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PowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPA Time Value of Money Concepts 6 Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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6 - 2 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)

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6 - 3 Compound Interest Assume we deposit $1,000 in a bank that earns 6% interest compounded annually. What is the balance in our account at the end of three years?

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6 - 4 Compound Interest

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6 - 5 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 deposit $1,000 for three years that earns 6% interest compounded annually. $1, × 1.06 = $1, and $1, × 1.06 = $1, and $1, × 1.06 = $1,191.02

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6 - 6 Future Value of a Single Amount Writing in a more efficient way, we can say.... $1, = $1,000 × [1.06] 3 FV = PV (1 + i ) n Future Value Future Value Amount Invested at the Beginning of the Period Interest Rate Interest Rate Number of Compounding Periods Number of Compounding Periods

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6 - 7 Using the Future Value of $1 Table, we find the factor for 6% and 3 periods is So, we can solve our problem like this... FV = $1,000 × FV = $1, Future Value of a Single Amount

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6 - 8 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.

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6 - 9 Present Value of a Single Amount Remember our equation? FV = PV (1 + i) n We can solve for PV and get.... FV (1 + i ) n PV =

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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. today What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually?

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Present Value of a Single Amount i =.08, n = 5 Present Value Factor = $20,000 × = $13, If you deposit $13, now, at 8% annual interest, you will have $20,000 at the end of 5 years. Present Value of $1 Table

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FV = PV (1 + i ) n Future Value Future Value Present Value Present Value Interest Rate Interest Rate Number of Compounding Periods Number of Compounding Periods There are four variables needed when determining the time value of money. If you know any three of these, the fourth can be determined. Solving for Other Values

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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% Present Value of $1 Table $1,000 = $1,092 × ? $1,000 ÷ $1,092 = Search the PV of $1 table in row 2 (n=2) for this value.

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Some notes do not include a stated interest rate. We 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 noninterest-bearing notes. Accounting Applications of Present Value Techniques—Single Cash Amount

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Statement of Financial Accounting Concepts No. 7 “Using Cash Flow Information and Present Value in Accounting Measurements” The objective of valuing an asset or liability using present value is to approximate the fair value of that asset or liability. Expected Cash Flow Approach

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Basic Annuities An annuity is a series of equal periodic payments. Period 1Period 2Period 3Period 4 $10,000

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An annuity with payments at the end of the period is known as an ordinary annuity. Ordinary Annuity End of year 1 $10, Today End of year 2 End of year 3 End of year 4

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Annuity Due An annuity with payments at the beginning of the period is known as an annuity due. Beginning of year 1 $10, Today Beginning of year 2 Beginning of year 3 Beginning of year 4

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Future Value of an Ordinary Annuity To find the future value of an ordinary annuity, multiply the amount of the annuity by the future value of an ordinary annuity factor.

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Future Value of an Ordinary Annuity We plan to invest $2,500 at the end of each of the next 10 years. We can earn 8%, compounded interest annually, on all invested funds. What will be the fund balance at the end of 10 years?

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Future Value of an Annuity Due To find the future value of an annuity due, multiply the amount of the annuity by the future value of an annuity due factor.

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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.

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Present Value of an Ordinary Annuity You wish to withdraw $10,000 at the end of each of the next 4 years from a bank account that pays 10% interest compounded annually. How much do you need to invest today to meet this goal?

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PV1 PV2 PV3 PV4 $10, Today Present Value of an Ordinary Annuity

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Present Value of an Ordinary Annuity If you invest $31, today you will be able to withdraw $10,000 at the end of each of the next four years.

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Present Value of an Ordinary Annuity Can you find this value in the Present Value of Ordinary Annuity of $1 table? More Efficient Computation $10,000 × = $31,698.60

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Present Value of an Annuity Due Compute the present value of $10,000 received at the beginning of each of the next four years with interest at 6% compounded annually.

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Accounting Applications of Present Value Techniques—Annuities Because financial instruments typically specify equal periodic payments, these applications quite often involve annuity situations. Long-term Bonds Long-term Leases Pension Obligations

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