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Chapter 7

Chapter 7. The Time Value of Money. Time Value. Process of expressing The present value of $1 invested now in future terms. (Compounding) Compounding – Process by which interest is paid on interest that was previously earned. The future value of $1 invested in terms of the present

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Chapter 7

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  1. Chapter 7 The Time Value of Money

  2. Time Value • Process of expressing • The present value of $1 invested now in future terms. (Compounding) Compounding – Process by which interest is paid on interest that was previously earned. • The future value of $1 invested in terms of the present Future Value of a dollar – Amount to which a single payment will grow at some rate of interest. • Payments are either: • a single payment • A series of equal payments (an annuity)

  3. Time Value • Time value of money problems may be solved by using: • Interest tables • Financial calculators • Software

  4. Variables for Time Value of Money Problems • PV = present value • FV = future value • PMT = annual payment • N = number of time periods • I = interest rate per period

  5. Future Value • Future value of $1 takes a single payment in the present into the future. • General equation for the future value of $1: P0(1 + i)n = Pn FV = PV (1 + i)n

  6. Future Value Illustrated • PV = -100 • I = 5 • N = 20 • PMT = 0 • FV = ? • = 265.30

  7. Greater Terminal Values • Higher interest rates • Longer time periods • Result in greater terminal values

  8. Greater Terminal Values

  9. Present Value • Present value of $1 brings a single payment in the future back to the present. Present Value – Current value of a dollar to be received in the future. Discounting – Process of determining present value.

  10. Present Value • General equation for the present value of $1:P0 = Pn (1+i)n PV = FV [ 1 / (1 + i)n ] • PV = Present Value • FV = Future Value • i = Interest Rate per Period • n = Number of Compounding Periods

  11. Present Value Illustrated • FV = 100 • I = 6 • N = 5 • PMT = 0 • PV = ? • = -74.73

  12. Lower Present Values • Higher interest rates • Longer time periods • Result in lower present values

  13. Lower Present Values

  14. Financial Calculators and Excel • Express the cash inputs (PV, FV, and PMT) as cash inflows and cash outflows • At least one of the cash variables must be • an inflow (+) • an outflow (-)

  15. Simple Interest • Simple Interest – No Compounding • Good to have if you withdraw interest each period. • SI = Principal (PV) x rate (i) x time (n)

  16. Future Value of a Single Amount Example • You buy a stock for $10 and expect the price to increase 9 percent annually. After 10 years, what is the anticipated price of the stock?

  17. Future Value of a Single Amount Example • The unknown: FV • The givens: • PV = 10 • PMT = 0 • N = 10 • I = 9 The answer: $23.67

  18. FV Interpretation • A $10 stock will be worth $23.67 after 10 years if its price grows 9% annually.

  19. Present Value of a Single Amount Example • What is the cost of a stock that was sold for $23.67, held for 10 years and whose value appreciated 9 percent annually?

  20. Present Value of a Single Amount Example • The unknown: PV • The givens: • FV = 23.67 • PMT = 0 • N = 10 • I = 9 The answer:$10

  21. Interpretation • $23.67 received after ten years is worth $10 today if the rate of return is 9 percent.

  22. Interpretation of Future and Present Values These two problems are mirror images: • In the first case, the $10 is compounded into its future value ($23.67). • In the second case, the future value ($23.67) is discounted back to its present value ($10).

  23. Rate of Return Example • A stock was purchased for $10 and sold for $23.67 after 10 years. What was the return?

  24. Future Determination of the Interest Rate(can use Present too) • The unknown: I • The givens: • PV = 10 • PMT = 0 • N = 0 • FV = 23.67 The answer: 9%

  25. Interpretation • The yield on a $10 investment that was sold after 10 years for $23.67 is 9%.

  26. Non-annual Compounding • More than one interest payment a year • State Interest rates are always annual interest rates. • More frequent compounding

  27. Non-annual Compounding • Multiply number of years by frequency of compounding • Divide interest rate by frequency of compounding

  28. Periods less than One Year • Same variables as in all time value problems except N < 1. • Calculate by dividing the number of days by 365.

  29. Illustration for Return on Investment • What is the return on an investment that costs $98,543 and pays $100,000 after 45 days?

  30. Determination of Return • The unknown: I • The givens: • PV = -98,543 • N = 0.1233 (45/365) • FV = 100,000 • PMT = 0 The answer: 12.64%

  31. Interpretation • $98,543 invested for 45 days grows to $100,000 at 12.64 percent.

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