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The Tools of Finance. Chapter 27. Time Value of Money. A dollar received in the future does not have the same purchasing power as a dollar today Why? Inflation Interest helps dollars grow to maintain their purchasing power. Simple Interest. Principle x Rate x Time

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Time value of money
Time Value of Money

  • A dollar received in the future does not have the same purchasing power as a dollar today

  • Why? Inflation

  • Interest helps dollars grow to maintain their purchasing power


Simple interest
Simple Interest

  • Principle x Rate x Time

    • Principle is an amount borrowed or invested

    • Rate is the annual rate of interest paid or earned

    • Time is a function of one year

  • If you invest $10,000 for one year at 6%

  • 10,000 x .06 x 1 = $600

  • 10,000 x .06 x 4 = $2,400 for four years

  • At the end of four years you have $12,400


Compound interest
Compound Interest

  • Interest earning interest

  • What if the interest earned each year is allowed to grow as part of the investment?

    Yr 1: 10,000 + (10,000 x .06 x 1) = 10,600

    Yr 2: 10,600 + (10,600 x .06 x 1) = 11,236

    Yr 3: 11,236 + (11,236 x .06 x 1) = 11,910

    Yr 4: 11,910 + (11,910 x .06 x 1) = 12,625

  • You come out ahead by $225


Compound interest1
Compound Interest

Compound interest is an exponential function: the bigger it gets the faster it grows

Future value = Present value x (1 + r)n

FV = $10,000 x (1 + .06)4

FV = $12,625


Variables
Variables

  • Present Value (PV)

    • The value of an investment or amount borrowed today

    • Principle only, no time no interest

  • Future Value (FV)

    • Principle + interest at some time in the future

  • N is the number of compounding periods

  • Ris the interest rate per compounding period


Compounding vs discounting
Compounding vs. Discounting

Compounding is the process of adding interest: take a present value or principle payments and add interest to arrive at a future value

FV = PV x (1+r)n


Compounding vs discounting1
Compounding vs. Discounting

Discounting moves in the opposite direction: take a future value with principle and interest and remove the interest

PV = FV /(1+r)n


Other considerations
Other Considerations

  • Risk aversion

  • Diversification (firm-specific risk vs. market risk)

  • Risk vs. Return

  • Asset valuation

    • Value & Price

    • Capital gains & dividends

    • Random walk & index funds



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