Chapter 7: Financial Analysis

Learning Objectives

After reading this chapter, you should be able to:

Calculate net present value (NPV) for forest management scenarios
Understand the components of forest financial analysis
Use ws3’s financial functions to evaluate management plans
Compare alternative management strategies using financial metrics

What Is Financial Analysis in Forest Planning?

Financial analysis evaluates the economic viability of forest management plans. It answers questions like:

Is this harvest schedule profitable?
Which management strategy maximizes returns?
How sensitive is the plan to changes in timber prices?
What is the optimal rotation age?

Key financial metrics:

Net Present Value (NPV): Total value of all cash flows, discounted to present
Internal Rate of Return (IRR): Discount rate that makes NPV = 0
Benefit-Cost Ratio (BCR): Total benefits divided by total costs
Rotation Age: Age that maximizes NPV per hectare

Net Present Value

Net Present Value (NPV) is the most important financial metric in forest planning. It accounts for the time value of money: a dollar today is worth more than a dollar tomorrow.

\[\begin{split}NPV = \\sum_{t=0}^{T} \\frac{R_t - C_t}{(1 + r)^t}\end{split}\]

Where: - $R_t$ = Revenue in period $t$ - $C_t$ = Cost in period $t$ - $r$ = Discount rate - $T$ = Planning horizon

        graph TD
  REV["Revenue<br/>(harvest sales)"] --> NPV["NPV Calculation"]
  COST["Costs<br/>(harvesting, silviculture)"] --> NPV
  DISC["Discount rate<br/>(time value of money)"] --> NPV
  NPV --> PROF["Profitability<br/>decision"]

Using ws3’s Financial Functions

ws3 provides financial analysis functions in the ws3.financial module.

Calculating NPV

# Financial calculations are done in pure Python (no ws3.financial module).
# Define cash flows for each period
revenues = [0, 0, 50000, 80000, 100000, 120000, 110000, 90000, 70000, 50000]
costs = [10000, 5000, 20000, 25000, 30000, 35000, 30000, 25000, 20000, 15000]

# Calculate NPV at 5% discount rate
discount_rate = 0.05
npv = sum(
    (r - c) / (1 + discount_rate) ** t
    for t, (r, c) in enumerate(zip(revenues, costs))
)
print(f"NPV: ${npv:,.0f}")

# Calculate NPV at different discount rates
for rate in [0.02, 0.05, 0.08, 0.10]:
    npv = sum(
        (r - c) / (1 + rate) ** t
        for t, (r, c) in enumerate(zip(revenues, costs))
    )
    print(f"NPV at {rate*100:.0f}%: ${npv:,.0f}")

Calculating IRR

The Internal Rate of Return (IRR) is the discount rate that makes NPV equal to zero. It represents the inherent rate of return of the investment.

# Calculate IRR using numpy (or scipy.optimize)
import numpy as np
from scipy.optimize import brentq

# Net cash flows
net_flows = [r - c for r, c in zip(revenues, costs)]

# IRR is the discount rate that makes NPV = 0
def npv_at_rate(rate):
    return sum(cf / (1 + rate) ** t for t, cf in enumerate(net_flows))

irr = brentq(npv_at_rate, -0.99, 0.99)
print(f"IRR: {irr*100:.1f}%")

# Compare to discount rate
if irr > 0.05:
    print("Project is profitable at 5% discount rate")
else:
    print("Project is not profitable at 5% discount rate")

Rotation Economics

The optimal rotation age is the age that maximizes NPV per hectare. This is a fundamental concept in forest economics.

        graph TD
  AGE["Rotation age"] --> VOL["Volume at harvest"]
  AGE --> COST["Costs over rotation"]
  VOL --> REV["Revenue at harvest"]
  COST --> NPV["NPV"]
  REV --> NPV
  NPV --> OPT["Optimal rotation age<br/>(max NPV)"]

The Faustmann formula calculates the optimal rotation age:

\[V'(T) / V(T) = r / (1 - e^{-rT})\]

Where: - $V(T)$ = Volume at age $T$ - $V'(T)$ = Marginal growth at age $T$ - $r$ = Discount rate

Using ws3 to Find Optimal Rotation

from ws3.forest import ForestModel
from ws3.core import Curve

# Define a volume curve
volume_curve = Curve(
    label="DF_volume",
    points=[(age, vol) for age, vol in
            zip(range(0, 201, 10),
                [0, 2, 10, 30, 70, 130, 210, 300, 390, 460, 510,
                 540, 560, 575, 585, 590, 595, 598, 600, 601, 602, 602])]
)

# Calculate NPV for each rotation age
prices = 50  # $/m³
costs = 10000  # Fixed costs per hectare
discount_rate = 0.05

npv_by_age = []
for age in range(10, 201, 10):
    volume = volume_curve(age)
    revenue = volume * prices
    # Discounted revenue minus costs
    npv = (revenue - costs) / (1 + discount_rate) ** age
    npv_by_age.append((age, npv))

# Find optimal rotation age
optimal_age, max_npv = max(npv_by_age, key=lambda x: x[1])
print(f"Optimal rotation age: {optimal_age} years")
print(f"Maximum NPV: ${max_npv:,.0f}")

Sensitivity Analysis

Financial analysis should include sensitivity analysis to understand how results change with different assumptions:

# Sensitivity to timber prices
print("Sensitivity to timber prices:")
base_price = 50
for price in [30, 40, 50, 60, 70]:
    # Adjust revenues for new price
    adjusted_revenues = [r * price / base_price for r in revenues]
    npv_adj = sum(
        (r - c) / (1 + 0.05) ** t
        for t, (r, c) in enumerate(zip(adjusted_revenues, costs))
    )
    print(f"  Price = ${price}/m³: NPV = ${npv_adj:,.0f}")

# Sensitivity to discount rates
print("\nSensitivity to discount rates:")
for rate in [0.02, 0.05, 0.08, 0.10, 0.15]:
    npv = sum(
        (r - c) / (1 + rate) ** t
        for t, (r, c) in enumerate(zip(revenues, costs))
    )
    print(f"  Rate = {rate*100:.0f}%: NPV = ${npv:,.0f}")

Common Financial Mistakes

Ignoring discounting: Failing to account for the time value of money
Using nominal vs. real values: Mixing nominal and real prices
Ignoring costs: Only considering revenue, not harvesting/silviculture costs
Overlooking risk: Not accounting for uncertainty in prices and volumes
Incorrect rotation age: Using biological maturity instead of economic optimum

Exercises

Exercise 1 (Easy): Calculate the NPV of a simple harvest scenario with revenues of $100,000 in year 20 and costs of $10,000 in year 0.

Exercise 2 (Medium): Find the optimal rotation age for a Douglas-fir stand with the volume curve defined in this chapter.

Exercise 3 (Hard): Perform a sensitivity analysis on the optimal rotation age with respect to discount rate and timber price.