time_uncertainty

time_uncertainty - Overview:Time and Uncertainty...

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Overview:Time and Uncertainty Intertemporal Prices and Present Value Uncertainty Irreversible Investments and Option Value Economics of Time: Some Issues Cash now versus cash payments in the future? Future payments are uncertain? When should we undertake a new project – now, later or never? How do we manage resources over time? – When do we end a profitable project? – How do we use up a non-renewable resource?
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Intertemporal Prices Interest rate r, Today is t = 0: $1 invested today becomes $(1 + r) at t = 1 $1 invested today becomes $(1 + r) 2 at t = 2, etc. Today’s price of ($1 at t = 1) is 1/(1+r) (I.e. $ 1/(1+r) invested today becomes $1 at t = 1) Today’s price of ($1 at t = 2) is 1/(1+r) 2 , etc. Present Value Present Value of a stream of cash flows is the value in today’s prices PV = C 0 + C 1 /(1+r) + C 2 /(1+r) 2 + ….+ C T /(1+r) T where C t is the (positive or negative) cash flow at time t PV Criterion: Invest in projects with PV > 0 r is “discount rate,” PV often computed for many values
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Example Consider two projects, A and B Present Value t = 0 1 2 3 r = 1 % 1 0 % Project A -200 50 50 120 15 -23 Project B 100 50 50 -220 -15 21 Difference B - A -30 45 (Timing of payments matters, with discount rate very important)
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Choice under Uncertainty Another aspect of future cash flows is uncertainty. This is modeled via random variables with a distribution. How do you react to uncertainty?
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time_uncertainty - Overview:Time and Uncertainty...

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