Time value of money

Time value of money - EC150: Financial Economics Slide Set...

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EC150: Financial Economics EC150: Financial Economics Slide Set 2: Time Value of Money Based on RWJ Chapter 4
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Money has “time value” Money has “time value” Why? Because interest rates (and expected returns) are positive. Implies that: A dollar today is worth more than a dollar tomorrow (e.g, power of compounding) Cash flows at different points in time cannot be added together. (see DowTheory Letters on web-site)
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To illustrate the basics: To illustrate the basics: Bank account accumulations. Bank account accumulations. You place PV = $1000 in an account that earns r = 8% interest, paid at the end of each year. Let FV n denote the balance after n periods. n = 1. FV 1 = 1000 + 1000(.08) = 1000(1.08) = $1080.00 n = 2. FV 2 = 1080 + 1080(.08) = 1080(1.08) = 1000(1.08) 2 = $1166.40 n = 3. FV 3 = 1166.4 + 1166.4(.08) = 1166.4(1.08) = 1000(1.08) 3 = $1259.71 In general, the balance after n periods can be determined from the initial balance and the interest rate as: FV n = PV(1+r) n
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0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 20 Year r = 5% r = 10% r = 15% r = 5% r = 10% r = 15% Accumulated (Future) Values FUTURE VALUE Year 1 2 5 10 20 5% 1.050 1.103 1.276 1.629 2.653 10% 1.100 1.210 1.331 2.594 6.727 15% 1.150 1.323 2.011 4.046 16.37 0 2 4 6 8 10 12 14 16 18 20 20 15 10 5 0 Future value of $1 Years
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Interest Rates and Future Interest Rates and Future Value Value Peter Minuit bought Manhattan Island from the Native Americans in 1621 for $24. How much is that worth today? FV n = PV (1+r) n n=379, PV=24, and let’s have r=.06 per year FV = 24 (1.06) 379 = $93.57 billion. Sensitivity Analysis: r=.05 and .07 FV = 24 (1.05) 379 = $2.58 billion. FV = 24 (1.07) 379 = $3.29 trillion.
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Present Values (Discounting) Present Values (Discounting) The same basic formula can be used to determine the current amount that is equivalent to (i.e. can grow to) a stated future amount, since: PV = FV n /(1+r) n Example: You need $20 million five years from now to fund a capital investment. If R = 6%, what amount can be set aside now to fund the investment? PV = 20.0/(1.06) 5 = 20.0/1.33823 = $14.945 million. Terminology: Here, r is referred to as the discount rate , and PV is referred to as the present value of FV n .
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PRESENT VALUES Present value of $1 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 12 14 16 18 20 r = 5% r = 10% r = 15% PRESENT VALUE Year 5% 10% 15% 1 .952 .909 .870 2 .907 .826 .756 5 .784 .621 .497 10 .614 .386 .247 20 .377 .149 .061 Years
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Intuition Intuition Again, the higher the discount rate, the less you value a future cash flow relative to cash today.
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Present Value Of A Series of Future Cash Present Value Of A Series of Future Cash Flows Flows In general, the present value of a stream of cash flows can be found using the following general valuation formula: PV C r C r C r C r C r N N N t t t t N = + + + + + + + + + = 1 1 2 2 2 3 3 3 1 1 1 1 1 1 ( ) ( ) ( ) ... ( ) ( ) = In words:
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Time value of money - EC150: Financial Economics Slide Set...

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