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April 23, 2014

April 23, 2014

Posted by **Bunyan Lumber, LLC, harvests timber and delivers l** on Thursday, October 27, 2011 at 8:26am.

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 $575

2P $ 555

3P $ 530

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 $450 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.

Yrs from today to Harvest (MBF) Timber Grade

begin harvest per acre 1P 2P 3P

20 7.2 15% 42% 43%

25 9.4 18 43 33

30 11.3 20 51 29

35 12.2 22 53 25

The company expects to lose 5 percent 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 $155 per MBF. A road system has to be constructed and is expected to cost $60 per MBF on average. Sales preparation and administrative costs, excluding office overhead costs, are expected to be $21 per MBF.

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

Cost Per Acre

Excavator piling $160

Broadcast Burning 280

Site Preparation 140

Planting costs 270

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 harvest period chosen will be repeated for the foreseeable future. The company's nominal required return is 10 percent, and the inflation rate is expected to be 3.7 percent per year. Bunyan Lumber has a 35 percent 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 $300, 000. The company has agreed that the required contribution will grow by 3.2 percent per year.

Question: When should the company harvest the forest?

- Managerial Finance -
**Bunyan Lumber, LLC, harvests timber and delivers l**, Thursday, October 27, 2011 at 8:27amCHAPTER 9

BUNYAN LUMBER, LLC

The company is faced with the option of when to harvest the lumber. Whatever harvest cycle the company chooses, it will follow that cycle in perpetuity. Since the forest was planted 20 years ago, the options available in the case are 40-, 45-, 50, and 55-year harvest cycles. No matter what harvest cycle the company chooses, it will always thin the timber 20 years after harvests and replants. The cash flows will grow at the inflation rate, so we can use the real or nominal cash flows. In this case, it is simpler to use real cash flows, although nominal cash flows would yield the same result. So, the real required return on the project is:

(1 + R) = (1 + r)(1 + h)

1.10 = (1 + r)(1.037)

r = .0608 or 6.08%

The conservation funds are expected to grow at a slower rate than inflation, so the real return for the conservation fund will be:

(1 + R) = (1 + r)(1 + h)

1.10 = (1 + r)(1.032)

r = .0659 or 6.59%

The company will thin the forest today regardless of the harvest schedule, so this first thinning is not an incremental cash flow, but future thinning is part of the analysis since the thinning schedule is determined by the harvest schedule. The cash flow from the thinning process is:

Cash flow from thinning = Acres thinned ℅ Cash flow per acre

Cash flow from thinning = 7,500($1,200)

Cash flow from thinning = $9,000,000

The real cost of the conservation fund is constant, but the expense will be tax deductible, so the aftertax cost of the conservation fund will be:

Aftertax conservation fund cost = (1 每 .35)($250,000)

Aftertax conservation fund cost = $162,500

For each analysis, the revenue and costs are:

Revenue = [﹉(% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 每 defect rate)

Tractor cost = (Cost MBF)(MBF per acre)(acres)

Road cost = (Cost MBF)(MBF per acre)(acres)

Sale preparation and administration = (Cost MBF)(MBF acre)(acres)

Excavator piling, broadcast burning, site preparation, and planting costs are the cost of each per acre times the number of acres. These costs are the same no matter what the harvest schedule since they are based on acres, not MBF.

Now we can calculate the cash flow for each harvest schedule. One important note is that no depreciation is given in the case. Since the harvest time is likely to be short, the assumption is that no depreciation is attributable to the harvest. This implies that operating cash flow is equal to net income. Now we can calculate the NPV of each harvest schedule. The NPV of each harvest schedule is the NPV of the first harvest, the NPV of the thinning, the NPV of all future harvests, minus the present value of the conservation fund costs.

