Tree Value

Case 5: Tree Values

Questions to address by each group before presentations as well as during the presentations:

1 What is the appropriate discount rate to use?

My assumption would be inflation + the price increase of lumber per year.

Avg. Inflation = 3% how did this come?

Avg. price increase above inflation for wood is 1-3% (we would go with 2%)

3%+2% = 5% how did this come?

This is the only thing I can think of, any other thoughts for this question would be great.

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4.14

3 What is the simple cash flow and PV for a hypothetical tree with no grade changes?

For one tree it would depend upon the size and growth. If we are assuming 2” growth in 10 years than it could be one of two values.

14” = 110 Board Feet/ Tree16” = 180 Board Feet/ Tree

Assume that the appropriate cost of capital is 240 basis points above the ten-year government bond rate. To calculate the cost of capital, should you add the 240 bp to a ten-year Treasury Bond that yielded 6.04% in June2000 or a ten-year Treasury Inflation Protected Security (TIPS) that yielded 4.14% in June 2007? How do you decide?

Using the TIPS would be more accurate an this instant as we don’t have the actual rate of inflation we can use the TIPS for the discount rate, the cash inflows than do not need to be adjusted for inflation and than we can just use a growth rate as the increased price above inflation. Thus we can ignore inflation as it will be adjusted by the TIPS. As a result we can get a more accurate PV.

$40/1,000 = 0.0400 per Board Feet.

Now we can calculate the cash flow of each tree as follows.

14” = 110 * .0400 = $4.40

16” = 180 * .0400 = $7.20

14” PV

Cash Inflow/1 + (discount rate – growth rate)

4.40/1 + (0.0438-0.02)

4.40/1.0238 = $4.2977

16” PV

7.20/1 + (0.0438-0.02)

7.20/1.0238 = $7.0326

What is the simple cash flow and PV for a hypothetical tree with grade changes?

Identical to problem #3 except there is a difference in price due to the increase in quality from Grade 4 to 3.


Now if we use TIPS + 240 basis point for are discount rate and the growth rate as 2% to take in consideration of the price increase of wood the cash flow will simply be $40 MBF for the growth model because the growth rate takes in consideration the increase in cash flows and the TIPS will price in inflation. Thus to calculate the value of each tree we must change the unit to 1 Board Feet as follows.

14” = 110 Board Feet/ Tree16” = 180 Board Feet/ Tree

$120/1,000 = 0.1200 per Board Feet.

Now we can calculate the cash flow of each tree as follows.

14” = 110 * .1200 = $13.20

16” = 180 * .1200 = $21.60

14” PV

13.20/1 + (0.0438-0.02)

13.20/1.0238 = $12.8931

16” PV

21.60/1 + (0.0438-0.02)

21.60/1.0238 = $21.0979

5 Define the alternative tree-cutting strategies. What cutting time maximizes value for each strategy? Pick the highest NPV of the alternatives.

Now if we use TIPS + 240 basis point for are discount rate and the growth rate as 2% to take in consideration of the price increase of wood the cash flow will simply be $120 MBF for the growth model because the growth rate takes in consideration the increase in cash flows and the TIPS will price in inflation. Thus to calculate the value of each tree we must change the unit to 1 Board Feet as follows.

There is three basic strategies, the first is to cut all of the valuable trees down now. The second option is to wait 10 years and than chop the trees down. The third option is to chop ½ of the trees down now and cut the rest of the trees down in 10 years.

The first option of cutting all the trees down now would be valued as followed.

1200 trees are 12” = 60 Board FT/Tree = 60*1200 = 72,000 Board Feet

1200 trees are 14” = 110 Board FT/ Tree = 110 * 1200 = 132,000 Board Feet

Total Board Ft = 204,000 Board Feet = 204,000/ 1000 = 204 MBF

204 MBF *$40 = $8,160.

The second option of cutting all of the trees down in 10 years would be valued as followed. Growth rate would only be 1” for every 10 years.

960 Grade 4 Trees how did this come?480 13” = 85 Board FT/ Tree = 85*480 = 40,800 Board Feet480 15” =145 Board FT/ Tree = 145*480 = 69,600 Board FeetTotal Grade 4 Board FT = 110,400 Board FT = 110,400/1000 = 110.4 MBF110.4 MBF Grade 4 = 110.4 * 40 = $4,416

1440 Grade 3 Trees720 13” = 85 Board FT/ Tree = 85*720 = 61,200 Board Feet720 15” =145 Board FT/ Tree = 145*720 = 104,400 Board Feet

Total Grade 3 Board FT = 165,600 Board FT = 165,600/1000 = 165.6 MBF165.6 MBF Grade 3 = 165.6 * 120 = $19,872Total Value of option two = $24,288

Now we must get the PV to compare it to option one since option two requires 10 years.

