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Chapter 9

Chapter 9. The Time Value of Money. PPT 9-1. TABLE 9-1 Future value of $1 (FV IF ). PPT 9-2. FIGURE 9-1 Relationship of present value and future value. PPT 9-3. TABLE 9-2 Present value of $1 (PV IF ). FIGURE 9-2 Compounding process for annuity. PPT 9-4. PPT 9-5. TABLE 9-3

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Chapter 9

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  1. Chapter 9 The Time Valueof Money

  2. PPT 9-1 TABLE 9-1 Future value of $1 (FVIF)

  3. PPT 9-2 FIGURE 9-1 Relationship of present valueand future value

  4. PPT 9-3 TABLE 9-2 Present value of $1 (PVIF)

  5. FIGURE 9-2 Compounding process for annuity PPT 9-4

  6. PPT 9-5 TABLE 9-3 Future value of anannuity of $1 (FVIFA)

  7. PPT 9-7 TABLE 9-5 Relationship of presentvalue to annuity

  8. PPT 9-8 TABLE 9-6 Payoff table for loan(amortization table)

  9. Determining the Yield on an Investment PPT 9-9 Formula Table Appendix Future value – single amount (9-1) FV = PV x FVIF 9-1 A Present value – single amount (9-2) PV = FV x PVIF 9-2 B Future value – annuity (9-3) FVA = A x FVIFA 9-3 C Present value – annuity (9-4) PVA = A x PVIFA 9-4 D Annuity equaling a future value (9-5) A = 9-3 C Annuity equaling a present value (9-6) A = 9-4 D FVA FVIFA PVA PVIFA

  10. Finding Present Value (first part) PPT 9-10 A1 A2 A3 A4 A5 Present $1,000 $1,000 $1,000 $1,000 $1,000 value 0 1 2 3 4 5 6 7 8

  11. Finding Present Value (second part) PPT 9-10 End of third period—Beginning of fourth period A1 A2 A3 A4 A5 Present $1,000 $1,000 $1,000 $1,000 $1,000 value 0 1 2 3 4 5 6 7 8 Each number represents the end of the period; that is, 4 represents the end of the fourth period. $3,993

  12. Finding Present Value (final part) PPT 9-10 End of third period—Beginning of fourth period $3,170 $3,993 A1 A2 A3 A4 A5 Present (single amount) $1,000 $1,000 $1,000 $1,000 $1,000 value 0 1 2 3 4 5 6 7 8

  13. Chapter 9 - Outline LT 9-1 • Time Value of Money • Future Value and Present Value • Annuity • 2 Questions to Ask in Time Value of Money Problems • Adjusting for Non-Annual Compounding

  14. Time Value of Money LT 9-2 The basic idea behind the concept of time value of money is: – $1 received today is worth more than $1 in the future OR – $1 received in the future is worth less than $1 today Why? – because interest can be earned on the money The connecting piece or link between present (today) and future is the interest rate

  15. Future Value and Present Value LT 9-3 Future Value (FV) is what money today will be worth at some point in the future FV = PV x FVIF FVIF is the future value interest factor (Appendix A) Present Value (PV) is what money at some point in the future is worth today PV = FV x PVIF PVIF is the present value interest factor (Appendix B)

  16. Annuity LT 9-4 Annuity: – a stream or series of equal payments to be received in the future • The payments are assumed to be received at the end of each period • A good example of an annuity is a lottery, where the winner is paid over a number of years

  17. 2 Questions to Ask in Time Value of Money Problems LT 9-5 Future Value or Present Value? Future Value: Present (Now)  Future Present Value: Future  Present (Now) Single amount or Annuity? Single amount: one-time (or lump) sum Annuity: same amount per year for a number of years

  18. Adjusting for Non-AnnualCompounding LT 9-6 • Interest is often compounded quarterly, monthly, or semiannually in the real world • Since the time value of money tables assume annual compounding, an adjustment must be made: – the number of years is multiplied by the number of compounding periods – the annual interest rate is divided by the number of compounding periods

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