40-year harvest schedule:

Revenue $39,800,250

Tractor cost 7,200,000

Road 2,700,000

Sale preparation & admin 945,000

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $22,505,250

Taxes 7,876,838

Net income (OCF) $14,628,413

The PV of the first harvest in 20 years is:

PVFirst = $14,628,413/(1 + .0608)20

PVFirst = $4,496,956

Thinning will also occur on a 40-year schedule, with the next thinning 40 years from today. The effective 40-year interest rate for the project is:

40-year project interest rate = [(1 + .0608)40] 每 1

40-year project interest rate = 958.17%

We also need the 40-year interest rate for the conservation fund, which will be:

40-year conservation interest rate = [(1 + .0659)40] 每 1

40-year conservation interest rate = 1,183.87%

Since we have the cash flows from each thinning, and the next thinning will occur in 40 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/9.8517

PVThinning = $939,286.45

The operating cash flow from each harvest on the 40-year schedule is $14,482,163, so the present value of the cash flows from the harvest are:

PVHarvest = [($14,628,413/9.5817)] / (1 + .0608)20

PVHarvest = $469,325.52

Now we can find the present value of the conservation fund deposits, which will begin in 20 years. The value of these deposits in 20 years is:

PVConservation = 每$162,500 每$162,500/11.8387

PVConservation = 每$176.226.22

And the value of the conservation fund today is:

PVConservation = 每$176,226.22/(1+ .0659)20

PVConservation = 每$49,182.52

So, the NPV of a 40-year harvest schedule is:

NPV = $4,496,956 + 939,286.45 + 469,325.52 每 49,182.52

NPV = $5,856,385.29

45-year harvest schedule:

Revenue $55,462,853

Tractor cost 9,840,000

Road 3,690,000

Sale preparation & admin 1,291,500

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $34,191,353

Taxes 11,966,973

Net income (OCF) $22,224,379

The PV of the first harvest in 25 years is:

PVFirst = $22,224,379/(1 + .0608)25

PVFirst = $5,087,231

Thinning will also occur on a 45-year schedule, with the next thinning 45 years from today. The effective 45-year interest rate for the project is:

45-year project interest rate = [(1 + .0608)45] 每 1

45-year project interest rate = 1,321.11%

We also need the 45-year interest rate for the conservation fund, which will be:

45-year conservation interest rate = [(1 + .0659)45] 每 1

45-year conservation interest rate = 1,666.38%

Since we have the cash flows from each thinning, and the next thinning will occur in 45 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/13.2111

PVThinning = $681,246.84

The operating cash flow from each harvest on the 45-year schedule is $22,024,504, so the present value of the cash flows from the harvest are:

PVHarvest = [($22,224,379/13.21111)] / (1 + .0608)25

PVHarvest = $385,073.30

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/16.6638

PVConservation = 每$174,800.29

And the value of the conservation fund today is:

PVConservation = 每$174,800.29/(1+ .0659)25

PVConservation = 每$35,458.26

So, the NPV of a 45-year harvest schedule is:

NPV = $5,087,231 + 681.246.84 + 385,073.30 每 35,458,26

NPV = $6,1118,092.40

50-year harvest schedule:

Revenue $64,610,783

Tractor cost 11,280,000

Road 4,230,000

Sale preparation & admin 1,480,500

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $41,170,283

Taxes 14,409,599

Net income (OCF) $26,760,684

The PV of the first harvest in 30 years is:

PVFirst = $26,760,684/(1 + .0608)30

PVFirst = $4,561,202

Thinning will also occur on a 50-year schedule, with the next thinning 50 years from today. The effective 50-year interest rate for the project is:

50-year project interest rate = [(1 + .0608)50] 每 1

50-year project interest rate = 1,808.52%

We also need the 50-year interest rate for the conservation fund, which will be:

50-year conservation interest rate = [(1 + .0659)50] 每 1

50-year conservation interest rate = 2,330.24%

Since we have the cash flows from each thinning, and the next thinning will occur in 50 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/18.0852

PVThinning = $497,644.82

The operating cash flow from each harvest on the 50-year schedule is $26,531,559, so the present value of the cash flows from the harvest are:

PVHarvest = [($26,760,684/18.0852] / (1 + .0608)30

PVHarvest = $497,644.82

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/23.3024

PVConservation = 每$171,485.25

And the value of the conservation fund today is:

PVConservation = 每$171,485.25/(1+ .0659)30

PVConservation = 每$25,283.50

So, the NPV of a 50-year harvest schedule is:

