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Financial Analysis

Larry Teeter

Auburn University

Timber management is inherently a long term proposition, so an appreciation of the fact that benefits received in the future are less valuable than the same benefits received in the present is important.  Discounted cash flow techniques including, for example, net present value, internal rate of return and benefit/cost ratio form the basis for addressing many of the operational questions facing timber managers. 

Capital Budgeting Criteria

Net present value is the most fundamental of these methods and basically tries to compare the value of benefits received in the future with capital required for investment today.  It hinges on the concept of a discount rate or acceptable/alternate rate of return.  This is a rate of return on investment that is available to the investor (timber manager/owner) through investments separate from the one being considered in the timber management question.  The technique determines a lump sum value in the present that is viewed as equivalent to receiving the projected stream of future revenues available through the timber investment.  The formula for calculating the present value of a stream of cash flows is:

Net Present Value = CF₀/(1+r)⁰ + CF₁/(1+r)¹ + CF₂/(1+r)² + CF₃/(1+r)³ + ... + CF_n/(1+r)ⁿ
where the CF_i are positive and negative cash flows occurring in year n and r is the discount rate.

As an example, a simple timber management regime might include investing in stand establishment in year 0 (-$250), revenue from thinnings at ages 15 ($400) and 20 ($400), and receipts from a final harvest at age 30 ($2400).  The net present value (NPV) of this regime at a 6% discount rate can be calculated as follows:

    NPV = -250/1.06⁰ + 400/1.06¹⁵ + 400/1.06²⁰ + 2400/1.06³⁰

            =   -250 + 166.91 + 124.72 + 417.86  

            =    459.49

When NPV is positive, the investment is deemed profitable since it is projected to earn in excess of the 6% required by the discount rate. This prescription yields a 6% return on the initial investment of $250 plus an additional 459.49 present value dollars.  Any investment analysis that produces a positive NPV is considered worthy since the discount rate represents the best investment return available other than the one being analyzed.  Many decisions in timber management are supported with this basic technique.  Evaluating the economic feasibility of a new silvicultural treatment simply requires an estimate of the treatment’s cost and the value of the growth and yield response to the treatment.  Then, assuming the timing of the final harvest is unchanged, the “with treatment” scenario cash flows can be compared to the “without treatment” scenario cash flows to see if NPV increases.  If it does, the treatment is considered profitable.

Internal rate of return (IRR) is also frequently used by forest managers.  It represents the rate of return earned by all investments in a cash flow scenario.  Mathematically, it is the discount rate ‘r’ that makes discounted revenues equal discounted costs:

       

Determining the IRR for a scenario with multiple cash flows is more difficult and involves a trial-and-error process best left to a financial calculator or a spreadsheet.  The cash flows referenced earlier for the timber stand management example yield an IRR of 10.7608%.  According to the criterion, if the IRR is greater than the rate available from alternative investments (alternate rate of return, discount rate, or firm hurdle rate) the appropriate decision would be to invest.  What logically follows then is that NPV would be 0 if the discount rate was set at 10.7608%.  This equivalence between the two financial measures (NPV and IRR) implies that, depending on the objectives of the decision maker and the cash flows associated with the particular financial scenario, either method should yield the same recommendation regarding the advisability of investment.

A third financial analysis tool used most frequently by public forest managers is Benefit/Cost ratio.  According to this criterion, if the ratio of discounted benefits to discounted costs exceeds 1, the investment being analyzed is efficient.  The B/C ratio can be represented using the variables defined previously:

                                               =   B/C ratio                                         

This measure will also yield a decision to invest or not that is equivalent to the NPV and IRR criteria.  If the NPV is positive (indicating a recommendation to invest), the IRR will be greater than the discount rate and the B/C ratio will be greater than 1.  If NPV is negative (indicating that the alternative represented by the discount rate is a better investment), the IRR will be less than the discount rate and the B/C ratio will be less than one.

Applications

Each of these criteria has inherent problems.  NPV and B/C ratio each require advance knowledge of the appropriate discount rate that represents the expected return on the next best investment alternative.  For timber management firms and government agencies, this information may be given or relatively straightforward to determine.  For private (family) timberland owners this rate may be more difficult to determine precisely.  A solution to this dilemma may be sensitivity analysis to determine how sensitive the decision (invest/do not invest) is over a range of possible discount rates that are assumed to bracket the actual discount rate.  An additional shortcoming of the B/C ratio is that by itself, it does not provide any indication of the magnitude of the net discounted returns.  A similar complaint can be made for IRR.  The measure is simply a rate of return (or in the B/C case, a ratio), with no associated information about the dollar magnitude of net returns expected.  If the objective of the firm (government/NGO/landowner) is to maximize benefits, NPV provides more information about the ability of a particular investment to reach that goal.  In addition, although there is no need to provide an a priori estimate of the alternate rate of return, some benchmark must be established for judging whether a particular IRR is sufficient or not. 

