02_Time_Value_of_Money-Day_3-2011.01.31v2

# 02_Time_Value_of_Money-Day_3-2011.01.31v2 - Time Value of...

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Time Value of Money Day 3: Multiple Cash Flows Thomas Hogan FNAN 301 February 3, 2011

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Agenda Timelines Present value of multiple cash flows Perpetuities What is a perpetuity? Fixed perpetuities Growing perpetuities
Timelines Graphic to illustrate the time value of money Timeline basics: Positive cash flows are drawn up, negative cash flows down Time 0 is the reference point, often today Time t is in t periods after the reference point Period 1 is between time 0 and time 1 and ends at time 1 Period t is between time t-1 and time t and ends at time t C 0 is the cash flow at time 0 C t is the cash flow at time t Example of C 0 today, C 3 in year 3 = \$100

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Notes on Timelines Timelines help us understand the timing and pattern of cash flows. They are a good first step to solving a problem. Cash flow (CF) is negative when money is paid out and positive when money comes in. Periods are assumed to be years unless told otherwise. A cash flow that takes place "in period t" should be assumed to take place at the end of period t. The payment is said to occur "at time t" or "in t periods" from the time of investment.
Ex. 1: Timeline (solving for PV) Jenny got a loan from the bank. She must repay \$15,000 in 10 years. The interest rate on the loan is 9%. How much did Jenny borrow? FV = PV×(1+r) t PV = FV / (1+r) t PV = 15,000 / (1+0.09) 10 = \$6,336.16

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Ex. 2: Timeline (solving for r) Peter put \$500 in the bank 5 years ago. Now he has \$900. What interest rate did he earn? FV = PV×(1+r) t r = (FV / PV) 1/t - 1 → r = (900 / 500) 1/5 -1 = 0.1247 = 12.47%
Unusual Time Periods Often we must analyze investments which begin at times other than today (past or future). We can value these by adjusting the compound interest formula where k = time period at the beginning of the investment and t = time period at the end of the investment. FV t = PV k ×(1+r) t-k Remember that "present value" is the value at the beginning of the investment period, which may not be today. The "future value" is the value at the end of the investment, which may not be in the future.

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Ex. 2: FV of a Future CF Nick's parents promised him \$5,000 when he graduates in 2 years. He plans to invest the money in a bond paying 12%. How much money will he have 5 years from now? Draw a timeline: or Note: t - k = the amount of time money is invested. Solve for FV t = PV k ×(1+r) t-k → FV 5 = PV 2 ×(1+r) 5-2 = 5,000×(1+0.12) 3 = \$7,024.64
Ex. 3: Int. Rate on Past CFs 8 years ago, Jennifer invested \$12,000 in a savings account. She had \$16,000 when she took it out last year. What was the interest rate on her account? Draw a timeline:

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02_Time_Value_of_Money-Day_3-2011.01.31v2 - Time Value of...

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