## 2. Capital budgeting

In forestry, capital budgeting is an approach to deciding on how to invest money ("capital budget") so its value is maximized. Hence, we compare different investment projects in order to choose the most profitable one by taking into account projects that are outside of the forestry sector. The positive interest rate (the opportunity cost of capital) implies that what we basically want is a mix of projects without maximizing any particular one (i.e., forestry output). By maximizing the total social wellbeing from all activities combined means also that we are not maximizing the physical timber output (i.e., m3 per ha) on commercial timberlands.

For capital budgeting, we need to know (or predict) that for every investment option the timing of all revenues and costs (including the initial investment cost) and the interest rate will be used in discounting. In addition, we need criteria for ranking investments and choosing the best one. We will briefly introduce three of the several available criteria. We will then apply these criteria to reject/accept a simplified forestry investment.

Criteria #1: Net present value

Net present value (NPV) is the present value (PV) of revenues minus the present value (PV) of costs. Importantly, single revenues and costs are each discounted first and after that discounted values are summed to get NPV.

where Rn=revenues in each year n, Cn=costs in each year n, r=discount rate, percent/100, n=an index for years and T=number of years of discounting.

If NPV is zero or greater, a project is acceptable for an investor. The NPV provides the amount that the investor could pay in addition to an initial investment cost in year 0 and still earn a r*100 percent rate of return.

Criteria #2: Benefit/cost ratio

The benefit/cost ratio is useful in allocating a fixed sum of money between different investment alternatives. The B/C ratio for a project is the present value of revenues divided by the present value of costs. If the B/C ratio for an investment project is one or greater, the project is acceptable. When the B/C ratio is 1, the NPV is 0.

Criteria #3: Internal rate of return

The Internal rate of return (IRR) of a project is the discount rate where the present value of revenues minus the present value of costs (i.e. NPV) equals zero.

A project is acceptable if IRR≥r, where r is rate of return from the next best investment opportunity (i.e., the minimum acceptable rate of return).

The three criteria are very closely related. For a single project they provide a similar reject/accept decision. When the discount rate exceeds project's IRR, and the NPV is negative and B/C<1 then the project is rejected by any of the three criteria. When the IRR exceeds the discount rate, NPV>0 and B/C>1 the project is acceptable by all criteria.

However, by ranking several projects from best to worst, using the criteria introduced, we do not always have the same ordering. The ranking becomes more important when capital is limited. However, this issue is excluded at this stage. It is also possible that for certain projects (with late costs) the NPV may be zero at more than one value of r. In this case, a project may have multiple IRRs and the investment is said to be ambiguous.

The NPV for an illustrative forestry project (like in Table E3) shows that the investor could pay 838 €/ha in addition to 1 000 €/ha- in initial investment costs and still earn a 4 % rate of return. Since r=0.04 is lower than IRR, BC-ratio is greater than one and the NPV is greater than zero, the project can be acceptable by all criteria.

Table E3: Cash flow (€/ha) and the three investment criteria for a forestry (stand establishment) project

 Year Revenue/Cost Present value (r=0.04) 0 - 1000 -1000 6 -200 -158 30 +800 +247 45 +3000 +514 60 +13000 +1236 PV revenues (r=0.04) 1996 PV costs (r=0.04) 1158 NPV (r=0.04) 838 BC-ratio (r=0.04) 1.72 IRR 5.12% (a trial and error approach with Excel)

The cost of artificial regeneration by planting (2000 Norway Spruce seedlings per ha in year 0) is 1,000 € per ha (site preparation= 200 €, seedling material =400 €, work=280 € and planning=120 €) and the cost of precommercial thinning (year 6)= 200 € per ha. The revenues come from two thinnings (years 30 & 45) and from the final cut (year 60).

In Table E4 we can see that the discount rate plays a critical role in investment calculations (in general and especially) in forestry projects with a very long production period (see also Figure E8: discounting).

Table E4: NPVs and B/C ratios for a stand establishment project (cash flow in table E3) at different discount rates

 Discount Rate NPV (€/ha) B/C 0.02 4457 4.78 0.04 838 1.72 0.05 66 1.06 0.0512 (IRR) 0 1.00 0.06 -390 0.66 0.08 -824 0.27

Figure E8: Discounting: Present value of 1000 euros future cutting revenue (in year 30) at 3 %, 5 % and 7 % interest rates

In general, if capital markets are well functioning with a lending rate of interest equaling the deposit rate of interest, it is justified to use investment calculations from the interest rate of capital markets. But if this is not the case, the choice between lending and the deposit rate of interest depends on whether an investor is a borrower or a saver. For example, a private non-industrial forest owner with a loan is justified to use (after-tax) a lending rate of interest for a risk-free investment option.

Interestingly, there seems to be a notable interest rate differential between forest management rules in the United States and Europe. Chang (2001) reviews some studies where according to the Southern United States, pine stands are managed under a 6-8% interest rate,1 whereas the implied interest rate in management decisions in a German area has been 1.2-1.3% and in Lithuania a 0-2% interest rate is suggested for State forestry. Chang (2001) also presents the question of "how can the interest rate in the United States, possibly where capital is the most abundant in the world, be higher than Lithuania, where capital is relatively scarce?"

1. On the other hand, the U. S. Forest Service chooses the rotation age that maximizes maximum sustained yield, MSY on its commercial timber production stands (Klemperer 2003, p. 221). This rule implies, roughly speaking, a 0 % discount rate (see ECON4).

### One Response to “2. Capital budgeting”

1. mwawula emmanuel Says:
As a forestry student at Makerere University in Uganda, i appreciate ur site because it is a good source of information for my coarse work in FOREST ECONOMICS.