### Dr-Benjamin PP

```Net Present Value (NPV) for a
Single Rotation
• NPV may include the initial cost of land and land
value at time r
n
NPV 
where,

t0
N
t
(1  i)
t
Nt = net cash flow in year t (Rt - Ct)
Rt = revenue in year t
Ct = expenditure year t
n = r = rotation length
i = discount rate
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
PV1
1st rotation
PV0 of
perpetual
series
PV2
2nd rotation
PV3
3rd rotation
PV1 = PV2 = PV3 = ………PVn
PVn
nth rotation
• 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,
t = index on year” 0, 1, 2, . . . r
Rt = revenues in tth year
Ct = expenditures in tth year
i = discount rate
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
```