1. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-1 Ch 4, TVOM, Learning Goals Concept of time value of money (TVOM). Calculate for a single cash flow, ordinary annuity, annuity due, and mixed cash flow: – PV – FV – Rate of return (or growth rate) – Number of periods Calculate payment for an annuity. Calculate effective annual rate.

2. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-2 The Role of Time Value in Finance Most financial decisions involve costs & benefits that are spread out over time. Time value of money (TVOM) allows comparison of cash flows from different periods, because cash flows occurring now are worth __________________ than cash flows occurring in the future.

3. Time Value of Money Example: – Is it better to invest $100,000 in a product that returns a total of $200,000 after one year, or one that returns $220,000 after two years? Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-3

4. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-4 Computational Aids Algebraically Interest Factor Tables Financial Calculators Electronic Spreadsheets

5. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-5 Simple Interest With simple interest, you don’t earn interest on interest. Year 1: 5% of $100=$5 + $100 = $105 Year 2: 5% of $100=$5 + $105 = $110 Year 3: 5% of $100=$5 + $110 = $115 Year 4: 5% of $100=$5 + $115 = $120 Year 5: 5% of $100=$5 + $120 = $125

6. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-6 Compound Interest With compound interest, a depositor earns interest on interest! Year 1: 5% of $100.00= $5.00 + $100.00= $105.00 Year 2: 5% of $105.00= $5.25 + $105.00= $110.25 Year 3: 5% of $110.25 = $5.51+ $110.25= $115.76 Year 4: 5% of $115.76= $5.79 + $115.76= $121.55 Year 5: 5% of $121.55= $6.08 + $121.55= $127.63

7. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-7 Time Value Terms PV 0 =present value or beginning amount i= interest rate FV n =future value at end of “n” periods n=number of compounding periods A=an annuity (series of equal payments or receipts)

8. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-8 Four Basic Models FV n = PV 0 (1+i) n = PV x (FVIF i,n ) PV 0 = FV n [1/(1+i) n ] = FV x (PVIF i,n ) FVA n = Pmt (1+i) n - 1= Pmt x (FVIFA i,n ) i PVA 0 = Pmt 1 - [1/(1+i) n ] =Pmtx (PVIFA i,n ) i

9. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-9 Future Value of a Single Amount The future value technique uses compounding to find the future value of each cash flow at the end of an investment’s life and then sums these values to find the investment’s future value. We speak of compound interest to indicate that the amount of interest earned on a given deposit has become part of the principal at the end of the period.

10. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-10 Present Value of a Single Amount Present value is the current dollar value of a future amount of money. It is the amount today that must be invested at a given rate to reach a future amount. Calculating present value is also known as ___________________________. The discount rate is often also referred to as the opportunity cost, the discount rate, the required return, or the cost of capital.

11. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-11 Annuities Annuities are periodic cash flows of equal size. Annuities can be either inflows or outflows. An ordinary (deferred) annuity has cash flows that occur at the ______________ of each period. An annuity due has cash flows that occur at the __________________________ of each period.

12. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-12 Annuities

13. Present Value of a Perpetuity Perpetuity: cash flow stream that lasts forever. PV = Pmt / I Example: how much would I need to deposit to withdraw $1,000 each year forever I my account earns 8%? PV = $1,000 / 08 = $12,500 Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-13

14. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-14 Future Value of a Mixed Stream (cont.)

15. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-15 Present Value of a Mixed Stream

16. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-16 Compounding Interest More Frequently Than Annually Compounding more frequently than once a year results in a _____________________ effective interest rate because you are earning on interest on interest more frequently. As a result, the effective interest rate is greater than the nominal (annual) interest rate.

17. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-17 Compounding Interest More Frequently Than Annually (cont.)

18. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-18 Compounding Interest More Frequently Than Annually (cont.) A General Equation for Compounding More Frequently than Annually

19. Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-19 EAR = (1 + i/m) m - 1 Nominal & Effective Annual Rates of Interest The nominal interest rate is the stated or contractual rate of interest charged by a lender or promised by a borrower. The effective interest rate is the rate actually paid or earned. In general, the effective rate > nominal rate whenever compounding occurs more than once per year

20. Rule of 72 The “rule of 72” is an approximation technique that can be used for some simple TVOM problems: – An amount invested at rate i will double in 72/i years (n = 72 / i) – If an investment doubles in value in n years, the rate of return is 72 / n (i = 72 / n) Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 4-20