Bunyan Lumber, LLC, harvests timber and delivers logs to timber mills for sale. The company was founded 70 years ago by Pete Bunyan. The current CEO is Paula Bunyan, the granddaughter of the founder. The company is currently evaluating a 5,000 acre forest it owns in Oregon. Paula has asked Steve Boles, the company's finance officer, to evaluate the project. Paula's concern is when the company should harvest the timber.

Lumber is sold by the company for its "pond value". Pond value is the amount a mill will pay for a log delivered to the mill location. The price paid for logs delivered to a mill is quoted in dollars per thousands of board feet (MBF), and the price depends on the grade of the logs. The forest Bunyan Lumber is evaluating was planted by the company 20 years ago and is made up entirely of Douglas fir trees. The table below shows the current price per MBF for the three grades of timber the company feels will come from the stand:

Timber Grade Price Per MBF
1P $1, 050
2P 925
3P 770

Steve believes that the pond value of lumber will increase at the inflation rate. The company is planning to thin the forest today, and it expects to realize a positive cash flow of $1,000 per acre from thinning. The thinning is done to increase the growth rate of the remaining trees, and it is always done 20 years following a planting.

The major decision the company faces is when to log the forest. When the company logs the forest, it will immediately replant saplings, which will allow for a future harvest. The longer the forest is allowed to grow, the larger the harvest becomes per acre. Additionally, an older forest has a higher grade of timber. Steve has compiled the following table with the expected harvest per acre in thousands of board feet, along with the breakdown of the timber grade:

Years from today Harvest (MBF) Timber Grade
to begin harvest per acre 1P 2P 3P

20 6 10% 40% 50%
25 7.6 12 42 46
30 9 15 42 43
35 10 16 43 41

The company expects to lose 5% of the timber it cuts due to defects and breakage.

The forest will be clear-cut when the company harvests the timber. This method of harvesting allows for faster growth of replanted trees. All of the harvesting, processing, replanting, and transportation are to be handled by subcontractors hired by Bunyan Lumber. The cost of the logging is expected to be $140 per MBF. A road system has to be constructed and is expected to cost $50 per MBF on average. Sales preparation and administrative costs, excluding office overhead costs, are expected to be $18 per MBF.

As soon as the harvesting is complete, the company will reforest the land. Reforesting costs include the following:

Per Acre Cost
Excavator piling $150
Broadcast burning 300
Site preparation 145
Planting costs 225

All costs are expected to increase at the inflation rate.

Assume all cash flows occur at the year of harvest. For example, if the company begins harvesting the timber 20 years from today, the cash flow from the harvest will be received 20 years from today. When the company logs the land, it will immediately replant the land with new saplings. The return is 10% and the inflation rate is expected to be 3.7% per year. Bunyan Lumber has a 35% tax rate.

Clear cutting is a controversial method of forest management. To obtain the necessary permits, Bunyan Lumber has agreed to contribute to a conservation fund every time it harvests the lumber. If the company harvested the forest today, the required contribution would be $100,000. The company has agreed that the required contribution will grow by 3.2% per year. When should the company harvest the forest?
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so far i have broken the problem down into 20,25, & 30 years:
then i know i suppose to take
calcuation of revenue per acre, from here i am totally lost. please assist.

To solve this problem, we need to calculate the net cash flow for each year, taking into account the revenue from the harvest, costs, and the required contribution to the conservation fund. We then calculate the present value of each net cash flow using the return rate and the inflation rate. The year with the highest present value represents the optimal time to harvest the forest.

Let's start by calculating the net cash flow for each year:

For the 20-year harvest:
Revenue per acre:
Harvest (MBF) * (1 - 5% timber loss) * Price per MBF

Costs per acre:
Thinning cash flow - $1,000
Excavator piling cost - $150
Broadcast burning cost - $300
Site preparation cost - $145
Planting costs - $225
Logging cost - Harvest (MBF) * $140
Road system cost - Harvest (MBF) * $50
Sales preparation and administrative costs - Harvest (MBF) * $18
Conservation fund contribution - $100,000 (growing at 3.2% per year)

Net cash flow:
Revenue per acre - Costs per acre - Conservation fund contribution

Calculate the net cash flow for the 20-year harvest.

For the 25-year harvest, use the same calculation as above but with the values for that specific year.

Do the same for the 30-year harvest.

Now that we have the net cash flow for each year, we need to calculate the present value of these cash flows.

To calculate the present value, we use the formula:
Present Value = Cash Flow / (1 + r)^t
where r is the return rate and t is the number of years into the future.

Calculate the present value for the net cash flow for each year, using the return rate and the inflation rate of 3.7%.

Compare the present values for each year and determine the year with the highest present value. This year represents the optimal time to harvest the forest.

I hope this helps you understand the steps to solve the problem. Let me know if you have any further questions.