$5.24T —> current value of California

bought 1848, for 4.6$ million

8.25% ARR over 176 years!

***

Purchase History of California and Estimation of Annualized Rate of Return (ARR)

1. Purchase History of California

Acquisition through the Treaty of Guadalupe Hidalgo (1848):

• Mexican-American War (1846-1848): The conflict between the United States and Mexico culminated in the signing of the Treaty of Guadalupe Hidalgo on February 2, 1848.

• Territory Acquired: Under the treaty, Mexico ceded a vast region to the United States, known as the Mexican Cession. This territory included present-day California, Nevada, Utah, and parts of Arizona, New Mexico, Colorado, and Wyoming.

• Financial Terms:

• The United States agreed to pay $15 million to Mexico.

• Additionally, the U.S. assumed $3.25 million in debts owed by Mexico to American citizens.

• Significance:

• The acquisition significantly expanded U.S. territory, fulfilling the concept of Manifest Destiny—the belief that the U.S. was destined to expand across the North American continent.

• California’s inclusion was particularly valuable due to its vast natural resources and strategic Pacific coastline.

2. Estimating the Annualized Rate of Return (ARR) for California

To estimate the ARR from the acquisition cost to the present-day land value of California, we’ll follow these steps:

1. Determine California’s Share of the Purchase Price

2. Estimate the Current Land Value of California

3. Calculate the ARR using the Compound Annual Growth Rate (CAGR) formula

4. Present the Final Estimate

Step 1: Determine California’s Share of the Purchase Price

Total Purchase Price:

• $15 million for the entire Mexican Cession.

Area Comparison:

• Total Area of Mexican Cession:

• Approximately 529,189 square miles.

• Area of California:

• Approximately 163,696 square miles.

Calculating California’s Proportion:

California’s Share of the Purchase Price:

Step 2: Estimate the Current Land Value of California

Total Area of California in Acres:

Estimating Average Land Value per Acre:

California’s land values vary widely due to:

• Urban Areas: Cities like Los Angeles, San Francisco, and San Diego have extremely high land values.

• Agricultural Land: Central Valley and other agricultural regions have high-value farmland.

• Deserts and Mountains: Less valuable in terms of land price but may have mineral resources.

Approach to Estimation:

• Urban Land Value: Can exceed $1 million per acre.

• Agricultural Land Value: Averages around $10,000 to $20,000 per acre.

• Overall Average Value: For a conservative estimate, we’ll use an average land value of $50,000 per acre.

Calculating the Total Current Land Value:

• Estimated Current Value: $5.24 trillion

Step 3: Calculating the Annualized Rate of Return (ARR)

Variables:

• Present Value (PV): $4,641,000 (California’s share in 1848)

• Future Value (FV): $5,238,272,000,000 (Estimated current land value)

• Number of Years (n):

ARR (CAGR) Formula:

Calculations:

1. Compute the Growth Factor:

2. Calculate CAGR Using Logarithms for Precision:

• Result:

• Annualized Rate of Return (ARR): Approximately 8.25%

Step 4: Summary

• Initial Investment (1848): $4,641,000

• Estimated Current Value (2024): $5.24 trillion

• Annualized Rate of Return: 8.25% over 176 years

Important Considerations

• Simplifications and Assumptions:

• Average Land Value: The use of $50,000 per acre is a rough estimate to balance the extremely high urban land values with lower rural and undeveloped land values.

• Land Value vs. Property Value: The estimate focuses on land value alone, excluding the value of buildings and other improvements.

• Inflation and Purchasing Power: The calculation doesn’t adjust for inflation or changes in the purchasing power of money over time. $4.6 million in 1848 had significantly more purchasing power than the same amount today.

• Exclusion of Economic Benefits: The calculation doesn’t account for the economic activities, resource extraction, technological advancements, or strategic value that California has contributed to the United States.

• Historical Context:

• Population Growth: California’s population has grown from about 92,597 in 1850 to nearly 40 million today, significantly impacting land value.

• Economic Development: California is now the largest state economy in the U.S. and ranks among the largest economies globally.

• Discovery of Gold: The California Gold Rush (1848-1855) began shortly after the acquisition, dramatically increasing the region’s population and economic importance.

• Limitations:

• Data Availability: Precise current land values are difficult to ascertain due to fluctuations in the real estate market and lack of comprehensive data.

• Cultural and Ethical Considerations: The acquisition and subsequent development had profound effects on Indigenous populations and the environment, which are not reflected in monetary calculations.

Conclusion

Estimating the Annualized Rate of Return from the purchase of California in 1848 to its current estimated land value yields an approximate ARR of 8.25% over 176 years. This figure illustrates the substantial appreciation in land value and underscores California’s significant role in the economic growth of the United States.

Note: This estimation is a simplified calculation intended for illustrative purposes. Actual land values can vary widely based on numerous factors, and historical financial comparisons over such long periods involve complexities not fully captured in this brief analysis.