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Testing the Profitability of Making a Change

(Appendix to Step 6 of Business Planning)

A criterion that farmers will likely apply in deciding whether to adopt an alternative is whether it increases the farm's profits. One method to estimate an alternative's impact on profit is to develop a pro forma income statement for the business as it would be operated if the alternative is adopted. The profit estimated on this statement could then be compared to a pro forma income statement developed for the current business. Generally, it is assumed that the owners will pursue the option that is projected to generate the most profit.

Will the Business Always Maximize Profit?

However, farm owners occasionally may adopt an alternative even though it may negatively impact profit. Reasons for such a strategy might include

• the alternative provides the owner satisfaction other than the income it generates (similar to a hobby); or
• incurring a loss at this time leads to an opportunity to earn greater profits in the future.

Likewise, a business may not maximize profit if a production factor beyond the owners' control deviates from what the owners expected at the time they made their decisions (such as the weather).

How Will the Change Impact Production?

A difficulty in analyzing an alternative is identifying what will be affected by the change. That is, as inputs are added, removed, or redirected within the business, the owners may not know for certain the amount by which output will be affected. If the owners do not fully understand all the interrelationships among the firm's enterprises, they may not recognize all the commodities or products that might be impacted. This information is necessary, however, to project the impact of an alternative; and therefore, warrants some explanation.

The relationship between the quantity of input and the quantity of output that it produces is referred to as the production function or production response. Many farm business may not have a good understanding of their production functions because the relationship is difficult to measure. Different growing conditions (weather, disease), changing inputs (seed varieties), and evolving production technology (new equipment, advanced livestock medicines) can all simultaneously impact output. As a result, it is difficult to isolate the cause of variation in production.

Despite not specifically knowing the production function, some general observations can be made. For example, more input means more output (if the firm is in a situation where additional input would result in reduced output, the manager faces a problem that needs immediate attention). The corollary is that less input will mean less output.

Diminishing Marginal Productivity

Farmers also know from experience that there is a point where adding input to the production effort will result in less additional production. This decrease in response to additional input is referred to as diminishing marginal productivity. The concept applies in all circumstances whether the input is fertilizer, seed, feed, labor, cash, or any other input. If the quantity of one input is continuously increased without increasing the quantity of other resources, the increase in production due to the additional input will diminish .

Example. A farmer who currently applies 100 pounds of fertilizer per acre intends to increase the fertilizer application by 15 pounds (for a total of 115 pounds per acre) and projects that this will increase yield by 1.8 bushels. If the farmer adds another 15 pounds to each acre (for a total of 130 pounds), the yield probably will increase another 1.1 bushels per acre. This phenomena of a smaller amount of additional production as more input is used is called diminishing marginal productivity.

Experience has taught two other points:

• once diminishing marginal productivity occurs, additional quantities of the same input will never reverse the diminishing trend; and
• all businesses will be experiencing diminishing marginal productivity when it is earning its maximum profit.

Sources of Information about Production Response

The results of pro forma income statements will be most beneficial if the data used in the projections are as accurate as possible. Sources of information about production response include

• published data,
• adult farm management instructors,
• extension/university personnel,
• private consultants, and
• the farmer's own experience (written data as well as memory)

The best source is farmers' own documented data because that information reflects their business and resources, and having been written down, it is not subject to "selective recall." Some of this information has already been assembled as part of step 1 when owners described the relationship between quantity of input and quantity of output as they specified their production "recipes." But that information is just one combination of inputs; it most likely does not indicate the level of production if a slightly different set of resources (such as more fertilizer) is used to produce the commodity.

Is the Correct Information Being Gathered?

Based on this understanding of the necessary level of detailed production records, farmers may want to review whether their current recordkeeping practice is gathering the production and financial data necessary for future decisions.

Price and Cost Projections

The challenge of projecting future prices and costs was addressed in step 3 of this planning process when farmers were invited to think about the future and write down their ideas. If necessary, those projections can be reviewed or revised at any time better information becomes available.

Additional Revenue

The additional revenue due to adopting an alternative usually can be computed as the quantity of additional production times the commodity's market price. But in some situations, as with feeding livestock, determining the additional revenue is more complicated.

Example: a 750-pound feeder animal could be sold for $.78 per pound, thereby generating $585 in revenue. But if that animal is fed to 850 pounds and sold for $.74 per pound, the revenue would be $629. The additional 100 pounds increased revenue by $44, or $.44 per pound for the last 100 pounds. This increase in revenue per pound is less than the market price. It is the $.44 per pound revenue that needs to be compared to the cost of adding that pound to the animal's weight.

Short-hand procedures

Developing a pro forma income statement for the farm (although appropriate) may involve more work than necessary. Instead of including the entire farm business in the analysis, the alternative's impact on profit can be estimated by evaluating only the parts of the business that would change if the alternative is adopted. The general rule would be that as long as the revenue resulting from the alternative is greater than its costs, the alternative would increase the farm's total profit. Such a "short-hand" analysis would not indicate the farm's total profit should the alternative be adopted; it only reveals the projected change in the farm's profit.

