The Forestry Source - February 2011 - (Page 13)
Here’s How to...
Value Pre-Commercial Timber Stands (A Second Look)
Table 1. The effects of land opportunity costs on precommercial stand valuation, from “Here’s How to... Value Precommercial Timber Stands,” by Thomas J. Straka, The Forestry Source, August 2010.
By B. Bruce Bare n the August 2010 edition of The Forestry Source, Professor Thomas J. Straka discussed how to “Value Precommercial Timber Stands.” Through several numerically correct examples he demonstrated how this valuation should be conducted. However, owing to the inherent complexity of forest valuation, several issues require further clarification to help readers gain a deeper understanding of valuation methodology. Perhaps the most important is the omission of any reference to the soil expectation value (SEV) associated with the sample timber investment illustration carried throughout the article. The SEV provides the maximum value of an acre of bare land devoted to the perpetual production of timber crops over a given production cycle. In his article, Professor Straka assumes a simple even-aged timber investment under conditions of certainty wherein a new plantation is established on a bare acre at a cost of $150/acre with a planned clearcut at age 25, yielding a projected harvest income of $2,550/acre. A real interest rate of 8 percent is used to bring all costs and revenues to a common point in time. Under Professor Straka’s assumption that this cycle of costs and revenues repeats in perpetuity, the SEV associated with the investment is: SEV = [-$150*(1.08)25 + $2,550] / [(1.08)25 -1] = $260.36/acre
Table 2. The effect of interest rates on pre-commercial stand valuation, from “Here’s How to... Value Precommercial Timber Stands,” by Thomas J. Straka, The Forestry Source, August 2010
methods were defined by Martin Faustmann in his 1849 treatise.1 The first method provides for compounding all costs incurred at 8 percent until age 12. In the example, we have two costs: stand establishment and land rent. Thus, we calculate the value of the stand at age 12 as: H = $150*(1.08)12 + (.08*$260.36)*[(1.08)12 -1]/.08 = $773.00/acre In this calculation, the land rent is $20.83/acre (i.e., 0.08*$260.36) and represents the annual opportunity cost of keeping the land in its current use under the stated conditions. The stand value (H) only accounts for the economic value of the pre-commercial crop and does not include the land value. We must add the land value (SEV) to the stand value (H) to obtain the total value of the investment (i.e., the land and timber value = $1,033.36/ acre). The second method provides for discounting all revenues and costs expected from age 12 until the end of the first rotation. Here, we calculate the value of the stand at age 12 as: h = $2,550/(1.08)13 - (.08*$260.36) *[(1.08)13 -1] / [.08*(1.08)13] = $773.00/acre The two methods yield identical results for the stand value, because we assume that the current 12-year-old stand has been
Under the above conditions, this is the maximum amount a prudent investor will be willing to spend to purchase an acre of bare forestland and then grow successive crops of timber in perpetuity and earn 8 percent on the investment. This is a critical piece of information to an investor, because it means that any land cost greater (less) than $260.36/acre will earn less (more) than an 8 percent return on investment. In fact, as Straka shows, if we assume that bare land costs $400/acre, the return on investment drops to 6.95 percent. An investor requiring an 8 percent return would not pursue the timber investment under these assumptions. Next, the issue of placing a value on an acre of immature timber is addressed. In the illustrative example, we wish to find the economic value of a 12-year-old acre of pre-commercial timber. If we assume that this acre is managed under the conditions stated above, we have two ways to determine the value sought. Both of these
managed under the same economic and biological conditions as all future 12-yearold stands. If this is not the case, the second method must be used to obtain the correct stand value (h). This is so because we must always use values associated with the best future use of the land in our stand value calculation. Even assuming that the land is best used for continued timber production, it is very likely that the SEV for future timber crops will be different (hopefully higher) than what we calculated when the 12-year-old timber stand was established. If so, the higher land rent will exert economic pressure to harvest the current stand before age 25. This can readily be seen in the formula for the stand value (h), where the present value of the annual land rent is subtracted from the present value of the expected harvest value. If a higher future land value is assumed, a higher annual land rent is incurred each year the current stand is retained. This leads to the harvest of the current stand sooner than otherwise planned. Because further calculation is needed to determine the best time to harvest the current stand prior to age 25, I do not pursue this issue further in this article. Although Professor Straka initiates his investment analysis using an 8 percent real interest rate, he soon introduces additional interest rates into the discussion. While any interest rate can be used in an investment analysis, the rationale for doing so must be well articulated. To illustrate, if we set the real interest rate
