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Capitalizing to determine value of a long-term asset

An important decision for a business manager is determining the price to pay for a long-term asset such as a building or a tract of land. Similarly, a manager must be prepared to determine at what price to sell a long-term asset. In both situations, the fundamental question is "how does one determine the value of a long-term asset?"

General Rule

The value of an asset is the revenue it will generate for its owner.  This revenue includes the income received from the sale of the products produced by the asset, plus the resale value when the asset is disposed of in the future.  However, the cost of operating the asset to produce the products must be subtracted from the revenue.

• Example.  The current value of farmland reflects 1) the revenue that will be generated in the future by selling the commodities produced on the land, 2) minus the cost of producing those commodities, and 3) plus the land's future selling price.
• For the purpose of this overview discussion, a long term asset means any asset or investment (whether tangible or intangible) that will generate revenue more than one year into the future.

Need to Discount Future Earnings to Present Value

Because the revenue from the asset will be received over time, future earnings must be discounted to present value.  Also, each future earnings or payment must be estimated or calculated, if they are expected to vary over time, before discounting them to present value. 

• Example.  A investment is expected to return $100 one year from now, another $112 two years from now, and soon thereafter be sold for $500.  Assuming a discount rate of 5%, the present value of the first payment is $95.24 (100/(1+.05)^1), the present value of the second payment is $101.59 (112/(1+.05)^2), the present value of payment for selling the asset is $453.51 (500/(1+.05)^2), and the total present value of this short-term investment is $650.34 (95.24 + 101.59 + 453.51). Accordingly, an investor who imposes a 5% discount rate on future income, would be willing to pay no more than $650.34 for this asset.
  
• A computer spreadsheet can help illustrate these calculations. 

• Cells D2, A4, A5, A6, C4, C5 and C6 are used to input the values.
• Cell D4 is the formula =C4/(1+D$2)^A4; cell D5 is the formula =C5/(1+D$2)^A5; cell D6 is the formula =C6/(1+D$2)^A6; these cells provide the present value of each payment.
• Cell D7 is the formula =sum(D4:D6); it provides the final answer.
• This spreadsheet can readily be modified to accommodate different situations; for example, additional rows can be inserted below row 7 if the investment will provide more than two future payments (before being sold).  Also, the time period can be expressed to reflect portions of years; for example, 1.75 years would be the appropriate time period if the payment will be received 21 months from now (21 months /12 months).
• Be sure the time period for the discount rate and the time periods until payment are the same; for example, if the discount rate is expressed as an annual rate, the time periods until payment will be the number of years, but if the discount rate is expressed as a monthly rate, the time periods until payment must be expressed as the number of months.

Role of Assumptions

This analytical process requires the analyst (often the business manager) to make numerous assumptions or projections about future events, especially if the future payments will result from a business that purchases inputs from which a commodity is produced and marketed (such as farmland).  In that case, assumptions may include

• quantity of future sales,
• price of future sales (implies an assumption about the impact of inflation and demand on the selling price),
• time of future sales,
• type and quantity of future inputs (implies an assumption about production technology),
• cost of future inputs (implies an assumption about the impact of inflation on input costs),
• time when future inputs will be used, and
• a discount rate (probably a nominal or market interest rate, that is, a real rate adjusted for anticipated general rate of inflation).

Inflation is mentioned three times in this list -- selling price, input costs and discount rate.  However, the inflation rate (or price changes) may be different for each of these items; thus a manager may need to consider each of these factors individually.

• If the manger wanted to assume that inflation will equally affect the three factors, present prices for production and inputs and a real interest rate could be used to complete the analysis. More on the distinction between real and nominal interest rate in another section.

Short-hand Method to Calculate Long-term Asset Value

If the manager anticipates owning the asset for a long-time, such as a tract of land for 40 years, the resale value may not have much of an impact on the present value because the revenue is not expected to be received for such a long time. However, the annual revenue throughout that time will have a major impact on the value of the asset. Accordingly, a short-hand method to calculate the value of a long-term asset is

V = R/d

where:  V is value of the long-term asset,
R is annual earnings of long-term asset, and
d is a real discount rate.

Note that the resale value of this long term asset is not explicitly considered in the short-hand formula.

 

• Using a real discount rate implies (assumes) that the annual earnings will change by the general rate of inflation in the economy; this may or may not be an accurate assumption.  
• Example.  Annual earnings from the asset is expected to be $37 but will change with inflation, and the real discount rate is 3.5%.  The value of this long-term asset would be $1,057.