NPV = $4,561,202 + 497,644.82 + 252,206.52 每 25,283.50

NPV = $5,285,770.21

55-year harvest schedule:

Revenue $72,972,113

Tractor cost 12,600,000

Road 4,725,000

Sale preparation & admin 1,653,750

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $47,543,363

Taxes 16,640,177

Net income (OCF) $30,903,186

The PV of the first harvest in 35 years is:

PVFirst = $30,903,186/(1 + .0608)35

PVFirst = $3,922,074

Thinning will also occur on a 55-year schedule, with the next thinning 55 years from today. The effective 55-year interest rate for the project is:

55-year project interest rate = [(1 + .0608)55] 每 1

55-year project interest rate = 2,463.10

We also need the 55-year interest rate for the conservation fund, which will be:

55-year conservation interest rate = [(1 + .0659)55] 每 1

55-year conservation interest rate = 3,243.60%

Since we have the cash flows from each thinning, and the next thinning will occur in 55 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/24.6310

PVThinning = $365,392.74

The operating cash flow from each harvest on the 55-year schedule is $30,647,248, so the present value of the cash flows from the harvest are:

PVHarvest = [($30,903,186/24.6310] / (1 + .0608)35

PVHarvest = $159,233.03

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/32.4360

PVConservation = 每$169,097.37

And the value of the conservation fund today is:

PVConservation = 每$169,097.37/(1+ .0659)35

PVConservation = 每$18,121.00

So, the NPV of a 55-year harvest schedule is:

NPV = $3,922,074 + 365,392.74 + 159,233.03 每 18,121.00

NPV = $4,428,578.40

The company should use a 45-year harvest schedule since it has the highest NPV. Notice that when the NPV began to decline, it continued declining. This is expected since the growth in the trees increases at a decreasing rate. So, once we reach a point where the increased growth cannot overcome the increased effects of compounding, harvesting should take place. There is no point further in the future which will provide a higher NPV.

- Managerial Finance -
**Bunyan Lumber, LLC, harvests timber and delivers l**, Thursday, October 27, 2011 at 8:27amCHAPTER 9

BUNYAN LUMBER, LLC

The company is faced with the option of when to harvest the lumber. Whatever harvest cycle the company chooses, it will follow that cycle in perpetuity. Since the forest was planted 20 years ago, the options available in the case are 40-, 45-, 50, and 55-year harvest cycles. No matter what harvest cycle the company chooses, it will always thin the timber 20 years after harvests and replants. The cash flows will grow at the inflation rate, so we can use the real or nominal cash flows. In this case, it is simpler to use real cash flows, although nominal cash flows would yield the same result. So, the real required return on the project is:

(1 + R) = (1 + r)(1 + h)

1.10 = (1 + r)(1.037)

r = .0608 or 6.08%

The conservation funds are expected to grow at a slower rate than inflation, so the real return for the conservation fund will be:

(1 + R) = (1 + r)(1 + h)

1.10 = (1 + r)(1.032)

r = .0659 or 6.59%

The company will thin the forest today regardless of the harvest schedule, so this first thinning is not an incremental cash flow, but future thinning is part of the analysis since the thinning schedule is determined by the harvest schedule. The cash flow from the thinning process is:

Cash flow from thinning = Acres thinned ℅ Cash flow per acre

Cash flow from thinning = 7,500($1,200)

Cash flow from thinning = $9,000,000

The real cost of the conservation fund is constant, but the expense will be tax deductible, so the aftertax cost of the conservation fund will be:

Aftertax conservation fund cost = (1 每 .35)($250,000)

Aftertax conservation fund cost = $162,500

For each analysis, the revenue and costs are:

Revenue = [﹉(% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 每 defect rate)

Tractor cost = (Cost MBF)(MBF per acre)(acres)

Road cost = (Cost MBF)(MBF per acre)(acres)

Sale preparation and administration = (Cost MBF)(MBF acre)(acres)

Excavator piling, broadcast burning, site preparation, and planting costs are the cost of each per acre times the number of acres. These costs are the same no matter what the harvest schedule since they are based on acres, not MBF.