$24,288/1 + (0.0438-0.02)

$24,288/1.0238 = $23,723.39

240 Trees at Grade 4 with 2” growth120 trees = 14” = 110 Board Feet/ Tree = 120*110 = 13,200 Board Feet120 trees = 16” = 180 Board Feet/ Tree = 120*180 = 21,600 Board Feet

Total Board Feet for Grade 4 = 34,800 = 34,800/1000 = 34.8 MBF

34.8 MBF Grade 4 = 34.8 * 40 = $1,392

960 Trees at Grade 3 with 2” growth480 trees = 14” = 110 Board Feet/ Tree = 480*110 = 52,800 Board Feet480 trees = 16” = 180 Board Feet/ Tree = 480*180 = 86,400 Board Feet

Total Board Feet for Grade 3 = 139,200 = 139,200/1000 = 139.2 MBF

139.2 MBF Grade 3 = 139.2 * 120 = $16,704Total Value of option three = $18,096.

Now we must get the PV to compare it to option one since option three requires 10 years.

$18,096/1+ (0.0438-0.02)$18,096/1.0238 = $17,675.32

The third option of cutting ½ the trees down now and the other ½ of the trees down in 10 years is valued as followed. We assume that we get no cash inflow from the trees we harvest now as that is the cost to manage the forest.

Assuming that we only have a ten year time frame it appears that option two, allowing the forest to grow another ten years before we chop down the good trees would net you the most money at a PV of $23,723.39 where as chopping them all down now would net you the least amount of money at a PV of $8,160. Managing the forest has a value in the middle with $17,675.32. Based on these three options, option number two would be the best for the ten year period.

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Year Inches Board/FT $/Board/FT $ Value Discount PV 0 10 20 0.04 0.8 - $0.80 5 11 40 0.04 1.6 0.0238 $1.56

10 12 60 0.04 2.4 0.0238 $2.34 15 13 85 0.04 3.4 0.0238 $3.32 20 14 110 0.04 4.4 0.0238 $4.30 25 15 145 0.04 5.8 0.0238 $5.67 30 16 180 0.04 7.2 0.0238 $7.03 35 17 230 0.04 9.2 0.0238 $8.99 40 18 280 0.04 11.2 0.0238 $10.94 45 19 315 0.04 12.6 0.0238 $12.31 50 20 350 0.04 14 0.0238 $13.67

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When would you recommend cutting a 50 year old tree that is 10” DBH? Assume no grade changes and that a hypothetical tree takes five years to grow one inch in DBH. What if it takes 10 years to grow one inch DBH? If you would recommend different times to cut the tree, please explain why reach different conclusions.

It really depends upon the time frame. If time is not an issue for Mr. Smith than the longer he can wait the more value he can get from the trees. As illustrated in the table below the PV continue to increase based upon the years he waits. The maximum amount that he can get is 20” growth in 50 years. Trees in the area do not grow pass the 20”, thus the best time to cut the trees would be in 50 years when the tree is 100 years old. Anything past 50 years the PV would start to decline as there is no growth. If Mr. Smith cannot wait 50 years, than it is in his best interest to chop the trees down at the latest time as possible so that the most growth can occur.

Now if growth was only 1” for every ten years than it would take 100 years to reach maximize profit potential. Again the longer he waits the PV still moves positive it just takes double the amount of time to reach the same PV. Now the problem is that I don’t think Mr. Smith is going to live another 100 years, so again it really depends upon his time frame, but regardless the time, the longer Mr. Smith has the more money he will make because of growth and price increase over time.

When would you recommend cutting a 50 year old tree that is 10” DBH, grows at the rate of one inch DBH each five years, and also increases one grade with each 2” growth in DBH? Is the decision the same if the tree is growing at the rate of 1” DBH over ten years?

