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Mastering Time Value of Money for Financial Success

Understand the mechanics of compounding and discounting, relationships between time and interest rates, and solve calculations using PV, FV, PMT for lump sums and annuities. Learn to read formulas, improve financial decisions, and use financial calculator keys effectively. Dive into examples for compound interest, future value, present value, and annuity calculations.

emmanuel-garrett
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Mastering Time Value of Money for Financial Success

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  1. Chapter 5 – Important Stuff • Mechanics of compounding / discounting • PV, FV, PMT – lump sums and annuities • Relationships – time, interest rates, etc • Calculations: PV’s, FV’s, loan payments, interest rates

  2. Time Value of Money (TVM) • Time Value of Money – relationship between value at two points in time • Today versus tomorrow; today versus yesterday • Because an invested dollar can earn interest, its future value is greater than today’s value • Problem types: monthly loan payments, growth of savings account; time to goal

  3. Financial Calculator Keys • PV - Present value • FV - Future value • PMT - Amount of the payment • N - Number of periods (years?) • I/Y - Interest rate per period

  4. TI Calculator ManualStrongly Suggested Readings • Getting Started – page 6 and 7 • Overview – page 1-4, 1-10 and 1-20 • Worksheets – pages 2-14 and 2-15 • TVM – 3-1 to 3-9 • Cash Flow - All

  5. Calculator Tips Decimals and Compounding Periods • 2nd (gray), Format (bottom row), 4, enter, CE/C (lower left) - hit twice • Compounding: 2nd , I/Y, 1, enter, CE/C – extremely important !! • Right arrow key fixes “misteaks” • One cash flow must be negative or error

  6. Compound Interest @ 6% YearBeginInterestFV 1 $100.00 $6.00 $106.00 2 106.00 6.36 112.36 3 112.36 6.74 119.10

  7. Future Value (FV) Algebraically FVn = PV (1 + i)n Underlies all TVM calculations Keystrokes: 100 +/- PV; 3 N; 0 PMT; 6 I/Y; CPT FV = 119.10 One cash flow must be negative Error 5 means you forgot a negative sign

  8. Future Value Interest Factor Year@2%@6%@10% • 1.020 1.060 1.100 • 1.040 1.124 1.210 3 1.104 1.191 1.611 10 1.219 1.791 2.594

  9. Reading the Formulas and TablesFVn = PV* (1 + i)n • Plain English = The future value in period n is the present value (PV) times the quantity (i plus the interest rate) raised to the nth power where n equals the number of compounding periods. • Future value of $500 invested 3 yrs @ 6% • From table: FV6%, 3 yr. = 500 *1.191 = 595.50

  10. Future Value of $100

  11. FV Can Be Increased By 1. Increasing the length of time it is compounded 2. Compounding at a higher rate And/or 3. Compounding more frequently

  12. FV – Other Keystrokes • How long for an investment to grow from $15,444 to $20,000 if earn 9% when compounded annually? Must solve for N. 15444 +/- PV; 20000 FV; 0 PMT; I/Y 9; CPT N = 3 years • What rate earned if start at $15,444 and reach $20,000 in 3 years? Solve for I/Y. 15444 +/- PV; 20000 FV; 0 PMT; 3 N; CPT I/Y = 9%

  13. Time to Double Your Money“Rule of 72” • Enter 100 PV; 200 FV, 10 I/Y, solve for N or • Use Rule of 72 – says number of years to double is approximately equal to 72 divided by the interest rate. • Doubling time ≈ 72 Interest Rate

  14. Present Value (PV) If I earn 10%, how much must I deposit today to have $100 in three years? $75.10 This is “inverse compounding” Discount rate – interest rate used to bring (discount) future money back to present For lump sums (only) PV and FV are reciprocals

  15. Present Value Formula [ 1 ] PV = FVn[ (1 + i) n ] PVIF and FVIF for lump sums only are reciprocals. For 5% over ten years FVIF = 1.629 = 1 / .614 PVIF = .614 = 1 / 1.629

  16. Present Value Interest Factor @2%@5%@10% Year 1 .980 .952 .909 Year 2 .961 .907 .826 Year 3 .942 .864 .751 Year 10 .820 .614 .386