In general though, when investigating the advisability (invest or not) of a single timber management investment, either of the three techniques should provide the same decision.  Problems can develop, however, when using the techniques to 1) choose the ‘best’ project from among a list of competing ones of the same duration, or 2) comparing the performance of investments of unequal duration.           

Of these two exceptions, the more important question for many forest managers is evaluating competing investments that involve differences in investment term, which is often specified as rotation length.  This includes questions about determination of the financially optimal rotation length or the value of silvicultural treatments that provide the opportunity for adjusting the rotation length.

The Faustmann Equation

The single rotation NPV calculation has a focus on assessing the returns to management activities and ignores the primary asset responsible for timber production, land.  In 1849, Martin Faustmann proposed a method to calculate an estimate of the value of the land asset.  Land Expectation Value (LEV, a.k.a. soil expectation value, bare land value) provides an estimate of the value of land when its most valuable use is forestry.  An assumption of the method is that forestry will continue to be the most profitable use of the land in the future, so returns from timber rotations after the initial one are explicitly considered in the assessment of land value.

According to Faustmann, land’s value in forestry can be measured by determining the present value of a perpetual series of net revenue payments associated with a series of perpetual forest rotations.  The future value of the first payment received at the end of the first rotation would be:

Where all variables are defined as previously.  Conceptually, a net return will be received at the end of each rotation, and this amount can be thought of as a periodic annuity, payable at the end of each future rotation into perpetuity.  By incorporating this payment in the equation for the NPV of a perpetual periodic annuity and including the present value of perpetually recurring annual benefits and costs we arrive at the Faustmann equation:            

Where a and c are annual revenues and costs, respectively, and have been treated separately from the other management costs and revenues (following Klemperer 1996).  The Faustmann equation will return a present value larger than the single rotation NPV formula and is closer to the true bare land value because it acknowledges the value of future rotations.   Note that this may not correspond to the market value of land for forestry since there might be competing uses for the land that have higher value.  In addition, other investors may have higher/lower opportunity costs of capital and their corresponding LEVs would be lower/higher as a result.  Finally, the managerial strategy presented here may not be the optimal one.  Other strategies may yield a higher LEV.

Although some landowners might be interested in knowing the bare land value of their properties, the more common use of the LEV equation is for ranking alternative management strategies to determine the best plan for establishing and managing a timber stand.  As mentioned above, a number of elements come together to form what is known as a timber management prescription.  Different initial stand densities, different intermediate treatments (fertilization, pruning, weed control), different thinning plans and different rotation ages can be combined to characterize a unique management prescription that can be evaluated using the Faustmann formula.  Ranking alternative prescriptions using single rotation NPV or some other (possibly IRR) criteria is problematic unless the rotation lengths are equal.  This is because when the competing investments have different investment lives (such as comparing a 25-year rotation to a 30-year rotation) assumptions have to be made about the potential for reinvesting the returns from the shorter investment to equal the term of the longer one.  LEV on the other hand compares both prescriptions over an infinitely long investment horizon.  Both prescriptions (investments) are assumed to repeat indefinitely after the first rotation.  Their LEVs then can be compared directly to determine the most profitable management strategy.   

An alternative to LEV for this type of application is Equivalent Annual Annuity (sometimes called Equivalent Annual Income).  Since LEV represents the present value of the land asset managed according to a particular timber management regime into perpetuity, the Equivalent Annual Annuity is the annual annuity/income/rental payment in perpetuity that would be equivalent to receiving the LEV sum today.  This measure (EAA) might be useful when comparing the value of the land in its use for timber production to its value in some other use such as agriculture where income or rental payments are received annually.  This method implicitly associates each investment with an infinite time horizon (as does LEV) and assumes that NPV is known.  Then EAA can be determined:

where r is the discount rate and t is the term of the investment (or rotation age).  Maximum EAA indicates the preferred investment.

The foregoing discussion presents some of the most basic and common methods for evaluating timber stand management alternatives.  Many variations of these methods have been developed to incorporate forecasts of future market conditions, taxes, environmental and market risks, and the value of other products and services (in addition to timber) provided by the timber stand over the course of a rotation.   More complicated models incorporating the same basic methods may be necessary when the management of a given stand is constrained by management actions taken on adjacent stands or other stands in a forest management portfolio.