future cash flow backward through discounting: PV = FV ÷ (1 + r)^n. A timeline helps organize the dates and amounts before calculating. Always state the rate, period, and other assumptions, and remember that nominal dollar amounts do not necessarily represent the same purchasing power over time.
Evidence & citations10 sources
Time value of money is the principle that the value of a cash flow depends on when it is received or paid. (supported)
With periodic compounding at a constant rate, future value can be calculated as FV = PV × (1 + r)^n, where r is the rate per period and n is the number of periods. (supported)
For a single future cash flow under the same assumptions, present value can be calculated as PV = FV ÷ (1 + r)^n. (supported)
A timeline can organize the dates, periods, and amounts of cash flows before a TVM calculation is performed. (supported)
Inflation can reduce the purchasing power of a fixed amount of money over time, so nominal dollar amounts and real purchasing power are distinct concepts. (supported)
Knowledge check
Test what you just learned.
Complete this short assessment for Time Value of Money. You will get explanations immediately after grading.
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