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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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