2Learning Goals1. Understand the concept of future value, their calculation for a single amount, and the relationship of present to future cash flow.Find the future value and present value of both an ordinary annuity and an annuity due, and the present value of a perpetuity.
3Learning Goals4. Calculate the present value of a mixed stream of cash flows.*5. Understand the effect that compounding more frequently than annually has on future value and the effective annual interest rate.
4The 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.Question?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?
5The 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.Answer!It depends on the interest rate!
6Basic Concepts Future Value: compounding or growth over time Present Value: discounting to today’s valueSingle cash flows & series of cash flows can be consideredTime lines are used to illustrate these relationships
7Computational Aids Use the Equations Use the Financial Tables Use Financial CalculatorsUse Spreadsheets
10Basic Patterns of Cash Flow The cash inflows and outflows of a firm can be described by its general pattern.The three basic patterns include a single amount, an annuity, or a mixed stream:
11With simple interest, you don’t earn interest on interest. Year 1: 5% of $100 = $5 + $100 = $105Year 2: 5% of $100 = $5 + $105 = $110Year 3: 5% of $100 = $5 + $110 = $115Year 4: 5% of $100 = $5 + $115 = $120Year 5: 5% of $100 = $5 + $120 = $125
12With compound interest, a depositor earns interest on interest! Year 1: 5% of $ = $ $ = $105.00Year 2: 5% of $ = $ $ = $110.25Year 3: 5% of $ = $ $ = $115.76Year 4: 5% of $ = $ $ = $121.55Year 5: 5% of $ = $ $ = $127.63
13Time Value Terms PV0 = present value or beginning amount k = interest rateFVn = future value at end of “n” periodsn = number of compounding periodsA = an annuity (series of equal payments or receipts)
15Algebraically and Using FVIF Tables Future Value ExampleAlgebraically and Using FVIF TablesYou deposit $2,000 today at 6% interest. How much will you have in 5 years?$2,000 x (1.06)5 =$2,000 x = $2,676.40
16Nominal & Effective Rates 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 yearEAR = (1 + k/m) m -1
17Nominal & Effective Rates For example, what is the effective rate of interest on your credit card if the nominal rate is 18% per year, compounded monthly?EAR = ( /12) 12 -1EAR = %
18Present ValuePresent value is the current dollar value of a future amount of money.It is based on the idea that a dollar today is worth more than a dollar tomorrow.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 discounting.The discount rate is often also referred to as the opportunity cost, the discount rate, the required return, and the cost of capital.
19Algebraically and Using PVIF Tables Present Value ExampleAlgebraically and Using PVIF TablesHow much must you deposit today in order to have $2,000 in 5 years if you can earn 6% interest on your deposit?$2,000 x [1/(1.06)5] = $2,000 x = $1,494.52
20Present Value of a Perpetuity A perpetuity is a special kind of annuity.With a perpetuity, the periodic annuity or cash flow stream continues forever.PV = Annuity/kFor example, how much would I have to deposit today in order to withdraw $1,000 each year forever if I can earn 8% on my deposit?PV = $1,000/.08 = $12,500
21Future Value of an Ordinary Annuity Using the FVIFA TablesAnnuity = Equal Annual Series of Cash FlowsExample: How much will your deposits grow to if you deposit $100 at the end of each year at 5% interest for three years.FVA = 100(FVIFA,5%,3) = $315.25Year 1 $100 deposited at end of year = $100.00Year 2 $100 x .05 = $ $100 + $100 = $205.00Year 3 $205 x .05 = $ $205 + $100 = $315.25
22Future Value of an Ordinary Annuity Using Calculator/ExcelAnnuity = Equal Annual Series of Cash FlowsExample: How much will your deposits grow to if you deposit $100 at the end of each year at 5% interest for three years.Excel Function=FV (interest, periods, pmt, PV)=FV (.06, 5,100, )
23Present Value of an Ordinary Annuity Using PVIFA TablesAnnuity = Equal Annual Series of Cash FlowsExample: How much could you borrow if you could afford annual payments of $2,000 (which includes both principal and interest) at the end of each year for three years at 10% interest?PVA = 2,000(PVIFA,10%,3) = $4,973.70
24Present Value of an Ordinary Annuity Using ExcelAnnuity = Equal Annual Series of Cash FlowsExample: How much could you borrow if you could afford annual payments of $2,000 (which includes both principal and interest) at the end of each year for three years at 10% interest?Excel Function=PV (interest, periods, pmt, FV)=PV (.10, 3, 2000, )
25Present Value of a Mixed Stream Using TablesA mixed stream of cash flows reflects no particular patternFind the present value of the following mixed stream assuming a required return of 9%.