Year Inches Board/FT $/Board/FT $ Value Discount PV 0 10 20 0.04 0.8 - $0.80

10 12 60 0.12 7.2 0.0238 $7.03 20 14 110 0.26 28.6 0.0238 $27.94 30 16 180 0.445 80.1 0.0238 $78.24 40 18 280 0.845 236.6 0.0238 $231.10 50 20 350 0.845 295.75 0.0238 $288.87

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Year Inches Board/FT $/Board/FT $ Value Discount PV 0 12 60 0.12 7.2 0.0238 $7.03

10 13 85 0.12 10.2 0.0238 $9.96 20 14 110 0.26 28.6 0.0238 $27.94 30 15 145 0.26 37.7 0.0238 $36.82 40 16 180 0.445 80.1 0.0238 $78.24

The decision again depends upon the amount of time we have. Again the PV continues to grow overtime due to increase lumber + quality + price increase. So if Mr. Smith can allow the forest to stay for 50 years and is going to live for that time frame than I suggest that he doesn’t harvest until the forest is 50 years older. Now if he doesn’t have that long than I would suggest he harvest the forest in year 30 or 40 as you would get the most increase in PV in those years. Regardless the longer he waits the more he makes.

Now as for only 1” growth every Ten years, that just stretches the Time Frame to double the year amount. Thus it would take 100 years to reach the most potential. Obviously Mr. Smith is not going to live for 100 more years so in this case it again depends on exactly how many years Mr. Smith preference is. The longer he can wait the more he will make.

For the following questions, assume that all the trees in Mr. Smith’s forest have to be cut at the same time. If Mr. Smith simply lets his trees grow, would they increase in value? When would you recommend cutting the trees if they are simply left to grow? Assume the trees grow at a rate of 1” of DBH over ten years.If Mr. Smith simply lets his trees grow they would indeed increase in value due to there growth which would provide more wood and the increase in quality of the tree grade. Below is a chart of the PV of a tree based on the lowest quality of good trees that Mr. Smith forest has which is 12” and assuming that a quality increase occurs once a tree grows 2”. Again based on this the longer Mr. Smith has the more value the forest creates. Based on this growth of 1” every 10 years the forest will reach it’s maximum at 80 years, thus 80 years would give you the highest PV. Now it all depends upon the time frame that Mr. Smith has, but I don’t think he has 80 years unless he plans on leaving the asset to his family. So if he couldn’t wait that long than I would suggest to chop the wood around the 40-60 year mark as that area has the highest PV. Again it all depends upon Mr. Smith timeline, which I assume in reality is probably closer to the 10-20 year area. Regardless the timeline the longer he waits, the more he will make.

50 17 230 0.445 102.35 0.0238 $99.97 60 18 280 0.845 236.6 0.0238 $231.10 70 19 315 0.845 266.175 0.0238 $259.99 80 20 350 0.845 295.75 0.0238 $288.87

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10 What forest management strategy, if any, would you recommend to Mr. Smith?

If Mr. Smith decides to thin and manage his forest, how would this affect its value? Assume that half the trees are thinned and that the remaining trees grow at the rate of 2” in DBH ever ten years. Also assume that a forester’s management costs are offset by the value of the thinned trees.

If Mr. Smith managed his forest after cutting half of the trees he would leave him 30 trees per acre on 40 acres that would net him 1200 trees. This is assuming that no other trees improve in grade than the ones already considered good quality. Now due to managed forest there grade change would create more value, thus in 10 years 80% of the remaining trees would increase into a better grade, or 960 of the trees. Now all trees would have 2” in growth. Managing the forest will create more value in the long-term. But if we look at only a 10 year period it is actually better to just leave the forest alone and cut down all of the good trees in 10 years. This is because if you do not cut any trees down now you will have double the amount of trees to chop in 10 years. Now a managed forest has better growth rate by 1” and more trees will increase in grade level. But this does not offset the benefit of having double the amount of trees because those trees still grow and improve in grade level. Thus if the timeframe is only for 10 years it is best to just chop all of the good trees down in 10 years. Now if Mr. Smith has a longer time frame, than the managed forest will increase the most in value over time. Thus lets say Mr. Smith had 20 years than more trees would convert to 3 grade and 2 grade and have double the growth which could overcome the benefits of double the amount of trees in a unmanaged forest. So if you had a 20 year time frame a managed forest would create the most value. The longer the time the more a managed forest creates value. The lesser the time the more money an unmanaged forest will create.

