Topic1_notes - Topic 1: The Time Value of Money Reading:...

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Fin357 – Spring 08 - Huang 1 Topic 1: The Time Value of Money Reading: RWJ 5 and 6
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Fin357 – Spring 08 - Huang 2 Outline Future values Present values Power of compounding Compounding frequency Net Present Values (NPV) Perpetuities and annuities Applications
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Fin357 – Spring 08 - Huang 3 Some Basic Assumptions Three assumptions about people’s preferences: For now: 3. People prefer more money to less money 4. People would rather have money sooner than later (impatience) For later: 7. People prefer certainty to uncertainty (risk aversion)
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Fin357 – Spring 08 - Huang 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. r (or r t ) is the discount rate [or interest rate, cost of capital, opportunity cost (of capital), required return, expected return]. 0 1 2 3 4 r % CF 0 CF 4 CF 3 CF 2 CF 1 Period
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Fin357 – Spring 08 - Huang 5 A few examples 0 1 2 3 4 8 % 80 Year 0 1 2 3 4 1 % 100 Month 0 1 2 3 4 r 1 80 Year 100 100 -60 80 -20 r 2 r 3
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Fin357 – Spring 08 - Huang 6 How to Compare Cash Flows? Two easy questions 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? Projects C and D cost the same today, but D is expected to generate larger cash flows in the future than C. Which one do you prefer? A more subtle problem Securities E and F are equally risky. E promises $100 in two years, while F promises $108 in three years. Which one do you prefer? Approach: “move” cash flows for different projects to the same point in time for comparison!
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Fin357 – Spring 08 - Huang 7 A Few Definitions Future Value - Amount to which an investment will grow after earning interest. Present Value Value in today’s dollars of future expected cash flows. Simple Interest - Interest earned only on the original investment. (rarely used!) Compound Interest - Interest earned on original investment plus previously earned interest. Note: Assume compound interest unless specifically instructed otherwise.
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Fin357 – Spring 08 - Huang 8 What’s the FV of $100 invested for 3 years earning 10% simple interest? 0 1 2 3 10 % Years
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Fin357 – Spring 08 - Huang 9 What’s the FV of $100 invested for 3 years earning 10% compound interest? 0 1 2 3 10 % Years
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Fin357 – Spring 08 - Huang 10 Calculating Future Value 1 st way to think about it: Time 1 - $100 + $100(0.10) or $100(1.10) = $110.00 2 - $110 + $110(0.10) or $110(1.10) = $121.00 3 - $121 + $121(0.10) or $121(1.10) = $133.10 2 nd way to think about it: Time 1 - $100(1.10) = $100(1.10) 1 = $110.00 2 - $100(1.10)(1.10) = $100(1.10) 2 = $121.00 3 - $100(1.10)(1.10)(1.10) = $100(1.10) 3 = $133.10 t t r PV FV ) 1 ( 0 + × =
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Fin357 – Spring 08 - Huang 11 0 10 20 30 40 50 60 70 0 3 6 9 1 2 5 8 4 7 Number of Years FV of $1 0% 5% 10% 15% Power of Compounding Interest Rates
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Topic1_notes - Topic 1: The Time Value of Money Reading:...

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