A short-hand approach can help answer management questions such as, would the farm's profit increase if

• more output was produced by using more input (e.g., would it be profitable to add more fertilizer to the crop);
• different inputs were used to produce the commodity (e.g., what feed ration will generate the most profit; should conventional tillage practice be replaced with no-till/pesticide practice for weed control);
• the assets were used to produce a different commodity (e.g., should the cash be used to buy feed, additional herbicides, prepay long-term debt, or be deposited in a savings account in the bank);
• a long-term asset was purchased (e.g., is it sensible to buy this tractor that can be used in the operation for the next 12 years);
• the size or scale of the operation was changed (e.g., should the neighboring tract of land be purchased even though it also would require additional equipment, hired labor, and operating inputs).

Related questions include

• does the farm have enough resources to adopt the alternative, and
• what is the maximum price the owners should be willing to pay for a particular asset.

The next sections suggest several short-hand analytical methods for assessing each of these questions. The discussion also suggests some additional considerations and concerns.

Producing more output by using more input

A common question is whether the farm would increase its profits by producing a greater quantity of its commodities. But since additional production requires additional inputs, the question is "will the revenue from the added production exceed the cost of the additional input necessary to produce the added output."

The example of whether to apply additional fertilizer will be used again. The question is whether the cost of additional fertilizer is less than the revenue due to the added production that results from the extra fertilizer. As long as the added revenue exceeds the added cost, the farm's profit would increase. As suggested in a preceding section, the information needed to answer this question is

• how much additional input will be used,
• how much will the additional input cost,
• how much additional output will result from the additional input (that is, what is the production response), and
• how much additional revenue will be received as a result of the additional output.

There are two ways to think about this question; one is changing the level of input, the other is to change the level of output. Economists use different terminology for each method.

• If the manager changes the level of output,
  • the additional revenue is called marginal revenue (change in total revenue due to producing one more unit of output), and
  • the additional cost is marginal cost (change in total cost due to producing one more unit of output).
• If the manager changes the level of input,
  • the additional revenue is refer to as marginal value product (change in total revenue due to using one more unit of input to increase production), and
  • the additional cost is marginal input cost (change in total cost due to using one more unit of input to increase production).

Regardless of which approach is used, the answer to whether the alternative increases profit will be the same (otherwise, there is a mistake in the analysis). Generally, farmers tend to consider the question as one of changing the level of input (that is, marginal value product and marginal input cost).

An alternative to comparing added revenue to added cost is to express them as a ratio (added revenue/added cost). As long as the ratio is greater than 1, the alternative will increase the farm's profit. The advantage of the extra step to state the added revenue and added cost as a ratio will be demonstrated in subsequent sections.

Example. Should additional fertilizer (costing $.16 per pound) be used in raising corn (that sells for $2 per bushel)? The farmer currently applies 100 pounds of fertilizer per acre and wonders whether the farm would be more profitable if 15 additional pounds of fertilizer were applied (but without changing the amount of seed, pesticide, fuel, machinery, labor or any other input). The farmer expects production to increase 1.8 bushels per acre, so the added revenue of $3.60 exceeds the added cost of $2.40 [$3.60/$2.40 = 1.5]. The farm's profit would increase by adding the 15 pounds of fertilizer.

Example. Should the farmer apply another 15 pounds so total application is 130 pounds. Production will increase by 1.1 bushels; revenue would increase $2.20 at a cost of $2.40. Since marginal input cost exceeds the marginal value product, there is no reason to apply the last increment of 15 pounds of fertilizer [$2.20/$2.40 = .916].

Maximum Production Does Not Mean Maximum Profit

Even though increasing the fertilizer application to a total of 130 pounds would increase total production, it decreases profit because the added revenue from the grain produced by the last 15 pounds of fertilizer would be less than the added cost. This simple example illustrates that increasing production by adding input will not always lead to greater profit. Maximum production does not mean maximum profit. The profit maximizing level of production is less than maximum production.

Increment of Input

In the example, the fertilizer application was a 15-pound increment. However, if all 30 pounds would have been analyzed in one step, production would be estimated as increasing 2.9 bushels with revenue increasing $5.80, and costs increasing $4.80. This analysis would show that adding 30 pounds of fertilizer would increase profit by $1.00 per acre. What such an analysis fails to reveal, however, is that applying only 15 pounds and increasing yields by only 1.8 bushels generates an additional $1.20 per acre profit (compared to applying only 100 pounds). Analyzing a 30-pound increment hid the fact that the last 15 pounds of fertilizer decreased profit.

Business owners are responsible for deciding what quantity of input they want to use in their analysis/thought process. With an input like fertilizer, a farmer could assess it one pound at a time if there were sufficient data and the farmer was interested in repeating the analysis that often. If the input being considered is not divisible, such as hiring a worker or buying a tractor, owners have limited opportunity to define the increment to analyze.

Other Considerations

Comparing added revenue and added cost also can be used to determine the impact on profit if less inputs would be used. For example, many operators have considered whether to reduce the amount of herbicide they are using, but recognize that it may lead to lower production. The question they pose is whether the cost savings is more than the short- and long-run reduction in revenue; if yes, they would earn a greater profit by using less herbicide. A procedure for analyzing the long-run implications (discounting) is explained in a subsequent paragraph.