Now we can calculate the cash flow for each harvest schedule. One important note is that no depreciation is given in the case. Since the harvest time is likely to be short, the assumption is that no depreciation is attributable to the harvest. This implies that operating cash flow is equal to net income. Now we can calculate the NPV of each harvest schedule. The NPV of each harvest schedule is the NPV of the first harvest, the NPV of the thinning, the NPV of all future harvests, minus the present value of the conservation fund costs.

40-year harvest schedule:

Revenue $39,800,250

Tractor cost 7,200,000

Road 2,700,000

Sale preparation & admin 945,000

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $22,505,250

Taxes 7,876,838

Net income (OCF) $14,628,413

The PV of the first harvest in 20 years is:

PVFirst = $14,628,413/(1 + .0608)20

PVFirst = $4,496,956

Thinning will also occur on a 40-year schedule, with the next thinning 40 years from today. The effective 40-year interest rate for the project is:

40-year project interest rate = [(1 + .0608)40] 每 1

40-year project interest rate = 958.17%

We also need the 40-year interest rate for the conservation fund, which will be:

40-year conservation interest rate = [(1 + .0659)40] 每 1

40-year conservation interest rate = 1,183.87%

Since we have the cash flows from each thinning, and the next thinning will occur in 40 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/9.8517

PVThinning = $939,286.45

The operating cash flow from each harvest on the 40-year schedule is $14,482,163, so the present value of the cash flows from the harvest are:

PVHarvest = [($14,628,413/9.5817)] / (1 + .0608)20

PVHarvest = $469,325.52

Now we can find the present value of the conservation fund deposits, which will begin in 20 years. The value of these deposits in 20 years is:

PVConservation = 每$162,500 每$162,500/11.8387

PVConservation = 每$176.226.22

And the value of the conservation fund today is:

PVConservation = 每$176,226.22/(1+ .0659)20

PVConservation = 每$49,182.52

So, the NPV of a 40-year harvest schedule is:

NPV = $4,496,956 + 939,286.45 + 469,325.52 每 49,182.52

NPV = $5,856,385.29

45-year harvest schedule:

Revenue $55,462,853

Tractor cost 9,840,000

Road 3,690,000

Sale preparation & admin 1,291,500

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $34,191,353

Taxes 11,966,973

Net income (OCF) $22,224,379

The PV of the first harvest in 25 years is:

PVFirst = $22,224,379/(1 + .0608)25

PVFirst = $5,087,231

Thinning will also occur on a 45-year schedule, with the next thinning 45 years from today. The effective 45-year interest rate for the project is:

45-year project interest rate = [(1 + .0608)45] 每 1

45-year project interest rate = 1,321.11%

We also need the 45-year interest rate for the conservation fund, which will be:

45-year conservation interest rate = [(1 + .0659)45] 每 1

45-year conservation interest rate = 1,666.38%

Since we have the cash flows from each thinning, and the next thinning will occur in 45 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/13.2111

PVThinning = $681,246.84

The operating cash flow from each harvest on the 45-year schedule is $22,024,504, so the present value of the cash flows from the harvest are:

PVHarvest = [($22,224,379/13.21111)] / (1 + .0608)25

PVHarvest = $385,073.30

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/16.6638

PVConservation = 每$174,800.29

And the value of the conservation fund today is:

PVConservation = 每$174,800.29/(1+ .0659)25

PVConservation = 每$35,458.26

So, the NPV of a 45-year harvest schedule is:

NPV = $5,087,231 + 681.246.84 + 385,073.30 每 35,458,26

NPV = $6,1118,092.40

50-year harvest schedule:

Revenue $64,610,783

Tractor cost 11,280,000

Road 4,230,000

Sale preparation & admin 1,480,500

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $41,170,283

Taxes 14,409,599

Net income (OCF) $26,760,684

The PV of the first harvest in 30 years is:

PVFirst = $26,760,684/(1 + .0608)30

PVFirst = $4,561,202

Thinning will also occur on a 50-year schedule, with the next thinning 50 years from today. The effective 50-year interest rate for the project is:

