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INTRODUCTION TO INTERTEMPORAL ANALYSIS

INTRODUCTION TO INTERTEMPORAL ANALYSIS. Common Measures of Change. Change = (FV-PV) =(1,177.6 - 984.7) = 192.9 Percentage Change = (FV-PV)/PV =(1,177.6 - 984.7)/984.7 = .195 = 19.6% EX: Population of China (millions) 1980 984.0 1990 1,177.6.

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INTRODUCTION TO INTERTEMPORAL ANALYSIS

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  1. INTRODUCTION TO INTERTEMPORAL ANALYSIS

  2. Common Measures of Change Change = (FV-PV) • =(1,177.6 - 984.7) = 192.9 Percentage Change = (FV-PV)/PV • =(1,177.6 - 984.7)/984.7 = .195 = 19.6% • EX: Population of China (millions) • 1980 984.0 1990 1,177.6

  3. Not So Common Measure of Change: Compounding • The Formula • FV = PV*(1+g)T • Initial value / present value = PV • Final value / future value = FV • Average growth rate per period = g • Number of time periods = T

  4. Compounding Process: Alternative Problem

  5. Future Value Example • Q. What will the population of India be in the year 2020 if the population in 1985 was 751 million and the growth rate is 2.5% a year? • A. The initial value is 751, the growth rate is 2.5% (.0251), and the time horizon is 35 years. • FV = PV*(l+g)T = 751*(1.0251)35 • = 751*2.381 = 1,788 million

  6. Average Growth Rate Example • Q.What was average yearly rate of wage growth if wages grew from $102 in 1970 to $389 in 1989? • A. The present value is 102, the future value is 389, and the time period is 19. • g = (FV/PV)(1/19) -1 = (389/102).0526 -1 • =1.0729 - 1 = 7.29%

  7. Present Value Example • Q. How much will I need to save today to have $1,000 in 3 years if the interest rate is 8%.? • A. The end value is $1,000, the time horizon is 3 years, and the growth rate is 8%.. • PV = FV/(l+g)T = $1000/(1.08)3 • = $1000/1.2597= $793.83

  8. An Introduction to the Mathematics of Finance • Q: What is a Bond? • A: A promise to pay in the future • Q: What is the price of a Bond? • A: How much you need to pay today to ‘buy’ the future payment(s)? • Q: What does the bond’s price depend on? • A: How fast money grows

  9. Determining the Price of a Bond The Deal: • On January 1 you are offered the following deal: $100 on January 1 for the next three years The Starting Point: • A dollar a year from now is not worth a dollar today so we must convert the ‘future’ dollars to ‘‘present’ dollars.

  10. The Framework: • Compounding formula provides framework: PV = 100/(1+r) + 100/(1+r)2 + 100/(1+r) 2 r = expected interest rate (growth rate of money)

  11. Bond Prices and Interest Rates $100 in one year and $1,100 in two years. • @8%:Price = PV = 100/1.08 + 1100/1.082 • 92.59 + 943.07 = $1,035 • @10%:Price = PV = 100/1.1 + 1100/1.12 • 90.90 + 909.09 = $1,000 • @12%:Price = PV = 100/1.12 + 1100/1.122 • 89.3 + 876.91 = $966

  12. The Key to Intertemporal Analysis • The Compounding Formula • FV = PV*(1+g)T

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