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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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