Time Value of Money Revisited: Part 1 Terminology. Learning Outcomes. Time Value of Money

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1 Time Value of Money Revisited: Part 1 Terminology Intermediate Accounting II Dr. Chula King 1 Learning Outcomes Definition of Time Value of Money Components of Time Value of Money How to Answer the Question Present Value versus Future Value Compounding Discounting Time Line 2 Time Value of Money Refers to the fact that $1 in hand today is worth more than $1 promised at some time in the future The reason for the differential is that $1 today can be invested to earn a return, called interest. 3 1

2 Consider the Following I invest $100 in a savings account that pays 10% interest compounded annually = Consider the Following I invest $100 in a savings account that pays 10% interest compounded annually x1.10 = x1.10 = x1.10 = Components of Time Value of Money Problem Every Time Value of Money problem involves the following four items, three of which must be given: Present and/or Future value amount(s) Single Sum Annuity equal periodic payments or deposits A discount or compound rate of interest Number of periods Given three of the items, what is the value of the fourth item? 6 2

3 How to Answer the Question Financial calculator Mathematical formula Excel/Numbers Time Value of Money Tables 1: Future value of $1 (Future value of a single sum) 2: Present value of $1 (Present value of a single sum) 3: Future value of an ordinary annuity of $1 4: Present value of an ordinary annuity of $1 5: Future value of an annuity due of $1 6: Present value of an annuity due of $1 7 Present and Future Amounts A present amount is just that. It is the amount of money that I have or need to have at the present time A future amount is the amount of money that I will have in the future A single sum A dollar amount at one specified time in the future An annuity Equal, periodic deposits or payments occurring in the future. 8 Present Value versus Future Value Present Value Future Value # Periods n Present Value interest Future Value 100 interest

4 Discount or Compound Rate The interest rate that causes the differential between present value and future value Unless otherwise noted, always given as an annualrate, e.g., 10% peryear. 10 Compounding The accumulation of interest on principal/interest over time from the present to the future 100 x1.10 = x1.10 = The number of times during the year that compounding takes place 10% compounded annually 10% once per year 10% compounded semi annually 5% every six months 10% compounded quarterly 2.5% every three months. 11 Discounting The opposite of compounding The removal of interest on principal/interest over time from the future to the present = = 100 The number of times during the year that discounting takes place 10% compounded annually 10% once per year 10% compounded semi annually 5% every six months 10% compounded quarterly 2.5% every three months. 12 4

5 Time Line A graphical representation showing the timing of cash flows n The present time is denoted by 0. Time 1 is one period from the present time, time 2 is two periods from the present time, etc. Periods can be a year, six months, etc. 10% compounded annually one period per year 10% compounded semi annually two periods per year 10% compounded quarterly four periods per year. 13 Single Sum Problems Generally classified into one of two categories Known Present Value Future Value Present Value Known Future Value 14 Annuity Problems Equal periodic payment or deposit The amount of the payment or deposit is the same each period The time between payments or deposits is the same Discount or compound rate is the same for all payments or deposits Ordinary annuity payments or deposits occur at the end of the period Annuity due payments or deposits occur at the beginning of the period 15 5

6 Annuity Problems Generally classified into one of two categories Known Deposits Future Value Present Value Known Payments 16 Concluding Comments Part 2 Future Value of $1 (Single Sum) Part 3 Present Value of $1 (Single Sum)* Part 4 Future Value of an Annuity of $1 Ordinary Annuity Annuity Due Part 5 Present Value of an Annuity of $1* Ordinary Annuity Annuity Due 17 6