Suppose that the allocation of a natural resource during three years results in a stream of total surplus value of $100 per period t (i.e.: t = 0; 1; 2). Obtain the present value of this stream when the discount rate is r = 0:10 and also when it is r = 0:05. Annuity amount (A) = $100 Time Period (n) = 3 years Discount rate (r) = 10% or 0.10 & 5% or 0.05 Present value of this stream when the discount rate is 10%: PVA = PV = A (P/A, r, n) PV = 100 (P/A, 0.10, 3) PV = 248.69 Present value of this stream when the discount rate is 5%: PVA = PV = A (P/A, r, n) PV = 100 (P/A, 0.5, 3) PV = 272.3 (c) Alternatively, the resource could be fully extracted now (say, in the period t = 0), resulting in a total surplus $280 at t = 0 and 0 in every future period. Is this immediate extraction strategy preferred to the extraction strategy described in (a) when r = 0:10? What about when r = 0:05? What does this tell us about the intuitive meaning of discounting regarding intertemporal preferences?
(b) Suppose that the allocation of a natural resource during three years results in a stream of total surplus value of $100 per period t (i.e.: t = 0; 1; 2). Obtain the present value of this stream when the discount rate is r = 0:10 and also when it is r = 0:05.
Time Period (n) = 3 years
Discount rate (r) = 10% or 0.10 & 5% or 0.05
Present value of this stream when the discount rate is 10%:
PVA =
PV = A (P/A, r, n)
PV = 100 (P/A, 0.10, 3)
PV = 248.69
Present value of this stream when the discount rate is 5%:
PVA =
PV = A (P/A, r, n)
PV = 100 (P/A, 0.5, 3)
PV = 272.3
(c) Alternatively, the resource could be fully extracted now (say, in the period t = 0), resulting in a total surplus $280 at t = 0 and 0 in every future period. Is this immediate extraction strategy preferred to the extraction strategy described in (a) when r = 0:10? What about when r = 0:05? What does this tell us about the intuitive meaning of discounting regarding intertemporal preferences?
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