Chapter 27

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# Chapter 27 - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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
• 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 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
• 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 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. 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
• Risk aversion
• Diversification (firm-specific risk vs. market risk)
• Risk vs. Return
• Asset valuation
• Value & Price
• Capital gains & dividends
• Random walk & index funds