CHAPTER 7 C-1
CHAPTER 7
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:
The conservation funds are expected to grow at a slower rate than inflation, so the real return for the
conservation fund will be:
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:
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:
For each analysis, the revenue and costs are:
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.
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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
40-year harvest schedule:
Revenue $40,359,135
Tractor cost 9,870,000
Road 3,525,000
Sale preparation & admin 1,269,000
The PV of the first harvest in 20 years is:
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:
We also need the 40-year interest rate for the conservation fund, which will be:
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 thinnings on this schedule, which will be:
The operating cash flow from each harvest on the 40-year schedule is $14,036,838, so the present
value of the cash flows from the harvests are:
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Now we can find the present value of the conservation fund deposits. The present value of these
deposits is at Year 20 is:
And the value today is:
PVConservation = –$176,226.22/(1 + .0659)20
PVConservation = –$49,182.52
So, the NPV of a 40-year harvest schedule is:
45-year harvest schedule:
Revenue $47,051,600
Tractor cost 11,480,000
Road 4,100,000
Sale preparation & admin 1,476,000
The PV of the first harvest in 25 years is:
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:
We also need the 45-year interest rate for the conservation fund, which will be:
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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 thinnings on this schedule, which will be:
The operating cash flow from each harvest on the 45-year schedule is $16,832,140, so the present
value of the cash flows from the harvests are:
Now we can find the present value of the conservation fund deposits. The present value of these
deposits at Year 25 is:
And the value today is:
PVConservation = –$172,251.67/(1 + .0659)25
PVConservation = –$34,941.27
So, the NPV of a 45-year harvest schedule is:
50-year harvest schedule:
Revenue $49,699,440
Tractor cost 12,110,000
Road 4,325,000
Sale preparation & admin 1,557,000
The PV of the first harvest in 30 years is:
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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:
We also need the 50-year interest rate for the conservation fund, which will be:
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 thinnings on this schedule, which will be:
The operating cash flow from each harvest on the 50-year schedule is $17,944,836, so the present
value of the cash flows from the harvests are:
Now we can find the present value of the conservation fund deposits. The present value of these
deposits is at Year 30 is:
And the value today is:
So, the NPV of a 50-year harvest schedule is:
55-year harvest schedule:
Revenue $52,057,863
Tractor cost 12,670,000
Road 4,525,000
Sale preparation & admin 1,629,000
Excavator piling 750,000
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The PV of the first harvest in 35 years is:
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:
We also need the 55-year interest rate for the conservation fund, which will be:
55-year conservation interest rate = [(1 + .0659)55] – 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 thinnings on this schedule, which will be:
The operating cash flow from each harvest on the 55-year schedule is $18,937,011, so the present
value of the cash flows from the harvests are:
Now we can find the present value of the conservation fund deposits. The present value of these
deposits is at Year 35 is:
And the value today is:
PVConservation = –$169,509.87/(1 + .0659)35
PVConservation = –$17,950.88
So, the NPV of a 55-year harvest schedule is:
The company should use a 40-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
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