1. Copyright © 2009 Pearson Prentice Hall. All rights reserved. Chapter 4 Time Value of Money

2. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-2 Ch 4, Time Value of Money, Learning Goals 1.Concept of time value of money (TVOM). 2.Calculate for a single cash flow, ordinary annuity, annuity due, mixed cash flow & perpetuity: –PV –FV –Rate of return (or growth rate) –Number of periods 3. Calculate payment for an annuity. 4. Calculate effective annual rate.

3. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-3 The Role of Time Value in Finance Most financial decisions involve costs & benefits that are spread out over time. Time value of money allows comparison of cash flows from different periods.

4. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-4 Time Value of Money Example Would it be better for a company to invest $100,000 in a product that would return a total of $200,000 after one year, or one that would return $220,000 after two years?

5. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-5 Computational Aids Use Algebraic Equations Use the TVOM (interest factor) Tables Use Financial Calculators Use Electronic Spreadsheets

6. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-6 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 Pmt=an annuity (series of equal payments or receipts) m= # of times per year interest is compounded

7. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-7 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.

8. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-8 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.

9. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-9 Annuities Annuities are periodic cash flows of equal size. Annuities can be either inflows or outflows. An ordinary annuity has cash flows that occur at the ________________________________ of each period. An annuity due has cash flows that occur at the ________________________________ of each period.

10. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-10 Table 4.1 Comparison of Ordinary Annuity and Annuity Due Cash Flows ($1,000, 5 Years)

11. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-11 Present Value of a Perpetuity A perpetuity: a cash flow stream that continues forever PV = Pmt/i For example, how much would I have to deposit today in order to withdraw $1,000 each year forever if I earn 8% on my deposit? PV = $1,000/.08 = $12,500

12. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-12 Future Value of a Mixed Stream (cont.) Table 4.3 Future Value of a Mixed Stream of Cash Flows

13. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-13 Present Value of a Mixed Stream Table 4.4 Present Value of a Mixed Stream of Cash Flows

14. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-14 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.

15. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-15 Compounding Interest More Frequently Than Annually (cont.) Table 4.7 Future Value at the End of Years 1 and 2 from Investing $100 at 8% Interest, Given Various Compounding Periods

16. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 4-16 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