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

• 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

• 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)

SEV timeline

PV11st rotation

PV22nd rotation

PV33rd rotation

PVnnth rotation

PV0 of perpetual

series

PV1 = PV2 = PV3 = ………PVn

• Primary objective is to maximize profits from growing timber

• Situation specific (based on an individual’s costs, management regime, interest rate

• 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

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

Zobrist KW, WSU Extension Manual, EM030

• 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