The owner of a tree farm decides to harvest a stand of mature white pine trees. Each white pine yields approximately 62 board feet, the amount of lumber that can be milled from a 10-foot log that is 14 inches in diameter. The density of white pines is 120 trees per acre. The wholesale price-per- board-foot is $1.85.
a. What is the value per acre of white pines?
b. If the owner decides to harvest 18 acres of white pines, how much money will he make?
c. The owner must hire a timber company to cut down the trees. The timber company charges 30% of the wholesale value of the trees to perform this service. How much does the owner make after paying the timber campany? (Round to the nearest dollar.)
d. If the owner waits another 10 years, he will increase the yield of each tree to 127 board feet. Assuming the price-per-board-foot remains the same, how much more will he make if he waits?
The Correct Answer and Explanation is:
To solve this problem, we’ll break it down into steps for each question.
Given Information
- Board feet per tree: 62 board feet
- Density of trees per acre: 120 trees
- Price per board foot: $1.85
Part (a): Value per Acre of White Pines
To find the value per acre, we’ll calculate the board feet of lumber per acre and then find the total wholesale value.
- Calculate Board Feet per Acre:
- Each tree yields 62 board feet.
- With 120 trees per acre, the total board feet per acre is:
[
120 \text{ trees} \times 62 \text{ board feet/tree} = 7,440 \text{ board feet per acre}
]
- Calculate Value per Acre:
- Using the wholesale price of $1.85 per board foot:
[
7,440 \text{ board feet} \times 1.85 \text{ USD/board foot} = 13,764 \text{ USD per acre}
]
Part (b): Total Earnings for Harvesting 18 Acres
To find the earnings from harvesting 18 acres, multiply the value per acre by the number of acres:
[
13,764 \text{ USD/acre} \times 18 \text{ acres} = 247,752 \text{ USD}
]
Part (c): Earnings After Paying the Timber Company
The timber company charges 30% of the wholesale value. To find the net earnings after paying this fee:
- Calculate Timber Company Fee:
- The fee is 30% of the total wholesale value:
[
0.30 \times 247,752 = 74,326 \text{ USD}
]
- Calculate Net Earnings:
- Subtract the timber company’s fee from the total wholesale value:
[
247,752 – 74,326 = 173,426 \text{ USD}
]
Part (d): Additional Earnings if Waiting 10 Years
If the owner waits 10 years, the yield per tree increases to 127 board feet, assuming the price remains at $1.85 per board foot.
- Calculate New Value per Acre:
- With 120 trees per acre, each now yielding 127 board feet:
[
120 \times 127 = 15,240 \text{ board feet per acre}
] - At $1.85 per board foot:
[
15,240 \times 1.85 = 28,194 \text{ USD per acre}
]
- Calculate Total Value for 18 Acres After 10 Years:
- Multiply by the number of acres:
[
28,194 \times 18 = 507,492 \text{ USD}
]
- Calculate Additional Earnings:
- Subtract the original earnings for 18 acres from the future earnings:
[
507,492 – 247,752 = 259,740 \text{ USD}
]
Summary of Answers
- (a) Value per acre: $13,764
- (b) Total earnings for 18 acres: $247,752
- (c) Earnings after paying timber company: $173,426
- (d) Additional earnings if waiting 10 years: $259,740
Explanation
This problem demonstrates the financial evaluation of harvesting timber based on yield, density, price, and additional service fees. For each white pine tree, a yield of 62 board feet contributes to calculating the value per acre by considering both tree density and price per board foot. Multiplying board feet per acre by the wholesale price gives the gross revenue from one acre, which, when extended to 18 acres, provides total revenue. When the timber company charges 30% for its services, it’s necessary to deduct this fee to determine the net profit, emphasizing the impact of service fees on revenue in the timber industry.
The decision to wait 10 years reflects a strategic financial consideration; by allowing trees to mature further, the board feet per tree nearly doubles, significantly increasing potential revenue. This yield change boosts the value per acre from $13,764 to $28,194, illustrating how growth can increase income without additional acreage. The additional earnings ($259,740) represent the profit gained by maximizing tree maturity. This example reflects considerations in forestry and timber investment, where time and growth rates play critical roles in maximizing profits, influencing harvesting schedules and profit margins based on market price stability and tree growth forecasts.