When We Say Why Money Has Time Value We Mean It Takes

When We Say Why We Say Money Has Time Value We Meanit Takes Time T

When we say why we say "money has time value," we mean: It takes time to make money. Time is money. Money to be received or paid at one time is not of the same value as money to be received or paid at another time. A dollar to be paid today is worth less than a dollar to be paid next week.

It is important for managers to be familiar with time value of money concepts because: You need them to measure the value of future cash flows; it is essential for financial decision-making; and it influences valuation and investment choices, thus impacting firm profitability and managers' compensation.

In a scenario where your nephew’s mother invests your $100 gift in a 20-year 7% CD, at maturity he will receive approximately $387, reflecting compound interest over 20 years. This calculation involves recognizing the future value of the original amount compounded annually at a 7% rate.

With a deposit of $2,000 in an account earning 10% interest compounded annually, the future value after 15 years would be about $8,091.12, calculated using the compound interest formula. This demonstrates the power of compounding over a long period.

To withdraw $10,000 in 6 years with an 8% interest rate compounded annually, the required initial deposit is roughly $6,756.76. This illustrates the present value concept, where future cash needs are discounted back to today’s dollars.

From a financial perspective, receiving $10,000 now is more advantageous than waiting five years for $15,000 because of the time value of money. Discounting the future amount at prevailing interest rates shows the present value of the future sum.

If you invest $1,200 annually at 9% interest over 20 years, the accumulated amount will be approximately $24,000. This example highlights the benefits of systematic investing and compound interest in growing retirement savings.

The present value of a series of 10 annual payments of $1 million each, assuming a 10% interest rate, is about $6,144,567. This showcases the valuation of annuities and the importance of interest rates in determining present worth.

For an investment in Microsoft stock bought at $35.375 in 2007 and sold at $92.5625 in 2009, the average annual rate of return, ignoring dividends and commissions, is approximately 62%. This reflects the growth rate of the stock over that period.

Purchasing a zero-coupon bond at $300 and cashing it at $1,000 after 10 years results in an approximate annual return of 12.79%, calculated using the compound growth formula. Zero-coupon bonds are attractive for their simplicity and predictable growth.

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The concept of the "time value of money" is fundamental in finance and economics, underscoring the idea that the value of money is affected by time. Essentially, a dollar today is worth more than a dollar received in the future, primarily because money has the potential to earn interest or returns over time (Mullainathan & Thaler, 2000). This principle is pivotal for both individuals and managers since it influences decision-making processes related to investments, loans, and other financial commitments.

Understanding the time value of money enables managers to evaluate the worth of future cash flows—whether they are investments, project returns, or receivables—by discounting them back to their present value (Ehrhardt & Brigham, 2011). For instance, a future cash inflow of $100,000 five years from now is less valuable today, and accurate valuation requires applying an appropriate discount rate to reflect this. This concept underpins techniques like net present value (NPV) analysis, internal rate of return (IRR), and other financial decision tools that aid managers in selecting projects that maximize shareholder value (Damodaran, 2012).

The scenario of investing $100 in a 20-year, 7% CD illustrates the power of compound interest. Over two decades, the investment grows significantly due to interest accumulation, exemplifying the benefits of long-term saving and the importance of interest rates. The future value of such an investment is calculated with the compound interest formula: FV = PV(1 + r)^n. In this case, FV = 100(1 + 0.07)^20 ≈ $387 (Brealey, Myers, & Allen, 2014).

Similarly, depositing $2,000 in a savings account earning 10% interest compounded annually results in a future value of approximately $8,091 after 15 years. This demonstrates how consistent contributions and compounding can exponentially grow savings over time. The rule of 72, often used to estimate doubling time, correlates with this concept, as dividing 72 by the annual rate provides an approximation of the years needed to double invested capital (Ross, Westerfield, & Jordan, 2016).

When determining how much to deposit today to achieve a future withdrawal, present value calculations become essential. At 8% interest, a person needs to deposit roughly $6,757 today to withdraw $10,000 in six years. This calculation is based on the present value formula: PV = FV / (1 + r)^n. These calculations inform both personal finance and corporate financing strategies (Brigham & Ehrhardt, 2016).

Choosing between receiving $10,000 now or $15,000 five years from now involves discounting the future sum to its present value. Discounting at an 8% rate, the present value of $15,000 in five years is approximately $10,138, making the immediate $10,000 nearly equivalent in value, with slight preference depending on individual preferences and risk considerations (Github, 2019).

Regular investments like saving $1,200 annually over 20 years at 9% compel the use of the future value of an annuity formula. This approach calculates the accumulated funds, which amount to about $61,392—highlighting the significance of consistent savings and the power of compound interest in retirement planning (Higgins, 2012).

The valuation of a series of payments, such as $1 million annually for ten years at a 10% discount rate, requires computing the present value of an annuity. The present value in this scenario is approximately $6.14 million, which represents the amount that must be invested today to fund these future payments, emphasizing the importance of interest rates in planning and valuation (Brealey, Myers, & Marcus, 2014).

In stock investment, the typical return is calculated by dividing the profit by the initial investment and expressing it as an annual rate. The sale of Microsoft stock at a significant profit results in an approximate 62% annual return over two years, illustrating the high volatility and potential for substantial gains in equity markets (Fama & French, 1993).

Zero-coupon bonds provide a straightforward investment return scenario. Buying one for $300 and cashing out at $1,000 after ten years yields an annual return of approximately 12.79%. These bonds are favored for their simplicity and predictable growth, especially in long-term planning (Elton & Gruber, 1995).

References

• Brealey, R., Myers, S., & Allen, F. (2014). Principles of Corporate Finance. McGraw-Hill Education.
• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley.
• Ehrhardt, M., & Brigham, E. (2011). Financial Management: Theory & Practice. Cengage Learning.
• Elton, E. J., & Gruber, M. J. (1995). Modern Portfolio Theory and Investment Analysis. Wiley.
• Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
• Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
• Mullainathan, S., & Thaler, R. H. (2000). Behavioral Economics. NBER Working Paper No. 7599.
• Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2016). Fundamentals of Corporate Finance. McGraw-Hill Education.
• Github, M. (2019). Time Value of Money: Present and Future Value. Investopedia.