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**Unformatted text preview: **BADM 7090 Financial Management Unit I.B Basic Concepts: The Time Value of Money Text material: GSM, Ch. 3 D. Chance Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 2 of 43 Questions How do we calculate the future value of money invested today? How do we calculate the value today of money to be received in the future? How do these problems differ when there are multiple payments? Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 3 of 43 Present Value and Future Value Present value is the amount of money at one point in time that is equivalent in value, given a rate of interest, to an amount of money at a later point in time. Future value is the amount of money at a later point in time that is equivalent in value, given a rate of interest, to an amount of money at an earlier point in time. Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 4 of 43 The Interest Rate The rate that should be used to discount cash flows is a central focus of this course. At its most fundamental level, it must reflect the concept of an opportunity cost : The amount that you could earn by investing your money at the same risk. When we discuss discounting equity claims, we will not call this an interest rate. Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 5 of 43 Future Value Calculation Value of $1 today invested at rate r per period one period later: $1(1 ) This is called the compound factor. FV r = + 1 $1 $1(1 + r) Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 6 of 43 Future Value Calculation (cont.) Example Problem I.B(1) : What is the value of $100,000 compounded for one year at 6%? = $100,000(1.06) $106,000 Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 7 of 43 Future Value Calculation (cont.) The result extends to multiple periods, t . = + $1(1 ) t FV r 1 $1 2 t $1(1 + r)t Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 8 of 43 Future Value Calculation (cont.) Example Problem I.B(2) : What is the value of $100,000 compounded for two years at 6% per year? With multiple periods, interest compounds on itself. More on that later. = 2 $100,000(1.06) $112,360 Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 9 of 43 Present Value Calculation Value today of $1 to come in one period at the rate r- = = + + 1 $1 (1 ) (1 ) This is called the . PV r r discount factor 1 $1(1 + r)- 1 $1 Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 10 of 43 Present Value Calculation (cont.) Example Problem I.B(3) : What is the value today of $100,000 in one year at 6%? = $100,000 $94,340 (1.06) Version: 1/3/11 D. Chance BADM 7090 Unit IB p. 11 of 43 Present Value Calculation (cont.) The result extends to multiple periods, t ....

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