equal to 12 percent, our SEV = $0/acre. This means that if we desire to earn a rate of return of 12 percent, the most we can pay to purchase bare forestland is $0/acre. As previously described, an assumed land cost of less than $260.36/acre is consistent with a return on investment greater than 8 percent. More specifically, an assumed land cost of $0/acre yields a 12 percent return on investment. As Professor Straka shows in his Table 1, if we assume that our interest rate is 12 percent, such that the land has no value for producing timber under the assumed conditions (i.e., SEV = $0/acre), the value of a 12-year-old pre-commercial stand is $584.40/acre. This is simply the $150/acre stand-establishment cost compounded for 12 years at 12 percent. Thus, the land and timber value = $584.40/acre. Suppose the real interest rate is set to 6.95 percent. The corresponding SEV = $399.91/acre, the value of a 12-year-old stand = $831.66/acre, and the land and timber value = $1,231.57/acre. These stand values are shown in Table 1 of the original article, but readers must be aware that different interest rates are used when calculating each stand value shown in the table. Table 2 in the original article further demonstrates the effects of changing interest rates on stand values. This table also illustrates why we must select the proper valuation formula when calculating stand values. For instance, using an 8 percent real interest rate, the SEV = $260.36/acre, as previously shown. However, if we use a bare land value of $400/acre to value a 12-year-old timber stand, we must use the second stand value formula to calculate h = $684.71/acre. If we incorrectly use the first stand value formula, we find H = $984.99/acre, which is incorrect because the wrong land value is used in the calculation. This example clearly demonstrates that the second stand valuation formula, which utilizes the future bare land value (i.e., $400/acre) and not the land value in use at the time the 12-year-old timber crop was established (i.e., $260.36/acre) is the correct formula to use to value the 12-yearold timber stand. Thus, as shown above, if the land value in effect at the time the 12year-old timber stand is valued is $400/acre, an 8 percent interest rate produces a stand value of $684.71/acre. If we can purchase bare land for less than $260.36/acre when the interest rate is
(“How to” continues on page 14)
In Further Praise of Flagging
E. Richard Hoebeke, Cornell University, Bugwood.org
By Steve Wilent y invitation to share stories about “How have you used flagging, biodegradable or otherwise, an unusual way?” (at the end of the bit about biodegradable flagging in the December Field Tech) drew a response from Bill Love, CF, a private forestry specialist with the Idaho Department of Lands. Bill served as treasurer of the Selkirk Chapter, Inland Empire SAF, in 2010. He writes: “I suspect that your request for unusual uses for flagging reminded many of us field foresters of a time when nothing else would
get the job done. Or, more likely, flagging was the only thing we had with us to get the job done. That was my case one day back in the mid-1980s. While creeping down a steep, rocky road in 4-wheel drive lowrange (a road I probably should not have been on in the first place), a universal joint failed and one end of the front driveline hung down on the ground. You guessed it—a roll of flagging rescued me. Just for good measure I wrapped about half a roll of flagging around the driveline to secure it to the frame of the pick-up. This quick fix got me back to town 20 miles away just fine.” See? You really shouldn’t leave home
without a roll of two of flagging. Thanks for writing, Bill. By the way, the hanks of biodegradable flagging that I hung in the woods near my home appear to be good as new after three months of Pacific Northwest fall and winter weather. I’m beginning to wonder if they’ll biodegrade at all. Stay tuned for the latest flagging news. Have a story about a road you probably shouldn’t have been on in the first place (one that you’re willing to share with Source readers)? Let me know: firstname.lastname@example.org.
The Forestry Source
If you would like to try to load the digital publication without using Flash Player detection, please click here.