50-year project interest rate = [(1 + .0608)50] 每 1

50-year project interest rate = 1,808.52%

We also need the 50-year interest rate for the conservation fund, which will be:

50-year conservation interest rate = [(1 + .0659)50] 每 1

50-year conservation interest rate = 2,330.24%

Since we have the cash flows from each thinning, and the next thinning will occur in 50 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/18.0852

PVThinning = $497,644.82

The operating cash flow from each harvest on the 50-year schedule is $26,531,559, so the present value of the cash flows from the harvest are:

PVHarvest = [($26,760,684/18.0852] / (1 + .0608)30

PVHarvest = $497,644.82

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/23.3024

PVConservation = 每$171,485.25

And the value of the conservation fund today is:

PVConservation = 每$171,485.25/(1+ .0659)30

PVConservation = 每$25,283.50

So, the NPV of a 50-year harvest schedule is:

NPV = $4,561,202 + 497,644.82 + 252,206.52 每 25,283.50

NPV = $5,285,770.21

55-year harvest schedule:

Revenue $72,972,113

Tractor cost 12,600,000

Road 4,725,000

Sale preparation & admin 1,653,750

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $47,543,363

Taxes 16,640,177

Net income (OCF) $30,903,186

The PV of the first harvest in 35 years is:

PVFirst = $30,903,186/(1 + .0608)35

PVFirst = $3,922,074

Thinning will also occur on a 55-year schedule, with the next thinning 55 years from today. The effective 55-year interest rate for the project is:

55-year project interest rate = [(1 + .0608)55] 每 1

55-year project interest rate = 2,463.10

We also need the 55-year interest rate for the conservation fund, which will be:

55-year conservation interest rate = [(1 + .0659)55] 每 1

55-year conservation interest rate = 3,243.60%

Since we have the cash flows from each thinning, and the next thinning will occur in 55 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/24.6310

PVThinning = $365,392.74

The operating cash flow from each harvest on the 55-year schedule is $30,647,248, so the present value of the cash flows from the harvest are:

PVHarvest = [($30,903,186/24.6310] / (1 + .0608)35

PVHarvest = $159,233.03

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/32.4360

PVConservation = 每$169,097.37

And the value of the conservation fund today is:

PVConservation = 每$169,097.37/(1+ .0659)35

PVConservation = 每$18,121.00

So, the NPV of a 55-year harvest schedule is:

NPV = $3,922,074 + 365,392.74 + 159,233.03 每 18,121.00

NPV = $4,428,578.40

The company should use a 45-year harvest schedule since it has the highest NPV. Notice that when the NPV began to decline, it continued declining. This is expected since the growth in the trees increases at a decreasing rate. So, once we reach a point where the increased growth cannot overcome the increased effects of compounding, harvesting should take place. There is no point further in the future which will provide a higher NPV.

- Managerial Finance -
**Bunyan Lumber, LLC, harvests timber and delivers l**, Thursday, October 27, 2011 at 8:28amBUNYAN LUMBER, LLC

The company is faced with the option of when to harvest the lumber. Whatever harvest cycle the company chooses, it will follow that cycle in perpetuity. Since the forest was planted 20 years ago, the options available in the case are 40-, 45-, 50, and 55-year harvest cycles. No matter what harvest cycle the company chooses, it will always thin the timber 20 years after harvests and replants. The cash flows will grow at the inflation rate, so we can use the real or nominal cash flows. In this case, it is simpler to use real cash flows, although nominal cash flows would yield the same result. So, the real required return on the project is:

(1 + R) = (1 + r)(1 + h)

1.10 = (1 + r)(1.037)

r = .0608 or 6.08%

The conservation funds are expected to grow at a slower rate than inflation, so the real return for the conservation fund will be:

(1 + R) = (1 + r)(1 + h)

1.10 = (1 + r)(1.032)

r = .0659 or 6.59%

The company will thin the forest today regardless of the harvest schedule, so this first thinning is not an incremental cash flow, but future thinning is part of the analysis since the thinning schedule is determined by the harvest schedule. The cash flow from the thinning process is:

