Copyright © 2003 Pearson Education, Inc. Slide 4-0 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.

Copyright © 2003 Pearson Education, Inc. Slide 4-1 The Role of Time Value in Finance Many financial decisions involve costs & benefits that occur over several years. Cash flows occurring now are worth ______________ than cash flows occurring in the future; we must adjust for that difference. Time value of money (TVOM) allows comparison of cash flows from different periods.

Copyright © 2003 Pearson Education, Inc. Slide 4-2 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?

Copyright © 2003 Pearson Education, Inc. Slide 4-3 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

Copyright © 2003 Pearson Education, Inc. Slide 4-4 Compound Interest With compound interest, a depositor earns interest on interest! Year 1: 5% of $100.00= $ $100.00= $ Year 2: 5% of $105.00= $ $105.00= $ Year 3: 5% of $ = $5.51+ $110.25= $ Year 4: 5% of $115.76= $ $115.76= $ Year 5: 5% of $121.55= $ $121.55= $127.63

Copyright © 2003 Pearson Education, Inc. Slide 4-5 Computational Aids Techniques to solve TVOM problems: –Algebraically –TVOM (interest factor) Tables –Financial Calculators –Spreadsheets –“Rule of 72”

Copyright © 2003 Pearson Education, Inc. Slide 4-6 Time Value Terms PV =present value or beginning amount i= interest rate FV =future value n=number of periods Pmt=periodic payment on an annuity m = # of times per year interest is compounded

Copyright © 2003 Pearson Education, Inc. Slide 4-7 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) - 1= Pmt x (FVIFA i,n ) i PVA 0 = Pmt 1 - [1/(1+i) n ] = Pmt x (PVIFA i,n ) i

Copyright © 2003 Pearson Education, Inc. Slide 4-8 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.

Copyright © 2003 Pearson Education, Inc. Slide 4-9 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.

Copyright © 2003 Pearson Education, Inc. Slide 4-10 Annuities Annuities are periodic cash flows of equal size. Annuities can be either inflows or outflows. An ordinary annuity has CFs that occur at the ____________ of each period. An annuity due has CFs that occur at the _____________________ of each period.

Copyright © 2003 Pearson Education, Inc. Slide 4-11 Annuities

Copyright © 2003 Pearson Education, Inc. Slide 4-12 Present Value of a Mixed Stream

Copyright © 2003 Pearson Education, Inc. Slide 4-13 Future Value of a Mixed Stream

Copyright © 2003 Pearson Education, Inc. Slide 4-14 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

Copyright © 2003 Pearson Education, Inc. Slide 4-15 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.

Copyright © 2003 Pearson Education, Inc. Slide 4-16 Compounding Interest More Frequently Than Annually (cont.)

Copyright © 2003 Pearson Education, Inc. Slide 4-17 Compounding Interest More Frequently Than Annually (cont.) A General Equation for Compounding More Frequently than Annually

Copyright © 2003 Pearson Education, Inc. Slide 4-18 EAR = (1 + i/m) m - 1 Nominal & Effective Annual Rates of Interest The nominal interest rate is the stated 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

Copyright © 2003 Pearson Education, Inc. Slide 4-19 Rule of 72 The “rule of 72” is a rule of thumb, or 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 n years, the rate of return is 72/n (i = 72/n)