Net Present Value (NPV) for a Single Rotation
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Net Present Value (NPV) for a Single Rotation
• NPV may include the initial cost of land and land value at time r
where,Nt = net cash flow in year t (Rt - Ct)Rt = revenue in year tCt = expenditure year tn = r = rotation lengthi = discount rate
n
t 0t
t
i)(1 NNPV
All cash flows are put in present value terms: Discounted Cash Flow
Can make comparisons between cash flows that occur at different times
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• Are most forest properties purchased to only have one rotation?
• What does perpetuity mean?• Unreasonable management time frame?• Can account for the total economic potential
of the land• Can provide a common time horizon allowing
for direct comparison of management alternatives
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• Soil Expectation Value (SEV), Land Expectation Value (LEV), Bare Land Value
• NPV of expected revenues and costs of forest management in perpetuity
• When realistic, estimates the value of forest land• Identify optimal even-aged management regimes
(rotation decisions, thinning regimes, establishment, other treatments)
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SEV timeline
PV11st rotation
PV22nd rotation
PV33rd rotation
PVnnth rotation
PV0 of perpetual
series
PV1 = PV2 = PV3 = ………PVn
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• Primary objective is to maximize profits from growing timber
• Situation specific (based on an individual’s costs, management regime, interest rate
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• Can determine the management option (optimal rotation, thinning) that maximizes SEV,
• Confusion with market value, which is the equilibrium price for aggregate sales in the marketplace
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Soil Expectation Value (SEV) r
∑ [ (Rt-Ct) (1+i)r-t ] t = 0 SEV =
(1+i)r - 1
where,r = rotation length in years, i = discount rate
t = index on year” 0, 1, 2, . . . r
Rt = revenues in tth year
Ct = expenditures in tth year
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Zobrist KW, WSU Extension Manual, EM030
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• What does it mean if SEV < 0?– Future revenue exceeds future costs
• What does it mean if SEV > 0?– Future revenue does not cover future costs– Does that mean no one will purchase the land?
• What does it mean if SEV = 0?– You will earn exactly the given rate of return that
you have selected– You will cover costs but there is no money left to
cover the cost of the land itself