The best forest management strategy depends upon the time frame for Mr. Smith. If he only has 10 years, than I would recommend to not manage the forest and chop all of the good trees down in 10 years. Now if Mr. Smith has 20 years or more than I would suggest him to manage the forest. Regardless of the timeframe cutting all of the trees down now would not be suggested as it creates the less amount of value.

4.164

The appropriate discount rate to use

Our assumption would be govt bond rate + 200 bps for COC.

Govt Bond = 8% plus 200 bps COC 10

Avg. price increase above inflation for wood is 1-3% (we would go with 2%) growth

The simple cash flow and PV for a hypothetical tree with no grade changes?For one tree it would depend upon the size and growth. If we are assuming 2” growth in 10 years than it could be one of two values. With no grade change

Inches Board Feet/ Tree Cash flowsCoc PVIF Growth ratPV14" 110 0.04 4.4 10% 0.463 0.02 2.037216" 180 0.04 7.2 10% 0.463 0.02 3.3336

Assumption COC @ 10%

$ Grade 4 Per Tree per board feet40 1000 0.04PV = Cash Inflow*PVIF

The simple cash flow and PV for a hypothetical tree with no grade changes?For one tree it would depend upon the size and growth. If we are assuming 2” growth in 10 years than it could be one of two values. With no grade change

What is the simple cash flow and PV for a hypothetical tree with grade changes

There is a difference in price due to the increase in quality from Grade 4 to 3.


Inches Board Feet/ Tree Cash flowsCoc PVIF Growth ratPV14" 110 0.12 13.2 10% 0.463 0.02 6.111616" 180 0.12 21.6 10% 0.463 0.02 10.0008

$ Grade 4 Per Tree per board feet120 1000 0.12PV = Cash Inflow*PVIF


Define the alternative tree-cutting strategies. What cutting time maximizes value for each strategy? Pick the highest NPV of the alternatives.

The 1st option of cutting all the trees down now would be valued as followed.

Total Trees Inches No of trees Board Feet/ Tree Total board feet2400 12" 1200 60 72,000

14" 1200 110 132,000 204,000

The 2nd option of cutting all of the trees down in 10 years would be valued as followed. Growth rate would only be 1” for every 10 years.

Inches Board Feet/ Tree Total board feet40% 0f 2400 960Grade 4 Trees 480 13" 85 40,800

480 15" 145 69,600 110,400

Inches Board Feet/ Tree Total board feet60% of 2400 1440Grade 3 Trees 720 13" 85 61,200

720 15" 145 104,400 165,600

2400 1200 sell now1200 remaing

Inches Board Feet/ Tree Total board feet20% of total 240Grade 4 Trees 120 14" 110 13,200 2"Growth 120 16" 180 21,600

34,800

There is three basic strategies, the first is to cut all of the valuable trees down now. The second option is to wait 10 years and than chop the trees down. The third option is to chop ½ of the trees down now and cut the rest of the trees down in 10 years.

The 3rd option of cutting ½ the trees down now and the other ½ of the trees down in 10 years is valued as followed. We assume that we get no cash inflow from the trees we harvest now as that is the cost to manage the forest.

Grade 3 Trees 80% 9602"Growth 480 14" 110 52,800

480 16" 180 86,400 139,200

Now 8160 10After 10 yrs 11250 2050% now/50% after 10 8381 30

4050607080


Define the alternative tree-cutting strategies. What cutting time maximizes value for each strategy? Pick the highest NPV of the alternatives.

Per Trees No of trees $ Price for Grade 4 Total

1000 204 40 8160

The 2nd option of cutting all of the trees down in 10 years would be valued as followed. Growth rate would only be 1” for every 10 years.


1000 110.4 40 4416


1000 165.6 120 19872

Total Value 24288COC 10%PVIF 0.463$ PV 11,245.34


1000 34.8 40 1392

There is three basic strategies, the first is to cut all of the valuable trees down now. The second option is to wait 10 years and than chop the trees down. The third option is to chop ½ of the trees down now and cut the rest

The 3rd option of cutting ½ the trees down now and the other ½ of the trees down in 10 years is valued as followed. We assume that we get no cash inflow from the

1000 139.2 120 16704

Total 18096COC 10%Growth 2%PVIF 0.463$ PV 8,378.45


There is three basic strategies, the first is to cut all of the valuable trees down now. The second option is to wait 10 years and than chop the trees down. The third option is to chop ½ of the trees down now and cut the rest

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