Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Financial Terms
Scientific Terms
Disclaimer

The Time Value of Money

 Present Value How much you got now. Future Value How much what you got now grows to when compounded at a given rate

I give you 100 dollars. You take it to the bank. They will give you 10% interest per year for 2 year.

• The Present Value = \$ 100
• Future Value = \$121.
 FV= PV (1 + i )N
• FV = Future Value
• PV = Present Value
• i = the interest rate per period
• n= the number of compounding periods

Determine Future Value Compounded Annually
What is the future value of \$34 in 5 years if the interest rate is 5%? (i=.05)

• FV= PV ( 1 + i ) N
• FV= \$ 34 ( 1+ .05 ) 5
• FV= \$ 34 (1.2762815)
• FV= \$43.39.

Determine Future Value Compounded Monthly
What is the future value of \$34 in 5 years if the interest rate is 5%? (i equals .05 divided by 12, because there are 12 months per year. So 0.05/12=.004166, so i=.004166)

• FV= PV ( 1 + i ) N
• FV= \$ 34 ( 1+ .004166 ) 60
• FV= \$ 34 (1.283307)
• FV= \$43.63.

Determine Present Value Compounded Annually
You can go backwards too. I will give you \$1000 in 5 years. How much money should you give me now to make it fair to me. You think a good interest rate would be 6% ( You just made that number up). (i=.06)

• FV= PV ( 1 + i ) N
• \$1000 = PV ( 1 + .06) 5
• \$1000 = PV (1.338)
• \$1000 / 1.338 = PV
• \$ 747.38 = PV

O.K. so you give me \$ 747.38 today and in 5 years I'll give you \$1000. Sound fair?? You will get 6% interest on your money.

Determine Present Value Compounded Monthly
Here's that last one again, but with monthly compounding instead of annual compouding. (i equals .06 divided by 12, because there are 12 months per year so 0.06/12=.005 so i=.005)
• FV= PV ( 1 + i ) N
• \$1000 = PV ( 1 + .005) 60
• \$1000 = PV (1.348)
• \$1000 / 1.348= PV
• \$741.37 = PV

Detailed Explanation

The concept of the Time Value of Money (TVM) is fundamental to the field of finance and economics. It refers to the idea that the value of money today is different from its value at some point in the future, due to the potential for earning interest or returns on investments. In other words, money available today is worth more than the same amount of money at a future date.

One of the most important aspects of TVM is the concept of opportunity cost. When we choose to spend money today, we are foregoing the opportunity to invest that money and earn a return. Therefore, the decision to spend money now has an opportunity cost, which is the potential return that could have been earned if that money had been invested instead. This is why it is important to consider the time value of money when making financial decisions, as failing to do so could result in missed opportunities for wealth creation.

TVM is also important for investors, as it helps to determine the potential return on investments. By considering the time value of money, investors can evaluate the expected return on an investment and compare it to the opportunity cost of investing elsewhere. This can help them make more informed investment decisions and maximize their returns.

Another way in which TVM affects decision-making is through inflation. Inflation reduces the purchasing power of money over time, which means that the same amount of money will be worth less in the future than it is today. This is why it is important to consider inflation when evaluating the time value of money. For example, if inflation is expected to be 2% per year, then \$100 today will be worth only \$98 in one year. This means that investments must earn at least a 2% return just to keep pace with inflation.

TVM also has important implications for economic growth. In a healthy economy, money invested today will generate returns that can be used to fund future investment and growth. This is known as the multiplier effect, as the initial investment creates a ripple effect throughout the economy. However, if the time value of money is not considered, this effect may be muted or lost entirely. For example, if a company fails to invest in research and development today, it may miss out on potential innovations that could drive growth and profitability in the future.

Another important aspect of TVM is the concept of compounding. Compounding refers to the idea that investment returns can themselves earn returns over time. This means that even small investments made today can grow into large sums over time, due to the power of compounding. For example, if an investor puts \$1,000 into an investment that earns 8% per year, it will be worth \$2,159 after ten years. This is because the initial investment earns interest each year, and the interest itself earns interest in subsequent years.

The time value of money also has important implications for borrowing and lending. When borrowers receive a loan, they are essentially paying a fee for the use of money over time. This fee, known as interest, is the compensation that lenders receive for the risk they take in lending money. The interest rate on a loan reflects the time value of money, as it takes into account the potential return that could be earned on that money if it were invested elsewhere.

TVM is not a fixed concept. The time value of money can vary based on a number of factors, including inflation, interest rates, and risk. For example, the time value of money is generally higher in a high-inflation environment, as money loses value more quickly over time.

The concept of TVM has important applications in many areas of finance, including investments, loans, and retirement planning.

Investments are one of the primary applications of TVM. The future value of an investment can be calculated using TVM formulas, which take into account the interest rate, time period, and initial investment. By calculating the future value of an investment, investors can make informed decisions about which investments to choose and how long to hold them.

TVM is also important in the context of loans. Lenders use TVM formulas to calculate the present value of a loan, which takes into account the interest rate, time period, and repayment schedule. By calculating the present value of a loan, lenders can determine the amount of the loan that should be provided to borrowers, and the terms of repayment.

TVM is also relevant to retirement planning. By calculating the present value of their retirement savings and projecting future income needs, individuals can determine the amount of savings they need to achieve their retirement goals. This calculation takes into account the time value of money, inflation, and other economic factors.

The concept of TVM is important for several reasons. First, it allows individuals and organizations to make informed financial decisions based on the time value of money. By taking into account the future value of money, individuals and organizations can better plan for the future and make informed decisions about investments, loans, and retirement planning.

Second, TVM is important because it helps individuals and organizations to understand the impact of inflation on their finances. Inflation erodes the value of money over time, which means that a dollar today will be worth less in the future. By understanding the impact of inflation, individuals and organizations can make informed decisions about how to invest and save their money to preserve its value over time.

Third, TVM is important because it provides a framework for understanding the cost of borrowing money. By understanding the present value of a loan and the interest rate, borrowers can make informed decisions about whether to take out a loan and how much to borrow.

Despite its widespread use in finance, the concept of TVM has been subject to criticism from some economists and scholars. One critique of TVM is that it assumes that interest rates are constant over time, which may not always be the case in practice.

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