Cash flow from thinning = Acres thinned ℅ Cash flow per acre

Cash flow from thinning = 7,500($1,200)

Cash flow from thinning = $9,000,000

The real cost of the conservation fund is constant, but the expense will be tax deductible, so the aftertax cost of the conservation fund will be:

Aftertax conservation fund cost = (1 每 .35)($250,000)

Aftertax conservation fund cost = $162,500

For each analysis, the revenue and costs are:

Revenue = [﹉(% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 每 defect rate)

Tractor cost = (Cost MBF)(MBF per acre)(acres)

Road cost = (Cost MBF)(MBF per acre)(acres)

Sale preparation and administration = (Cost MBF)(MBF acre)(acres)

Excavator piling, broadcast burning, site preparation, and planting costs are the cost of each per acre times the number of acres. These costs are the same no matter what the harvest schedule since they are based on acres, not MBF.

Now we can calculate the cash flow for each harvest schedule. One important note is that no depreciation is given in the case. Since the harvest time is likely to be short, the assumption is that no depreciation is attributable to the harvest. This implies that operating cash flow is equal to net income. Now we can calculate the NPV of each harvest schedule. The NPV of each harvest schedule is the NPV of the first harvest, the NPV of the thinning, the NPV of all future harvests, minus the present value of the conservation fund costs.

40-year harvest schedule:

Revenue $39,800,250

Tractor cost 7,200,000

Road 2,700,000

Sale preparation & admin 945,000

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $22,505,250

Taxes 7,876,838

Net income (OCF) $14,628,413

The PV of the first harvest in 20 years is:

PVFirst = $14,628,413/(1 + .0608)20

PVFirst = $4,496,956

Thinning will also occur on a 40-year schedule, with the next thinning 40 years from today. The effective 40-year interest rate for the project is:

40-year project interest rate = [(1 + .0608)40] 每 1

40-year project interest rate = 958.17%

We also need the 40-year interest rate for the conservation fund, which will be:

40-year conservation interest rate = [(1 + .0659)40] 每 1

40-year conservation interest rate = 1,183.87%

Since we have the cash flows from each thinning, and the next thinning will occur in 40 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/9.8517

PVThinning = $939,286.45

The operating cash flow from each harvest on the 40-year schedule is $14,482,163, so the present value of the cash flows from the harvest are:

PVHarvest = [($14,628,413/9.5817)] / (1 + .0608)20

PVHarvest = $469,325.52

Now we can find the present value of the conservation fund deposits, which will begin in 20 years. The value of these deposits in 20 years is:

PVConservation = 每$162,500 每$162,500/11.8387

PVConservation = 每$176.226.22

And the value of the conservation fund today is:

PVConservation = 每$176,226.22/(1+ .0659)20

PVConservation = 每$49,182.52

So, the NPV of a 40-year harvest schedule is:

NPV = $4,496,956 + 939,286.45 + 469,325.52 每 49,182.52

NPV = $5,856,385.29

45-year harvest schedule:

Revenue $55,462,853

Tractor cost 9,840,000

Road 3,690,000

Sale preparation & admin 1,291,500

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $34,191,353

Taxes 11,966,973

Net income (OCF) $22,224,379

The PV of the first harvest in 25 years is:

PVFirst = $22,224,379/(1 + .0608)25

PVFirst = $5,087,231

Thinning will also occur on a 45-year schedule, with the next thinning 45 years from today. The effective 45-year interest rate for the project is:

45-year project interest rate = [(1 + .0608)45] 每 1

45-year project interest rate = 1,321.11%

We also need the 45-year interest rate for the conservation fund, which will be:

45-year conservation interest rate = [(1 + .0659)45] 每 1

45-year conservation interest rate = 1,666.38%

Since we have the cash flows from each thinning, and the next thinning will occur in 45 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/13.2111

PVThinning = $681,246.84

The operating cash flow from each harvest on the 45-year schedule is $22,024,504, so the present value of the cash flows from the harvest are:

