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In depth: Time Value of Money

In depth: Time Value of Money. 17. Interest makes a dollar to be received tomorrow less valuable than a dollar received today. Learning Objectives Explain the effect of interest on payment streams Compute the future and present value of single amounts

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In depth: Time Value of Money

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  1. In depth: Time Value of Money 17 Interest makes a dollar to be received tomorrow less valuable than a dollar received today • Learning Objectives • Explain the effect of interest on payment streams • Compute the future and present value of single amounts • Compute the future and present value of annuities • Reference: Time value of money tables

  2. Objective 17.1: Explain the effect of interest on payment streams • A payment stream can be: • a single amount, • a series of payments • any combination of both O17.1

  3. Interest Compensation or rent paid to the owner of cash for its use by others over time O17.1

  4. Future value The value in the future of a payment stream with the effect of interest included and expressed as a single value O17.1

  5. Future value (FV) Computing future value assumes some rate of interest What will this dollar be worth one year from today? At 8% per year FV = $1 x 1.08 FV = $1.08 Interest Principal O17.1

  6. Future value (FV) Interest Principal Any amount times 1 + interest rate equals the FV after one time period EXAMPLES $500 x 1.08 = $540 or $12 x 1.08 = $12.96 or $15,560 x 1.08 = $16,805 O17.1

  7. Future value (FV) Repeat the process for each interest period What will this dollar be worth two years from today? FV = $1 x 1.08 x 1.08 = $1.17 O17.1

  8. Future Value Single Amount PresentValue Single Amount Interest rate is 8% per year Interest earned Principal Year 5 Year 4 Year 3 Year 2 Year 1 Year 0 X 1.08 X 1.08 X 1.08 X 1.08 X 1.08 O17.1

  9. Present value The value today of a payment stream with the effect of interest removed and expressed as a single value O17.1

  10. Rule #1 A dollar received today is always more valuable than a dollar received in the future andA dollar received in the future is always less valuable than a dollar received today O17.1

  11. Present value (PV) If this dollar is received in one year, what is it worth today? To compute PV DIVIDE by 1+ the interest rate At 8% per year PV = $1 / 1.08 PV = $.93 O17.1

  12. Present value (PV) Any amount DIVIDED by 1 + interest rate equals the PV for one time period EXAMPLES $500 / 1.08 = $463 or $12 / 1.08 = $11 or $15,560/ 1.08 = $14,407 O17.1

  13. Present value Present Value FutureValue 4 0 1 2 3 DISCOUNTING $ SINGLE AMOUNT Reducing payment streams to their present value is called discounting O17.1

  14. Rule #2 The more time periods, the higher the future value and the more time periods, the lower the present value EXAMPLE –Future Value Value after 1 year = $50 x 1.08 = $54 Value after 2 years = $50 x 1.08 x 1.08 = $58 O17.1

  15. Rule #2 The more time periods, the higher the future value and the more time periods, the lower the present value EXAMPLE –Present value Value today if received in 1 year = $50 / 1.08 = $46 Value today if received in 2 years = $50 / 1.08 /1.08 = $43 O17.1

  16. Rule #3 The value in the future is always higher if the interest rate is higher and the value today is always lower if the interest rate is higher EXAMPLE –Present value O17.1

  17. Present Value Future Value Interest rate is 8% per year Fifth Year Principal Discounted Principal Year 5 Year 4 Year 3 Year 2 Year 1 Year 0 ÷1.08 ÷1.08 ÷1.08 ÷1.08 ÷1.08

  18. Present Value Future Value Interest rate is 25% per year Fifth Year Principal Discounted Principal Year 5 Year 4 Year 3 Year 2 Year 1 Year 0 ÷1.25 Much smaller than at 8% ÷1.25 ÷1.25 ÷1.25 ÷1.25

  19. Compounding During a time period (year), the computation of interest and the addition to or subtraction from principle. O17.1

  20. Rule #4 The more compounding periods the higher the future value and The more compounding periods the lower the present value. O17.1

  21. Compounding EXAMPLE –Future value A $5,000 savings deposit pays 4% per year compounded every six months. 4%/2 = 2% per six months $5,000 x 1.02 x 1.02 = $5,202.00 A $5,000 savings deposit pays 4% per year compounded every quarter. 4%/4 = 1% per quarter $5,000 x 1.01 x 1.01 x 1.01 x 1.01 = $5,203.02 More compounding periods = higher future value O17.1

  22. Objective 17.2: Compute the present and future value of single amounts Financial calculators also can be used Time value of money tables provide a short cut to the computation of present and future values. O17.2

  23. Future value tables The future value of $1 table below gives the future value of $1 at various interest rates and time periods. At 3%, the value of $1 in 4 years is $1.1255 Payment Stream is a Single Amount O17.2

  24. Compute future value of single amount EXAMPLE A $10,000 savings deposit pays 6% per year ( no compounding) What will the value of the deposit be in 5 years? From the table at 6%, $1 would be worth $1.3382, therefore, $10,000 x 1.3382 = $13,382 O17.2

  25. Present value tables The present value of $1 table below gives the present value of $1 at various interest rates and time periods. At 2%, the value today of $1 received in 5 years is $.9057 Payment Stream is a Single Amount O17.2

  26. Compute present value of single amount At 5%, what would a promise to receive $10,000 in four years ( no compounding) be worth today? EXAMPLE From the table at 5%, $1 would be worth $.8227, therefore, $10,000 x .8227 = $8,227 O17.2

  27. Objective 17.3: Compute the present and future value of annuities An annuity is series of equal payments, paid or received, each time period. A common example of an annuity is an installment loan payment such as an auto loan with identical payments every month. O17.3

  28. Annuity vs Single amount O17.3

  29. Present Value (annuity) Future Value (annuity) Interest rate is 8% per year Annuity payment Discounted Principal Year 5 Year 4 Year 3 Year 2 Year 1 ÷1.08 Year 0 ÷1.08 ÷1.08 ÷1.08 ÷1.08 O17.3

  30. Future value tables At 5%, the value of a $1 annuity for 5 years is $5.5256 The future value of an annuity of $1 table below gives future values at various interest rates and time periods. Payment Stream is an annuity O17.3

  31. Compute future value of an annuity Tony will deposit $1,000 per year in a savings account that pays 4% annually. What will the value of the deposit be in 5 years? EXAMPLE From the table at 4%, a $1 annuity would be worth $5.4163 in 5 years, therefore, $1,000 x 5.4163 = $5,416.30 O17.3

  32. Present value tables At 4%, the value today of $1 annuity for 4 years is $3.6299 The present value of an annuity of $1 table below gives present values at various interest rates and time periods. Payment Stream is an annuity O17.3

  33. Compute present value of an annuity A wealthy friend agrees to offer a loan to you at 6% for 5 years. You can promise to repay $1,000 per year. How much can you borrow? EXAMPLE From the table at 6%, a $1 annuity would be worth $4.2124 today, therefore, $1,000 x 4.2124 = $4,212.40 O17.3

  34. Reference: Time value of money tables For quick reference, the following slides are time value of money tables 17.4

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  43. End Unit 17

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