Time Value of Money Concepts Professor: Farima Fakoor, MBA Course: Acctg 100A

Simple Interest:

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 )

Compound Interest:

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?

Compound Interest:

Compound Interest

Future Value of a Single Amount:

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. $1,000.00 × 1.06 = $1,060.00 and $1,060.00 × 1.06 = $1,123.60 and $1,123.60 × 1.06 = $1,191.02

Future Value of a Single Amount:

Future Value of a Single Amount Writing in a more efficient way, we can say . . . . $1,191.02 = $1,000 × [1.06] 3 FV = PV × (1 + i ) n Future Value Amount Invested at the Beginning of the Period Interest Rate Number of Compounding Periods

Future Value of a Single Amount:

Using the Future Value of $1 Table, we find the factor for 6% and 3 periods is 1.19102. So, we can solve our problem like this. . . FV = $1,000 × 1.19102 FV = $1,191.02 Future Value of a Single Amount

Present Value of a Single Amount:

Present Value of a Single Amount One common scenario: 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.

Present Value of a Single Amount:

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 =

Present Value of a Single Amount:

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?

Present Value of a Single Amount:

Present Value of a Single Amount If you deposit $13,611.60 now, at 8% annual interest, you will have $20,000 at the end of 5 years. i = .08, n = 5 Present Value Factor = .68058 $20,000 × .68058 = $13,611.60 Present Value of $1 Table

Solving for Other Values:

FV = PV × (1 + i ) n Future Value Present Value Interest Rate 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

Determining the Unknown Interest Rate:

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 = .91575 Search the PV of $1 table in row 2 (n=2) for this value.

Accounting Applications of Present Value Techniques—Single Cash Amount:

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

Expected Cash Flow Approach:

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 The present value factor is obtained using the company’s credit-adjusted risk-free rate of interest.

Questions?:

Questions? 16

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