PVHarvest = [($22,224,379/13.21111)] / (1 + .0608)25

PVHarvest = $385,073.30

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/16.6638

PVConservation = 每$174,800.29

And the value of the conservation fund today is:

PVConservation = 每$174,800.29/(1+ .0659)25

PVConservation = 每$35,458.26

So, the NPV of a 45-year harvest schedule is:

NPV = $5,087,231 + 681.246.84 + 385,073.30 每 35,458,26

NPV = $6,1118,092.40

50-year harvest schedule:

Revenue $64,610,783

Tractor cost 11,280,000

Road 4,230,000

Sale preparation & admin 1,480,500

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $41,170,283

Taxes 14,409,599

Net income (OCF) $26,760,684

The PV of the first harvest in 30 years is:

PVFirst = $26,760,684/(1 + .0608)30

PVFirst = $4,561,202

Thinning will also occur on a 50-year schedule, with the next thinning 50 years from today. The effective 50-year interest rate for the project is:

50-year project interest rate = [(1 + .0608)50] 每 1

50-year project interest rate = 1,808.52%

We also need the 50-year interest rate for the conservation fund, which will be:

50-year conservation interest rate = [(1 + .0659)50] 每 1

50-year conservation interest rate = 2,330.24%

Since we have the cash flows from each thinning, and the next thinning will occur in 50 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/18.0852

PVThinning = $497,644.82

The operating cash flow from each harvest on the 50-year schedule is $26,531,559, so the present value of the cash flows from the harvest are:

PVHarvest = [($26,760,684/18.0852] / (1 + .0608)30

PVHarvest = $497,644.82

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/23.3024

PVConservation = 每$171,485.25

And the value of the conservation fund today is:

PVConservation = 每$171,485.25/(1+ .0659)30

PVConservation = 每$25,283.50

So, the NPV of a 50-year harvest schedule is:

NPV = $4,561,202 + 497,644.82 + 252,206.52 每 25,283.50

NPV = $5,285,770.21

55-year harvest schedule:

Revenue $72,972,113

Tractor cost 12,600,000

Road 4,725,000

Sale preparation & admin 1,653,750

Excavator piling 1,200,000

Broadcast burning 2,287,500

Site preparation 1,162,500

Planting costs 1,800,000

EBIT $47,543,363

Taxes 16,640,177

Net income (OCF) $30,903,186

The PV of the first harvest in 35 years is:

PVFirst = $30,903,186/(1 + .0608)35

PVFirst = $3,922,074

Thinning will also occur on a 55-year schedule, with the next thinning 55 years from today. The effective 55-year interest rate for the project is:

55-year project interest rate = [(1 + .0608)55] 每 1

55-year project interest rate = 2,463.10

We also need the 55-year interest rate for the conservation fund, which will be:

55-year conservation interest rate = [(1 + .0659)55] 每 1

55-year conservation interest rate = 3,243.60%

Since we have the cash flows from each thinning, and the next thinning will occur in 55 years, we can find the present value of future thinning on this schedule, which will be:

PVThinning = $9,000,000/24.6310

PVThinning = $365,392.74

The operating cash flow from each harvest on the 55-year schedule is $30,647,248, so the present value of the cash flows from the harvest are:

PVHarvest = [($30,903,186/24.6310] / (1 + .0608)35

PVHarvest = $159,233.03

Now we can find the present value of the conservation fund deposits. The present value of these deposits is:

PVConservation = 每$162,500 每 $162,500/32.4360

PVConservation = 每$169,097.37

And the value of the conservation fund today is:

PVConservation = 每$169,097.37/(1+ .0659)35

PVConservation = 每$18,121.00

So, the NPV of a 55-year harvest schedule is:

NPV = $3,922,074 + 365,392.74 + 159,233.03 每 18,121.00

NPV = $4,428,578.40

The company should use a 45-year harvest schedule since it has the highest NPV. Notice that when the NPV began to decline, it continued declining. This is expected since the growth in the trees increases at a decreasing rate. So, once we reach a point where the increased growth cannot overcome the increased effects of compounding, harvesting should take place. There is no point further in the future which will provide a higher NPV.

- Managerial Finance -
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