While at a local convenience store, you bought a lottery ticket and won $1,000. The ticket gives you the option of receiving (a) $1,000 today or (b) $1,000 one year from now. Time Value of Money Which do you choose? Convenience Store C- 2

Time Value of Money:

Time Value of Money $1,000 today Choose … Put it in a savings account Earn interest on it for one year Have an amount greater than $1,000 a year from now $1,000 today $1,000 a year from now C- C- 3

Time Value of Money:

Time Value of Money Essential in solving many business decisions such as: Valuing assets and liabilities Making investment decisions Paying off debts Establishing a retirement plan Implies that interest causes the value of money received today to be greater than the value of that same amount of money received in the future. C- 4

LO1 Simple Versus Compound Interest:

LO1 Simple Versus Compound Interest Interest Cost of borrowing money gives money its time value If you borrow $1,000 today and pay back $1,100 a year from now INTEREST 10% Value will be higher C- 5

Simple Interest:

Simple Interest Interest you earn on the initial investment only Simple Interest = Interest rate X Initial Investment X Time Time Simple Interest (= Initial Investment × Interest Rate) Outstanding Balance Initial investment $1,000 End of year 1 $1,000 × 10% = $100 $1,100 End of year 2 $1,000 × 10% = $100 $1,200 End of year 3 $1,000 × 10% = $100 $1,300 C- 6

Compound Interest:

Compound Interest Time Compound Interest (= Outstanding Balance × Interest Rate) Outstanding Balance Initial investment $1,000 End of year 1 $1,000 × 10% = $100 $1,100 End of year 2 $1,100 × 10% = $110 $1,210 End of year 3 $1,210 × 10% = $121 $1,331 Interest you earn on the initial investment and on previous interest. Yields increasingly larger amounts of interest earnings for each period of the investment. C- 7

LO2 Time Value of a Single Amount:

LO2 Time Value of a Single Amount Future Value Future value is how much an amount today will grow to be in the future. C- 8

Time Value of a Single Amount:

Time Value of a Single Amount FV = PV (1+ i ) n where: FV = future value of the invested amount PV= initial investment (or PV = present value) i = interest rate n = number of compounding periods Calculate using formula Future Value C- 9

Time Value of a Single Amount:

Time Value of a Single Amount Calculate using table Future Value C- 10

Time Value of a Single Amount:

Time Value of a Single Amount Calculate using calculator Future Value C- 11

Time Value of a Single Amount:

Time Value of a Single Amount Calculate using Excel Future Value C- 12

Interest Compounding More Than Annually:

Interest Compounding More Than Annually Suppose the three-year, $1,000 investment earns 10% compounded semi-annually , or twice per year. Number of Periods = 3 years times 2 = 6 periods Interest Rate per period = 10% annual rate by 2 = 5% FV = I × FV factor FV = $1,000 × 1.34010 = $1,340 Future value of $1; n = 6, i = 5% Semi-annual interest C- 13

Time Value of a Single Amount:

Time Value of a Single Amount Present Value The value today of receiving some larger amount in the future. C- 14

Time Value of a Single Amount:

Time Value of a Single Amount FV (1+ i ) n where: PV = present value FV = future value of the invested amount i = interest rate n = number of compounding periods Calculate using formula PV = Present Value C- 15

Time Value of a Single Amount:

Time Value of a Single Amount Calculate using table PV = FV × PV factor PV = $1,331 × 0.75131 = $1,000* *Rounded to nearest whole dollar Present Value C- 16

Time Value of a Single Amount:

Time Value of a Single Amount Calculate using calculator Present Value C- 17

Time Value of a Single Amount:

Time Value of a Single Amount Calculate using Excel Present Value C- 18

LO3 Time Value of an Annuity:

LO3 Time Value of an Annuity Many business transactions are structured as a series of receipts and payments of cash rather than a single amount. If we are to receive or pay the same amount each ( equal ) period, we refer to the cash flows as an annuity . Payments need not be monthly. They could be quarterly, semi-annually, annually, or any ( equal ) interval. Familiar examples of annuities are monthly payments for a car loan, house loan, or apartment rent. ___ ______ ____ ______ C- 19

Time Value of an Annuity:

Time Value of an Annuity Future Value C- 20

Time Value of an Annuity:

Time Value of an Annuity Calculate using table FVA = $1,000 × 3.3100 = $3,310 Future Value C- 21

Time Value of an Annuity:

Time Value of an Annuity Calculate using calculator Future Value C- 22

Time Value of an Annuity:

Time Value of an Annuity Calculate using Excel Future Value C- 23

Time Value of an Annuity:

Time Value of an Annuity Present Value C- 24

Time Value of an Annuity:

Time Value of an Annuity Present Value Calculate using table PVA = $1,000 × 2.48685 = $2,487 C- 25

Time Value of an Annuity:

Time Value of an Annuity Calculate using calculator Present Value C- 26

Time Value of an Annuity:

Time Value of an Annuity Present Value Calculate using Excel C- 27

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The Powerful Formulae (for Table use):

32 The Powerful Formulae (for Table use) FV = Future Value PV = Present Value FVIF = Future Value Interest Factor PVIF = Present Value Interest Factor PMT = Payment or Receipt FVIFA = Future Value Interest Factor for an Annuity PVIFA = Present Value Interest Factor for an Annuity 1) FV = PV x FVIF (from Future Value of $1 table ) Terminology/Abbreviations: 2) PV = FV x PVIF (from Present Value of $1 table) 3) FV annuity = PMT x FVIFA (from Future Value of Annuity table) 4) PV annuity = PMT x PVIFA (from Present Value of Annuity table) FORMULAE for Use of Tables

Using Financial Calculators:

Using Financial Calculators Illustration C-22 Financial calculator keys N = number of periods I = interest rate per period PV = present value PMT = payment FV = future value Section Three

Using Financial Calculators:

Using Financial Calculators Illustration C-23 Calculator solution for present value of a single sum Present Value of a Single Sum Assume that you want to know the present value of $84,253 to be received in five years, discounted at 11% compounded annually.

Using Financial Calculators:

Using Financial Calculators Illustration C-24 Calculator solution for present value of an annuity Present Value of an Annuity Assume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12%.

Using Financial Calculators:

Using Financial Calculators Illustration C-25 Useful Applications – Auto Loan A 3-year car loan has a 9.5% nominal annual interest rate, compounded monthly. The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase.

Using Financial Calculators:

Using Financial Calculators Useful Applications – Mortgage Loan You decide that the maximum mortgage payment you can afford is $700 per month. The annual interest rate is 8.4%. If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum purchase price you can afford? Illustration C-26

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