Topic02_tvm[1]

Topic02_tvm[1] - Thomas Moeller FINA 30153: Financial...

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Thomas Moeller FINA 30153: Financial Management 1 Topic 2 Time value of money Objectives 1. Understand time value of money 2. Value series of payments 3. Understand net present value 4. Distinguish between nominal and effective interest rate 5. Using the financial calculator
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Thomas Moeller FINA 30153: Financial Management 2 Quotes of the Day All things are difficult before they are easy. - Thomas Fuller (1654-1734) If you would like to know the value of money, go and try to borrow some. - Benjamin Franklin
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Thomas Moeller FINA 30153: Financial Management 3 1. Time value of money Three assumptions about people’s preferences: For now: 1. People prefer more money to less money 2. People would rather have money sooner than later (impatience) For later: 3. People prefer certainty to uncertainty (risk aversion) We will also talk about everything in terms of cash flows (e.g., not profits). We’ll come back to this point a few lectures from now.
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Thomas Moeller FINA 30153: Financial Management 4 Time Lines Show Timing of Cash Flows Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2. 0 12 3 4 r % CF 0 CF 4 CF 3 CF 2 CF 1 Period
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Thomas Moeller FINA 30153: Financial Management 5 Two easy questions ¾ Projects A and B are expected to produce the same cash flows for the foreseeable future, but A costs less than B. Which one do you prefer? ¾ Projects C and D cost the same today, but D is expected to generate larger cash flows in every period in the future than C. Which one do you prefer? A more subtle problem ¾ Securities E and F are equally risky and cost the same. E promises $100 in two years, while F promises $108 in three years. Which one do you prefer? Approach: ‘move’ cash flows to the same point in time for comparison.
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Thomas Moeller FINA 30153: Financial Management 6 Notation FV = future value PV = present value r = interest rate per period n = number of periods A = nominal amount of each payment if multiple payments are being analyzed g = growth rate of payments CF t = cash flow at time t
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Thomas Moeller FINA 30153: Financial Management 7 Future Value: Single Cash Flow |----------|----------|----------|----------|----------| - Formula: FV PV(1 r) n = + - Problem: Suppose you put $100 into a savings account today that will pay 10% interest for three years. How much will you have at the end of three years if you earn simple interest? Compound interest?
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Thomas Moeller FINA 30153: Financial Management 8 Future Value: Single Cash Flow 1st way to think about it: 2nd way to think about it:
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Thomas Moeller FINA 30153: Financial Management 9 Future Values with Compounding 0 10 20 30 40 50 60 0 3 6 9 12 15 18 21 24 27 Number of Years FV of $1 0% 5% 10% 15% Interest Rates
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Thomas Moeller FINA 30153: Financial Management 10 Present Value: Single Cash Flow |----------|----------|----------|----------|----------| - Formula: PV FV (1 r) n = + - Problem: Suppose you can choose one of the following prizes: 1) $1,000 now 2) $1,500 at the end of 4 years If the interest rate is 10%, which is the more valuable prize?
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Topic02_tvm[1] - Thomas Moeller FINA 30153: Financial...

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