Chapter 4 - Chapter 4 Net Present Value NPV: The One-Period...

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Chapter 4 Net Present Value
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NPV: The One-Period Case Suppose investor has the choice between (Choice 1) $10,000 delivered today (Choice 2) $11,424 delivered one-year from now Interest rates are 12%. Which option should the investor choose? One way to look at the problem Put the $10,000 in the bank, it will turn into $10,000 x 1.12 = $11,200 Since $11,200 < $11,424, choice 2 must be the superior choice The figure $11,200 is the future value of $10,000
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Another way to look at the problem What would a bank lend us if we promised them the $11,424 tomorrow? Answer: (11,424/1.12) = $10,200 $10,200 is known as the present value of $11,424 Since $10,200 > $10,000, choice 2 is again superior Definition of present value (PV) Let C1 be an expected cash flow in one period Let r be the one-period rate of return demanded by investors r is called the discount factor PV(C1) = C1/(1+r)
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Net Present Value Method to compare the benefits and the costs of an investment NPV = – initial cost + PV(future cash flow) Example: Land costs $85,000 today Can be sold tomorrow for a sure $91,000 Current interest rate is 10% NPV(purchasing the land) = -85,000 + (91,000/1.10) = -$2,273
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Present value and rates of return Expected return = (expected profit) / investment = (91,000 – 85,000) /85,000 = .0706 or 7.06% Rules (1) invest when expected return > r (rate of return rule) (2) invest when NPV > 0 (NPV rule) Rules are equivalent only when investment has single cash payoff (more on this later)
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Extensions Cash tomorrow (C1) is an expected value, not a sure thing Risky expected $1 tomorrow is worth less than a safe $1 tomorrow Implication : riskier cash flows should be discounted at a greater r How do you determine appropriate r? Guess return of similar risk investments. Referred to as the discount rate, hurdle rate, or opportunity cost of capital Consider again choice of 10,000 today vs. 11,424 in 1 year, if r=.15 then Future value of 10,000 is 10,000 x 1.15 = 11,500 > 11,424 Present value of 11,424 = 11,424/1.15 = $9,934 < 10,000 Either way, choice 1 (sure $10,000 today) is now the superior choice!
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NPV: The Multi-period Case The power of compounding The general formula for the future value of an investment over many periods can be written as FV = C 0×(1 + r ) T Where C 0 is cash flow at date 0 r is the appropriate interest rate T is the number of periods over which the cash is invested.
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Example Suppose Gerry McNamara invests $1.10 in a mutual fund Fund promises an annual return of 40% Gerry will withdraw his cash after 5 full years
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This note was uploaded on 10/17/2011 for the course ECON 101 taught by Professor Thompson during the Spring '11 term at Michigan State University.

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Chapter 4 - Chapter 4 Net Present Value NPV: The One-Period...

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