Posted by Bunyan Lumber, LLC, harvests timber and delivers l on Thursday, October 27, 2011 at 8:26am.
CHAPTER 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 ¡Á 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 ¨C .35)($250,000)
Aftertax conservation fund cost = $162,500
For each analysis, the revenue and costs are:
Revenue = [¡Æ(% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C$162,500/11.8387
PVConservation = ¨C$176.226.22
And the value of the conservation fund today is:
PVConservation = ¨C$176,226.22/(1+ .0659)20
PVConservation = ¨C$49,182.52
So, the NPV of a 40-year harvest schedule is:
NPV = $4,496,956 + 939,286.45 + 469,325.52 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C $162,500/16.6638
PVConservation = ¨C$174,800.29
And the value of the conservation fund today is:
PVConservation = ¨C$174,800.29/(1+ .0659)25
PVConservation = ¨C$35,458.26
So, the NPV of a 45-year harvest schedule is:
NPV = $5,087,231 + 681.246.84 + 385,073.30 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C $162,500/23.3024
PVConservation = ¨C$171,485.25
And the value of the conservation fund today is:
PVConservation = ¨C$171,485.25/(1+ .0659)30
PVConservation = ¨C$25,283.50
So, the NPV of a 50-year harvest schedule is:
NPV = $4,561,202 + 497,644.82 + 252,206.52 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C $162,500/32.4360
PVConservation = ¨C$169,097.37
And the value of the conservation fund today is:
PVConservation = ¨C$169,097.37/(1+ .0659)35
PVConservation = ¨C$18,121.00
So, the NPV of a 55-year harvest schedule is:
NPV = $3,922,074 + 365,392.74 + 159,233.03 ¨C 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.
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 ¡Á 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 ¨C .35)($250,000)
Aftertax conservation fund cost = $162,500
For each analysis, the revenue and costs are:
Revenue = [¡Æ(% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C$162,500/11.8387
PVConservation = ¨C$176.226.22
And the value of the conservation fund today is:
PVConservation = ¨C$176,226.22/(1+ .0659)20
PVConservation = ¨C$49,182.52
So, the NPV of a 40-year harvest schedule is:
NPV = $4,496,956 + 939,286.45 + 469,325.52 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C $162,500/16.6638
PVConservation = ¨C$174,800.29
And the value of the conservation fund today is:
PVConservation = ¨C$174,800.29/(1+ .0659)25
PVConservation = ¨C$35,458.26
So, the NPV of a 45-year harvest schedule is:
NPV = $5,087,231 + 681.246.84 + 385,073.30 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C $162,500/23.3024
PVConservation = ¨C$171,485.25
And the value of the conservation fund today is:
PVConservation = ¨C$171,485.25/(1+ .0659)30
PVConservation = ¨C$25,283.50
So, the NPV of a 50-year harvest schedule is:
NPV = $4,561,202 + 497,644.82 + 252,206.52 ¨C 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] ¨C 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] ¨C 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 = ¨C$162,500 ¨C $162,500/32.4360
PVConservation = ¨C$169,097.37
And the value of the conservation fund today is:
PVConservation = ¨C$169,097.37/(1+ .0659)35
PVConservation = ¨C$18,121.00
So, the NPV of a 55-year harvest schedule is:
NPV = $3,922,074 + 365,392.74 + 159,233.03 ¨C 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.
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