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Finance lecture - Feb 2002

# Finance lecture - Feb 2002 - University of Provence Earle...

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University of Provence Earle Traynham Professor and Dean College of Business Administration University of North Florida Jacksonville, Florida USA February 2002

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University of Provence I. First Principles of Valuation Future Value of Compounding Present Value and Discounting PV and FV of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities
University of Provence II. Valuing Stocks and Bonds Bonds and Bond Valuation Common Stock Valuation Net Present Value and Other Investment Criteria Opportunity Cost

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University of Provence III. Capital Budgeting Cash – The Majestic Mulch and Compost Company IV. Acquisitions and Divestitures
Future Value of Compounding Investing in a single period FV = P(1+r) 1 Where P = Principal invested, and r = the interest rate on the investment What is value of \$500 invested for 1 year at 10% FV = \$500(1+.10) 1 = \$500(1.1) 1 = \$500(1.10) = \$550

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Future Value and Compounding Investing for More Than One Period FV = P(1+r) t Where t = the number of periods in the future What is the FV of \$500 invested for 2 years at 10% FV = \$500(1+.10) 2 = \$500(1.21) = \$605
Present Value and Discounting PV = FV/(1+r) t , Where r is the discount rate for t periods in the future PV for Single Period of Time PV = \$70,000/(1+0.12) 1 = \$62,500 PV for Multiple Periods of Time PV = \$100,000/(1+.075) 8 = \$100,000/1.7835) = \$56,070

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The Rule of 72 Approximate time (in years) required to double an investment FV/PV = 2.0, take 72/r Example How long will it take a \$10,000 investment to reach \$20,000 at 8%? 72/8 = 9 years (actual = 9.006 years)
The Present and Future Value of Multiple Cash Flows Future Value – compound the accumulated value period by period, or calculate FV of each cash flow and sum them Example: assume you deposit \$2000 today, \$1000 in one year, and \$3000 in 2 years; all @ 8%. Calculate FV

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The Future Value of Multiple Cash Flows Calculate FV of each cash flow and sum FV = (\$2000)(1.08) 3 + (\$1000)(1.08) 2 + (\$3000)(1.08) 1 = \$2519.42 + \$1166.40 + \$3240 = \$6925.82
FV - compound the accumulated value period by period Time period 0: \$2000 Time period 1: (\$2000)(1.08) + \$1000 = \$3160 Time period 2: (\$3160)(1.08) +\$3000 = \$6412.80 Time period 3: \$6925.82

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The Present Value of Multiple Cash Flows Discount each amount to time period 0, and sum them Discount back one period at a time, summing as you go Example: What is present value of \$1000 per year (at end of year) for 5 years, at 6%?
PV – Discount each amount to time period 0, and sum PV = (\$1000)/(1.06) 1 + (\$1000)/ (1.06) 2 + (\$1000)(1.06) 3 +(\$1000) (1.06) 4 + (\$1000)(1.06) 5 = \$943.40 + \$890 + \$839.62 + \$792.09 + \$747.26 = \$4212.37

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PV – Discount back one period at at
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Finance lecture - Feb 2002 - University of Provence Earle...

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