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Understanding the Time Value of Money: Future and Present Value Concepts

This chapter covers the essential principles of the Time Value of Money (TVM), focusing on the distinction between future value (FV) and present value (PV). It illustrates the calculation of future and present values using various formulas, including FVIF and PVIF. Key concepts of annuities, compounding processes, and amortization are discussed to highlight how money's value changes over time due to interest rates. Real-world applications, such as determining the yield on investments and the significance of cash flow timing, are examined in detail.

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Understanding the Time Value of Money: Future and Present Value Concepts

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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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