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Time Value of Money

See Also:
Valuation Methods
Adjusted Present Value (AVP)
Net Present Value Method
Internal Rate of Return Method
Required Rate of Return

Time Value of Money (TVM)

Time value of money is the difference between an amount of money in the present and that same amount of money in the future. Having money now is more valuable than having money later.

The present amount is called the present value, the future amount is called the future value, and the appropriate rate that relates the two amounts is called the discount rate.

Present Value = Future Value / (1 + Discount Rate)

Future Value = Present Value x (1 + Discount Rate)

Time Value of Money Examples

Now, let’s look at time value of money examples. If you invest $100 (the present value) for 1 year at a 5% interest rate (the discount rate), then at the end of the year, you would have $105 (the future value). So, according to this example, $100 today is worth $105 a year from today.

$105 = $100 x 1.05

$100 = $105 / 1.05

Likewise, $100 a year from today, discounted back at 5%, is worth only $95.24 today.

$95.24 = $100 / 1.05

To calculate the time value of money for a period longer than one year, you simply raise the discount factor by the appropriate number of time periods. For example, to calculate the future value of $100 at 5% for 5 years:

$127.63 = $100 x (1.05)5

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time value of money, Time Value of Money Examples

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Present Value (PV)

See Also:
Future Value
Adjusted Present Value (APV)
Net Present Value Method
Investment Analysis
Discount Rate

Present Value (PV) Definition

The present value is simply the value of future dollars or currency in present day terms. The present value is simply answering the question how much a dollar in the future is worth today.

Present Value (PV) Explanation

The present value is often used in valuation to discount projections that companies make about themselves so they can figure out how much the company stock price is or maybe its equity value. The present value becomes useful because of inflation. If inflation were to increase at an increasing rate then the company would see the present day dollar as less valuable to them.

Present Value (PV) Formula

The present value formula is as follows:
PV = FV/((1 + i)n)

Where:
PV = Present Value
FV = Future Value
i = rate
n = number of years or periods

Present Value (PV) Example

Jim Bob has just won the lottery. He has the choice of accepting the $2 million now, or he can accept $1 million now and another $2 million 5 years from now. Which of the choices should Jim Bob take? Assume a rate of 8%.

Option #1 PV = $2 million

Option #2 PV = $500,000 + $1,361,166 = 1,861,166

PV calculation:
PV = 2 million/((1+.08)5) = $1,361,166

Option #1 is better because it is worth more to you today than the present payment plus the payment at the end.

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Present Value (PV)

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Future Value

See Also:
Valuation Methods
Net Present Value Method
Adjusted Present Value (APV) Method
Present Value (PV)
Opportunity Cost

Future Value Definition

Future value (FV) is the value of a sum of money at a future point in time for a given interest rate. The idea is to adjust the present value of a sum of money for the time value of money over the specified time period.

If the present value is $1.00, and the interest rate is 10%, then the FV of that dollar one year from now would be $1.10. If someone offered you a dollar now or a dollar one year from now, you’d prefer the dollar now. Because by taking the dollar now and investing it, it will be worth more than one dollar a year from now. By applying that same concept to larger quantities of money, you can see that money now is more valuable than the same amount of money later and that it is necessary to consider the time value of money when making financial decisions.

Future value can be calculated with simple interest or compound interest. Practically speaking, it is more useful to calculate future value using compound interest. Simple interest accounts for interest accumulation over time without compounding. It is simply the principal amount adjusted for the annual interest rate. Compound interest accounts for the interest earned on the value of previous interest earned.

Future Value Formula for Simple Interest

FV = Present Value x (1 + (Interest Rate x Time Periods))

One dollar at 10% for one year: $1.10 = $1.00 x (1 + (.10 x 1))

One dollar at 10% for five years: $1.50 = $1.00 x (1 + (.10 x 5))

Future Value Formula for Compound Interest

FV = Present Value x (1 + Interest Rate) Time Periods

One dollar at 10% for one year: $1.10 = $1.00 x (1 + .10)1

One dollar at 10% for five years: $1.61 = $1.00 x (1 + .10)5

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Future Value Definition, Future Value Formula for Simple Interest, Future Value

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Capital Asset Pricing Model

See Also:
Cost of Capital
Cost of Capital Funding
Arbitrage Pricing Theory
APV Valuation
Capital Budgeting Methods
Discount Rates NPV
Required Rate of Return

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is an equilibrium model that measures the relationship between risk and expected return of an asset based on the asset’s sensitivity to movements in the overall stock market.

CAPM is used to price the risk of an asset or a portfolio of assets. The model is based on the idea that there are two types of risk, systematic risk and idiosyncratic risk, and that the investor should be compensated for both types of risk, as well as, the time value of money. Systematic risk refers to market risk. Idiosyncratic risk refers to the risk of an individual asset. Time value of money refers to the difference between the present value of money and the future value of money. Also, use the model to measure the required rate of return for capital budgeting projects.

The CAPM states that an asset’s expected return equals the risk-free rate plus a risk premium. The risk-free rate refers to the return on an investment without risk, such as a US Treasury Bond, and represents the time value of money. The risk premium represents the incremental return for investing in a risky asset. In the CAPM, it is defined as the market premium, or the overall stock market return less the risk-free rate, multiplied by the beta of the asset. Beta is a factor that measures an asset’s sensitivity to movements in the overall stock market. According to the CAPM, riskier assets should yield higher returns.

The CAPM Formula

Expected Return = Risk-Free Rate + Beta (Market Return – Risk-Free Rate)

For example, if the risk free rate is 5%, the market return is 10%, and the stock’s beta is 2, then the expected return on the stock would be 15%.

15% = 5% + 2 (10% – 5%)

Problems with Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is based on assumptions. First, the model assumes that a riskier asset will yield a higher return. But this is not necessarily true. A risky asset could decline in value. Second, historical data determines beta. The model assumes this historical data an accurate predictor of future results. But the asset’s future volatility may not necessarily reflect its past volatility.

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Capital Asset Pricing Model

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