Bunyan Lumber LLC: Calculate when the company should harvest the timber
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?
Wait a few more years when the interest rates go back up. In this hampered economy it is better to buy gate logs and let your timber grow. This is what I am doing.
To calculate when Bunyan Lumber should harvest the timber, we need to consider the cash flows and costs associated with the project over time. We'll use the net present value (NPV) method to determine the optimal timing of the harvest.
1. Calculate the cash flows from thinning:
The company expects a positive cash flow of $1,000 per acre from thinning. Since the forest is 5,000 acres, the cash flow from thinning is 5,000 acres * $1,000 = $5,000,000.
2. Determine the expected harvest and timber grades:
The table provides information on the expected harvest per acre in thousands of board feet (MBF) for different years. Multiply the harvest per acre by the respective timber grade percentages to find the volume of each timber grade:
- At 20 years from today:
Harvest = 6 MBF per acre
Timber Grade 1P = 10% * 6 MBF = 0.6 MBF
Timber Grade 2P = 40% * 6 MBF = 2.4 MBF
Timber Grade 3P = 50% * 6 MBF = 3 MBF
- At 25 years from today:
Harvest = 7.6 MBF per acre
Timber Grade 1P = 12% * 7.6 MBF = 0.912 MBF
Timber Grade 2P = 42% * 7.6 MBF = 3.192 MBF
Timber Grade 3P = 46% * 7.6 MBF = 3.496 MBF
- At 30 years from today:
Harvest = 9 MBF per acre
Timber Grade 1P = 15% * 9 MBF = 1.35 MBF
Timber Grade 2P = 42% * 9 MBF = 3.78 MBF
Timber Grade 3P = 43% * 9 MBF = 3.87 MBF
- At 35 years from today:
Harvest = 10 MBF per acre
Timber Grade 1P = 16% * 10 MBF = 1.6 MBF
Timber Grade 2P = 43% * 10 MBF = 4.3 MBF
Timber Grade 3P = 41% * 10 MBF = 4.1 MBF
3. Calculate the discounted cash flows for each year of harvest:
We need to calculate the present value of the cash inflows and outflows associated with each year's harvest, taking into account the time value of money and the inflation rate.
- Calculate the contribution to the conservation fund:
Since the required contribution grows by 3.2% per year, we can calculate the total contribution for each year using the formula:
Total Contribution = $100,000 * (1 + 3.2%)^(years from today)
- Calculate the cash inflows from the timber harvest for each year:
Multiply the volume of each timber grade by the respective price per MBF:
Cash Inflows = (Timber Grade 1P * Price per MBF for 1P) + (Timber Grade 2P * Price per MBF for 2P) + (Timber Grade 3P * Price per MBF for 3P)
- Calculate the cash outflows for each year:
Include the costs of logging, road construction, sales preparation and administrative costs, and reforesting costs, all adjusted for inflation.
Net Cash Flow = Cash Inflows - Cash Outflows - Total Contribution
4. Discount the net cash flows to the present value:
Use the return rate of 10% to discount the net cash flows back to the present value. This will give us the NPV for each year's harvest.
NPV = Net Cash Flow / (1 + return rate)^(years from today)
5. Calculate the NPV for each year and choose the year with the highest NPV:
Calculate the NPV for each year's harvest using the discounted net cash flows. Choose the year with the highest NPV as the optimal timing for the harvest.
By comparing the NPVs for each year, you can determine when the company should harvest the forest. The year with the highest NPV will indicate when the project is most profitable.