Reversionary Factor: Understanding the Present Worth of Future Dollars

An in-depth look at the reversionary factor, a vital financial metric that calculates the present worth of one dollar to be received in the future using the interest rate and time period variables.

The reversionary factor is a mathematical factor that indicates the present worth of one dollar (or any monetary unit) to be received in the future. Essentially, it calculates the value today of a future sum of money using a specified interest rate and time period. It is identical to the concept of the present value of 1.

Formula

The formula for calculating the reversionary factor is given by:

$$ \text{Reversionary Factor} = \frac{1}{(1 + i)^n} $$

where:

• \( i \) = interest rate per period
• \( n \) = number of periods

Importance in Finance and Investment

The reversionary factor is critical in various financial decisions, including:

• Investment Appraisal: Determining the present value of future cash flows to assess the viability of an investment.
• Loan Amortization: Assessing the present value of future loan payments.
• Retirement Planning: Calculating the present value of future retirement funds.

Calculations and Examples

Example Calculation

Assume an interest rate of 5% (0.05) and a period of 3 years. The reversionary factor is calculated as follows:

$$ \text{Reversionary Factor} = \frac{1}{(1 + 0.05)^3} = \frac{1}{1.157625} \approx 0.8638 $$

This result implies that one dollar received in 3 years at a 5% interest rate is worth approximately $0.8638 today.

Historical Context

The concept of discounting future cash flows to their present value dates back to the foundations of financial worth analysis. Economists like Irving Fisher and John Maynard Keynes have contributed to developing these concepts in the 20th century, which now form the bedrock of modern finance and investment theory.

Applicability in Different Financial Scenarios

Discounted Cash Flow (DCF)

$$ \text{DCF} = \sum_{t=1}^{n} \frac{CF_t}{(1 + i)^t} $$

The discounted cash flow method uses the reversionary factor to determine the present value of a series of future cash flows, enabling businesses to make informed investment decisions.

Present Value (PV)

$$ \text{PV} = \frac{FV}{(1 + i)^n} $$

Present Value (PV) directly utilizes the reversionary factor to translate future values (FV) into today’s monetary terms.

Related Terms

• Discount Rate: The interest rate used in discounting future cash flows to their present values.
• Net Present Value (NPV): The sum of present values of individual cash flows, discounted using a given interest rate, minus the initial investment.
• Annuity: A series of equal payments at regular intervals, where the present value can be calculated using the reversionary factor for each payment period.

FAQs

What is the difference between reversionary factor and present value?

The reversionary factor specifically refers to the present value of one monetary unit to be received in the future, while the present value can refer to any future sum or cash flow discounted to the present.

When should the reversionary factor be used?

It should be used when calculating the discounted value of a fixed amount of money at a future time point. It is integral in financial modeling, investment analysis, and loan calculations.

References

1. Fisher, Irving. The Theory of Interest. 1930.
2. Keynes, John Maynard. The General Theory of Employment, Interest and Money. 1936.
3. Brealey, Richard A., Stewart C. Myers, and Franklin Allen. Principles of Corporate Finance. McGraw-Hill Education, 2016.

Summary

The reversionary factor is an indispensable tool in finance for translating future sums of money into their present-day worth. Its utility spans various financial analyses, including investment appraisal, loan amortization, and retirement planning. Understanding and applying the reversionary factor allows for better financial decision-making by accurately assessing the value of future cash flows today.