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Time Value of Money

Time Value of Money. TVM - Compounding $ Today Future $ Discounting. Future Value (FV). Definition -. FV n = PV(1 + i) n. 1. 2. 0. N. FV = ?. PV=x. Future Value Calculations.

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Time Value of Money

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  1. Time Value of Money • TVM - • Compounding • $ Today Future $ • Discounting

  2. Future Value (FV) • Definition - FVn = PV(1 + i)n 1 2 0 N FV = ? PV=x

  3. Future Value Calculations • Suppose you have $10 million and decide to invest it in a security offering an interest rate of 9.2% per annum for six years. At the end of the six years, what is the value of your investment? • What if the (interest) payments were made semi-annually? • Why does semi-annual compounding lead to higher returns?

  4. Future Value of an Annuity (FVA) • Definition - 0 1 2 N A A A FVA = ?

  5. Ordinary Annuity vs. Annuity Due Ordinary Annuity 0 1 2 N i% A A A Annuity Due 0 1 2 N i% A A A

  6. Future Value of an Annuity Examples • Suppose you were to invest $5,000 per year each year for 10 years, at an annual interest rate of 8.5%. After 10 years, how much money would you have? • What if this were an annuity due? • What if you made payments of $2,500 every six-months instead?

  7. Present Value (PV) • Definition - PV = P0 = FV / (1 + i)n 1 2 0 N FV = x PV= ?

  8. Present Value Calculations • How much would you pay today for an investment that returns $5 million, seven years from today, with no interim cashflows, assuming the yield on the highest yielding alternative project is 10% per annum? • What if the opportunity cost was 10% compounded semi-annually? • Why does semi-annual compounding lead to lower present values?

  9. Present Value of an Annuity (PVA) • Definition - 0 1 2 N A A A PVA = ?

  10. Present Value of an Annuity Examples • How much would you spend for an 8 year, $1,000, annual annuity, assuming the discount rate is 9%? • What if this were an annuity due? • What if you were to receive payments of $500 every six-months instead?

  11. TVM Properties • Future Values • An increase in the discount rate • An increase in the length of time until the CF is received, given a set interest rate, • Present Values • An increase in the discount rate • An increase in the length of time until the CF is received, given a set interest rate, • Note: For this class, assume nominal interest rates can’t be negative!

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