CHAPTER 9 C-1
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:
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:
r = .0659, or 6.59%
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:
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:
CHAPTER 9 C-2
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.
value of the conservation fund costs.
40-year harvest schedule:
Revenue
$73,956,303
Tractor cost
17,760,000
Road
7,215,000
Sale preparation & admin
2,442,000
Excavator piling
1,275,000
Broadcast burning
2,212,500
Site preparation
1,162,500
Planting costs
2,287,500
EBIT
$39,601,803
Taxes
13,860,631
Net income (OCF)
$25,741,172
The PV of the first harvest in 20 years is:
We also need the 40-year interest rate for the conservation fund, which will be:
CHAPTER 9 C-3
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:
So, the NPV of a 40-year harvest schedule is:
CHAPTER 9 C-4
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 = $11,250,000/13.2111
The operating cash flow from each harvest on the 45-year schedule is $38,354,492, so the present
value of the cash flows from the harvest are:
PVHarvest = [($38,354,492/13.21111)]/(1 + .0608)25
And the value of the conservation fund today is:
PVConservation = –$1,033,510.02/(1+ .0659)25
So, the NPV of a 45-year harvest schedule is:
NPV = $8,779,464.38 + 851,558.55 + 664,553.59 – 209,647.65
CHAPTER 9 C-5
effective 50-year interest rate for the project is:
50-year project interest rate = [(1 + .0608)50] – 1
50-year project interest rate = 1,808.52%
find the present value of future thinning on this schedule, which will be:
PVThinning = $11,250,000/18.0852
PVThinning = $622,056.02
value of the cash flows from the harvest are:
PVHarvest = [($47,663,546/18.0852]/(1 + .0608)30
PVHarvest = $449,205.91
55-year harvest schedule:
Revenue
$150,522,750
Tractor cost
36,000,000
Road
14,625,000
Sale preparation & admin
4,950,000
Excavator piling
1,275,000
Broadcast burning
2,212,500
Site preparation
1,162,500
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Planting costs
2,287,500
EBIT
$88,010,250
Taxes
30,803,588
Net income (OCF)
$57,206,663
The PV of the first harvest in 35 years is:
PVFirst = $57,206,663/(1 + .0608)35
PVFirst = $7,260,375.86
effective 55-year interest rate for the project is:
55-year project interest rate = [(1 + .0608)55] – 1
55-year project interest rate = 2,463.10%
value of the cash flows from the harvest are:
PVHarvest = [($57,206,663/24.6310]/(1 + .0608)35
PVHarvest = $294,765.40
Now we can find the present value of the conservation fund deposits. The present value of these
deposits is:
PVConservation = –$975,000 – $975,000/32.4360
PVConservation = –$1,005,059.19
And the value of the conservation fund today is:
CHAPTER 9 C-7
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.