• Cells B1 and B2 are used to input values; cell B3 is the formula +B1/B2 and provides the answer.

This formula (V=R/d), however, assumes no changes in quantity of sales or production technology.  It also assumes that inflation will have an equal impact on sale price, input costs, and interest rates.  But, the world is not that simple.  The remainder of this page describes an expanded methodology that relaxes some of the simplifying assumptions, but it does not reduce the number of assumptions (some would suggest that it significantly increases the number of assumptions).  The expanded methodology also increases the number of computations; fortunately computer programs (such as a spreadsheet) can help with these calculations.  The following section suggests such a spreadsheet.

Expanded Method to Calculate Long-term Asset Value

As stated above, the value of a long-term asset is the present value of its future earnings.  In the case of an asset that will be used in a business, revenue and operating expenses for each production period need to be considered.  Key considerations for farmland, for example, include type and quantity of commodities that will be produced, price or value of the commodities, type and quantity of inputs used, and input costs. 

• This is the same information used in preparing an enterprise analysis; thus the business owner who has prepared enterprise budgets can rely on existing information when valuing land (rather than having to gather all new information).  The owner needs to be certain, however, that the enterprise analyses are up-to-date.
• The purpose of this analysis is to determine the value of the land resource.  Therefore in preparing the enterprise analysis, the owner should subtract all costs except return to land; this would include subtracting an opportunity cost for non-land inputs, such as the owner's unpaid labor, management, and return to risk.

• Farmland often is used to raise several crops; for example, rotating crops is a common practice to reduce disease.  An owner will need to prepare several enterprise analyses if the land will be used to raise several crops.  This can be handled several ways, depending on how the land will be operated (one crop each year or several crops each year) and whether the analysis is calculating a per acre value or a value for the entire tract.  
  • Portion of land used to produce A, portion used to produce B and portion used to produce C in any given year.
  • Entire tract, multiple crops each year, such as, crop A in year 1, crop B in year 2, crop C in year 3,a nd crop A in year 4, etc.
  • Entire tract, single crop but rotating annually; such as, crop A on 50% of the land each year, crops B and C each on 25% of the land each year.

• The manager will need to prepare an analysis for each year if conditions are expected to change, such as which commodities will be produced, prices, costs, or technology (which impacts the inputs that will be used).  Such a large number of predictions about the future tend to become guesses the further into the future the analysis is extended  At some point in the analysis, the manager may stop trying to project all the details, but instead, rely on simplifying assumptions.  Simplifying the approach does not reduce the number of assumptions; it just reduces how many of them are explicitly considered.

• A computer helps assess how changing assumptions can impact the projected asset value.

The spreadsheet calculates the present value of the future earnings.  The spreadsheet does not eliminate or even reduce the number of assumptions that need to be made; instead the spreadsheet facilitates making those assumptions explicit.

• V = sum of present value of E (future earnings); value equals total present value of future earnings
• E = earnings for each future period (TR-TC); earnings equals sum of total revenue (including resale price) minus total explicit cost for each period asset is owned
• TR = total revenue equals quantity of output sold times the selling price
• TC = total cost equals sum of quantity of each input times the cost of each input
• Quantity of output = projected sale of product for each period of ownership
• Price =projected price for output sold each period of ownership
• Input quantity = projected quantity of each input used in operating the asset and producing the product
• C = projected cost of each input used in operating the asset and producing the product

• The spreadsheet uses enterprise budget/analysis as the basis of the calculations; that is, E = TR - TC.
• inflation rate for input cost, product price, and general inflation rate (this one impacts the discount rate).

Value does not Equal Cash Flow (Feasibility)

This procedure does NOT assess the feasibility of purchasing farm land, for example.  Restated, the analysis described on this page does not assess whether the land will generate enough cash inflow to pay all cash costs.  Additional analysis is necessary to answer that question.

Bottom Line

A farm manager may never go through all the complexities and details described on this page.  But what is important is for the manager to recognize that all these assumptions are embedded in any discussion about the value of land.

Last Updated June 21, 2007

Email: David.Saxowsky@ndsu.edu

This material is intended for educational purposes only. It is not a substitute for competent professional advice. Seek appropriate advice for answers to your specific questions.

E-Mail:sswandal@ndsuext.nodak.edu
Published by Agricusiness and Applied Economics
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