The Financial Analysis

The Time Value of Money

Financial evaluations can be of two types:

  1. those that recognize the time value of money
  2. and those that do not

The "time value of money" is simply an account for the notion that a dollar today is worth more than the same dollar 10 years from now.  When you get a dollar today, you can spend it immediately if you wish.  If you get a "promise" for a dollar instead of the dollar itself, you must wait.

Due to the uncertainty involved in the wait (i.e., the loaner changes his or her mind, dies, or inflation continues at its current rate) the dollar received is worth more than the promised dollar.  This brings us to the concept of interest rates.

Interest Rates

Measuring the value of money or capital involves 2 important factors: 

  1. time
  2. quantity

The cost of keeping money in a project, in our case a forestry project, is indicated by the interest or discount rate.  As the old saying goes, "time is money". Time costs money as do other inputs and the price of time is usually measured by the interest rate. In general, projects with a longer life require higher discount rates.

Investors know that money can be made by lending money.  People are willing to pay for the use of money.  When an investment grows at a specified interest rate, we call it compounding.  $100 invested at 5% for 5 years will yield $127.63 at the end of the 5 years.  To determine this, we multiply $100 by 1.05 in year one, again in year 2, and so on up to year 5.  This process can be simplified by using the formula:

Vn = Vo (1 + i)n

Where:

  • Vn =  the value at the end of the investment period
    Vo = value at the beginning of the investment
    i = interest rate
    n = number of periods (years)

So, referring back to our example, the above formula is applied:

V5 = $100 (1.05)5 = $127.63

This same relationship can be used in another common function which is the opposite of compounding: discounting.  Discounting begins with a future amount and determines its worth today.  Using our example above and some basic algebra, today's value of a payment of $127.63 received in year 5 would be found using the formula below:

Vo = Vn / (1 + i)n

Using this formula, we can plug in our numbers:

V0 = $127.63 / (1.05)5 = $100.00

There are a number of other more complex formulas used to calculate different types of terminating and infinite series of payments or costs.  Some of these are introduced below and in other extension publications that are linked elsewhere in this section.

Which Interest Rate Should You Use?

There are 2 types of interest rates: 

  1. real rate - does not reflect inflation
  2. nominal rate - does reflect inflation

A nominal interest rate is calculated by incorporating both a real rate and a general inflation rate using the following formula:

Nominal Rate = [(1 + Real Rate) × (1 + General Inflation Rate Per Period)] − 1

This formula can be manipulated to give us the real rate if the nomimal rate and general inflation rate are known:

Real Rate = [(1 + Nominal Rate) / (1 + General Inflation Rate Per Period)] − 1

Economists generally use the real rate because it gives a clearer picture of the project's true worth. You should be sure that your analysis is based on several appropriate real discount rates.

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Net Present Value (NPV)

Net Present Value (NPV) (or Present Net Worth (PNW)) recognizes money's time value by using the minimum acceptable rate of return (determined by you) to discount all costs and returns back to the time of project initiation (period 0 or period 1, depending on the timing of cash flow).  The discounted costs are then subtracted from the discounted revenues as shown below:

NPV = Present Value (Revenues) − Present Value (Costs)

For more information, view a sample NPV calculation for a hypothetical timber management scenario.

Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) shows the investment's actual rate of return.  The IRR is the discount rate when the present value (PV) of the costs is equal to the PV of the revenues, or when NPV equals zero.  The IRR is calculated using an iterative process to solve for the appropriate rate.  A spreadsheet program is a very useful tool for this type of calculation. 

A project with an IRR smaller than your minimum acceptable rate of return (MARR) is less profitable than one with an IRR greater than your MARR.

NPV and IRR are the two most widely used and accepted decision criteria.  Many investors, particularly nonindustrial private forest landowners are most comfortable with IRR because the final result is an interest rate.

Benefit / Cost (B/C) Ratio

Another way to use the present value of the costs and revenues to determine the present worth of a project or investment is the benefit/cost (B/C) ratio.  Here, we simply divide the present value (PV) of the revenues by the PV of the costs:

B/C = PV Revenues / PV Costs

This calculation gives you a "bang for your buck" estimate. A B/C value greater than one indicates that discounted benefits exceed costs. A B/C ratio less than one indicates that discounted costs exceed benefits. This ratio is often used to evaluate projects on public lands.

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Equal Annual Equivalent & Land Expection Value

Equal Annual Equivalent

The Equal Annual Equivalent (EAE) is simply the Net Present Value (NPV) converted to an annual value paid at the end of each year or period for the life of the investment.  It is calculated at the appropriate discount rate using this formula:

EAE = NPV [(i(1 + i)n] / [(1 + i)n − 1)]

Where:

  • i = interest rate 
    n = number of periods (years)

Land Expectation Value (LEV)

Finally, the Land Expectation Value (LEV) (or Soil Expectation Value (SEV)) is the present value of all future costs and revenues of a productive asset.  Put simply, it is the value of bare forest land.  Calculating LEV is similar to assuming that a project will be replicated an infinite number of times into the future.  This makes all projects have an infinite time horizon. 

The LEV is useful for estimating the bid price of bare land for growing successive rotations of even-aged timber.  Land purchase costs and land sale returns are not included in the calculation of LEV.  LEV is the net present value (NPV) for an infinite time horizon.  It is calculated using this formula:

LEV = NPV (1 + i)n / (1 + i)n − 1

Where:

  • i = interest rate 
    n = number of periods (years)

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