Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Time Value of Money Concepts 6 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That’s right! A dollar today is more valuable than a dollar to be received in one year. 6-3 Learning Objectives Explain the difference between simple and compound interest. 6-4 Simple Interest Interest amount = P × i × n Assume you invest $1,000 at 6% simple interest for 3 years. You would earn $180 interest. ($1,000 × .06 × 3 = $180) (or $60 each year for 3 years) 6-5 Compound Interest Compound interest includes interest not only on the initial investment but also on the accumulated interest in previous periods. Principal Interest 6-6 Assume we will save $1,000 for three years and earn 6% interest compounded annually. What is the balance in our account at the end of three years? Compound Interest 6-7 Compound Interest 6-8 Learning Objectives Compute the future value of a single amount. 6-9 Future Value of a Single Amount The future value of a single amount is the amount of money that a dollar will grow to at some point in the future. Assume we will save $1,000 for three years and earn 6% interest compounded annually. $1,000.00 × 1.06 = $1,060.00 and $1,060.00 × 1.06 = $1,123.60 and $1,123.60 × 1.06 = $1,191.02 6-10 Writing in a more efficient way, we can say . . . . $1,000 × 1.06 × 1.06 × 1.06 = $1,191.02 or $1,000 × [1.06] 3 = $1,191.02 Future Value of a Single Amount [...]... call these notes noninterest-bearing notes Even though the agreement states it is a noninterest-bearing note, the note does, in fact, include interest We impute an appropriate interest rate for a loan of this type to use as the interest rate  6-2 6 Expected Cash Flow Approach Statement of Financial Accounting Concepts No 7 “Using Cash Flow Information and Present Value in Accounting Measurements” The... asset or liability Expected Cash Flow × Risk-Free Rate of Interest Present Value 6-2 7 Learning Objectives Explain the difference between an ordinary annuity and an annuity due  6-2 8 Basic Annuities An annuity is a series of equal periodic payments  6-2 9 Ordinary Annuity An annuity with payments at the end of the period is known as an ordinary annuity End End 6-3 0 Annuity Due An annuity with payments at... = FV (1 + i) n 6-1 7 Present Value of a Single Amount Find the Present Value of $1 table in your textbook Hey, it looks familiar! 6-1 8 Present Value of a Single Amount Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at that time What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually? 6-1 9 Present Value... (n=2) for this value Accounting Applications of Present Value Techniques—Single Cash Amount Monetary assets and monetary liabilities are valued at the present value of future cash flows Monetary Assets Monetary Liabilities Money and claims to receive money, the amount which is fixed or determinable Obligations to pay amounts of cash, the amount of which is fixed or determinable 6-2 4 6-2 5 No Explicit Interest... 6-1 1 Future Value of a Single Amount $1,000 × [1.06]3 = $1,191.02 We can generalize this as FV = PV (1 + i) Future Future Value Value Present Present Value Value n Interest Interest Rate Rate Number Number of of Compounding Compounding Periods Periods 6-1 2 Future Value of a Single Amount Find the Future Value of $1 table in your textbook Find the factor for 6% and 3 periods  6-1 3 Future... FV $1 6-1 4 Learning Objectives Compute the present value of a single amount  6-1 5 Present Value of a Single Amount Instead of asking what is the future value of a current amount, we might want to know what amount we must invest today to accumulate a known future amount This is a present value question Present value of a single amount is today’s equivalent to a particular amount in the future  6-1 6 Present... known as an annuity due Beginning Beginning Beginning 6-3 1 Learning Objectives Compute the future value of both an ordinary annuity and an annuity due  6-3 2 Future Value of an Ordinary Annuity To find the future value of an ordinary annuity, multiply the amount of a single payment or receipt by the future value of an ordinary annuity factor  6-3 3 Future Value of an Ordinary Annuity We plan to invest... at the end of 10 years? 6-3 4 Future Value of an Annuity Due To find the future value of an annuity due, multiply the amount of a single payment or receipt by the future value of an ordinary annuity factor  6-3 5 Future Value of an Annuity Due Compute the future value of $10,000 invested at the beginning of each of the next four years with interest at 6% compounded annually  6-3 6 Learning Objectives Compute... the time value of money If you know any three of these, the fourth can be determined  6-2 2 Determining the Unknown Interest Rate Suppose a friend wants to borrow $1,000 today and promises to repay you $1,092 two years from now What is the annual interest rate you would be agreeing to? a 3.5% b 4.0% c 4.5% d 5.0% 6-2 3 Determining the Unknown Interest Rate Suppose a friend wants to borrow $1,000 today... 68058 = $13,611.60 If you deposit $13,611.60 now, at 8% annual interest, you will have $20,000 at the end of 5 years  6-2 0 Learning Objectives Solving for either the interest rate or the number of compounding periods when present value and future value of a single amount are known  6-2 1 Solving for Other Values FV = PV (1 + i)n Future Future Value Value Present Present Value Value Interest Interest . three years? Compound Interest 6-7 Compound Interest 6-8 Learning Objectives Compute the future value of a single amount. 6-9 Future Value of a Single. dollar to be received in one year. 6-3 Learning Objectives Explain the difference between simple and compound interest. 6-4 Simple Interest Interest amount