  17. Present Value of $100

  18. Keystrokes$100 @5% for ten years • For PV +/-100 FV; 0 PMT; 5 I/Y; 10 N; CPT PV = 61.39 • For I/Y 100 FV; 0 PMT; +/-61.39 PV; 10 N; CPT I/Y = 5 • For N 100 FV; +/-61.39 PV; 0 PMT; 5 I/Y; CPT N = 10 years

  19. PV Decreases If • Number of compounding periods (time) increases, • The discount rate increases, And/or 3. Compounding frequency increases

  20. Annuities • Series of equal dollar payments • Usually at the end of the year/period • If I deposit $100 in the bank each year starting a year from now, how much will I have at the end of three years if I earn 6%? $318.36 • We are solving for the FV of the series by summing FV of each payment.

  21. FV of $100 Annuity @ 6% End of PMTFVIF $ Year 3 $100 1.0000 * $100.00 Year 2 100 1.0600 106.00 Year 1 100 1.1236 112.36 $318.36 * The payment at end Year 3 earns nothing

  22. Annuity Keystrokes What will I have if deposit $100 per year starting at the end of the year for three years and earn 6%? 0 PV; 100+/- PMT; 3 N; 6 I/Y; CPT FV = 318.36 PV is zero - nothing in the bank today

  23. Present Value of an Annuity Amount we must put in bank today to withdraw $500 at end of next three years, earn 6% and have nothing left at the end? Present valuing each of three payments Keystrokes: 500+/- PMT; 0 FV; 3 N; 6 I/Y; CPT PV = 1,336.51

  24. PV of 5 Year $500 Annuity

  25. Nonannual Compounding • Invest for ten years at 12% compounded quarterly. What are we really doing? • Investing for 40 periods (10 * 4) at 3% (12%/4) • Make sure 2nd I/Y is set to 1. • Need to adjust rate per period downward which is offset by increase in N

  26. Nonannual Compounding • FVn = PV ( 1 + i/m) m * n • m = number of compounding periods per year so per period rate is i/m • And m * n is the number of years times the compounding frequency which adjusts to the rate per period

  27. Compounding $100 @10% CompoundingOne Year10 Years Annually $110.00 $259.37 Semiannually 110.25 265.33 Quarterly 110.38 268.51 Monthly 110.47 270.70

  28. Amortizing Loans • Paid off in equal installments • Makes it an annuity • Payment pays interest first, remainder goes to principal (which declines) • $600 loan at 15% over four years with equal annual payments of $210.16

  29. $600 Loan Amortization TotalTo IntTo PrinEnd Bal Year 1 210.16 90.00 120.16 479.84 Year 2 210.16 71.98 138.18 341.66 Year 3 210.16 51.25 158.91 182.75 Year 4 210.16 27.41 182.75 0

  30. Calculate a Loan Payment • $8,000 car loan payable monthly over three years at 12%. What is your payment? How many monthly periods in 3 yrs? 36 N Monthly rate? 12%/12 = 1%/mo = I/Y What is FV? Zero because loan paid out 8000+/- PV; 0 FV; 1.0 I/Y; 36 N; CPT PMT=265.71

  31. Perpetuities • Equal payments that continue forever • Like Energizer Bunny and preferred stock • Present Value = Payment Amount Interest Rate Preferred stock pays $8/yr, int rate- 10% Payment fixed at $8/ .10 = $80 market price

  32. NPV & IRR Uneven Cash Flows • Occur frequently in business problems • All we are doing is present valuing each cash flow, positive or negative • Need to switch to CF mode in calculator • Keystrokes in handout and on web page • Question on final but not FinCoach • Be sure to read 4-12 to 4-14 in manual and/or Table X in Appendix A of text

  33. Cash Flow Time Line Understanding time – big problem Remember number line from algebra Visualize in picture form when each cash flow occurs by time period, amount and sign. Time 0____1____2____3____4____5___→ Flows +200 +300 +50 → -100 0 0

  34. Present Value Irregular Flow

  35. Keystrokes You Should Know • Future value of a single payment • Present value for the same • Future value of an annuity • Annuity’s present value • Loans including monthly payments, effective rates and time to repay • Present value of a perpetuity

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