Opportunity Cost and Risk

The cost of implementing an alternative is more than the quantity of input times its market price. The cost also includes less visible components; primarily opportunity cost and risk.

In the examples above, the cash used to buy fertilizer is not available again until the grain is harvested, perhaps six months later. During this time, the cash could have been put to another use if it had not been spent on fertilizer. At a minimum, the cash would not have been borrowed (saving interest paid on a loan) or it could have been deposited in a bank account (and thereby earn interest). Thus, the fertilizer has an opportunity cost of the interest on the money from the time the fertilizer is paid for until the grain is harvested.

A farmer's minimum opportunity cost for capital probably is the rate banks are paying for deposits. For alternatives that require additional labor, the minimum opportunity cost of labor may be the minimum wage rate.

In addition, applying more fertilizer exposes farmers to increased risk . The likelihood or probability that the fertilizer will not increase the yield exceeds the likelihood that a bank will not return a deposit (plus the interest earned). This increased risk exposure is another factor to consider in determining the cost of adopting an alternative. Step 8 addresses risk analysis.

Using a different input

Another question that farmers need to address is whether using different inputs to produce their commodities would increase profit. A farmer can use cash to acquire labor, fuel, fertilizer, seed, or numerous other inputs; but which input makes the best use of the cash? The following example has the farmer considering alternative rations for feeding livestock.

Example. The farmer operates a feedlot and can mix various combinations of feedstuffs to provide the same nutritional value (after adjusting for varying digestability and palatability), but at different costs. Since the nutrition is the same, the output (pounds of livestock) and the revenue should be the same regardless which ration is used. But, the combinations of feedstuffs will differ and each ration will impose a different cost. The farmer will likely use the lowest-cost ration; that is, the ration with the greatest ratio (added revenue/added cost).

By using ratios, the farmer can analyze more than two rations simultaneously. The ratios facilitate selecting from among several alternatives in one analysis.

As suggested in a preceding section, the short-hand methods do not reduce the amount of data that needs to be collected, they only abbreviate the analysis. The farmer still needs to gather all the same data as would be necessary to prepare a pro forma income statement for the farm.

Producing a different commodity

A third question for the business owners is deciding how to use their resources. For example, should available cash be used to buy feed, additional herbicides, prepay long-term debt, or be deposited in a savings account in the bank. In this case, the cost of each alternative is the same (whatever increment of cash is being considered) but the added revenue will vary. Thus preparing a ratio (added revenue/added cost) for each increment of each alternative and then implementing the alternative with the highest ratio would be most profitable.

In this example, the first two alternatives (crop and livestock production) might quickly experience diminishing marginal productivity as more feed or herbicide is used. The ratio would not be constant as more cash is invested in the activity. Prepaying the debt would increase net revenue by reducing interest costs and would not experience diminishing marginal productivity until the debt is paid in total (unless a prepayment penalty will be imposed). The deposit in the bank is not likely to ever experience diminishing marginal productivity since no one has so much money that the banks would pay a lower interest rate as the amount deposited increases. In fact, the opposite is sometimes true (a higher interest rate is paid on the largest deposits).

Again, developing ratios allows several alternatives to be considered simultaneously, rather than necessitate a series of one-on-one comparisons.

Different input to produce a different output

It is helpful to recognize that most alternatives are more complex than the preceding examples. Many alternatives have positive effects -- increased revenue and decreased costs -- and negative effects -- decreased revenue or increased costs. There is more than just added costs and added revenue.

As long as positive effects exceed negative effects, adopting the alternative will increase the business' profit. This method of analysis is referred to as partial budgeting. Like other short-hand methods, the budget being developed only addresses those parts of the business that will be impacted by the change. The aspects of the business that will not be affected by the alternative are not considered because they will remain the same whether or not the change is made. The following table suggests a format for preparing a partial budget.

Sample Format of Partial Budget Analysis

Example. A soybean farmer has been using conventional tillage practices, but is considering no-till for the future. The farmer expects that the yield will decrease by 2 bushels (current market value of $4 per bushel) if no-till is adopted. Discontinuing the conventional tillage would save $20 per acre whereas as the increased herbicide application costs $17. In this case, the farmer would decrease profit by $4.91 per acre by replacing conventional tillage with herbicide.

Example of Partial Budget Analysis

Like other short-hand methods, opportunity costs, risk exposure, and other intangible considerations should not be overlooked when using a partial budget.

Enough resources to adopt the alternative

Another question that will be asked is whether the farm business has adequate resources to implement the alternative. This issue was first introduced in step 1 where the farmers are invited to assess how well the availability of their resources align with the needs. This assessment not only considers type and quantity of resources, but also the timing of availability and need. As discussed previously, a related question is whether the use is most profitable. Assessing all these questions at one time for a business with several enterprises, numerous inputs, many alternatives, and various time periods of needs or availability is almost incomprehensible, yet managers are expected (required) to make such evaluations.

A methodology has been developed to help such an analysis and is readily available as a computer program. The technique is called linear programming and offers decision makers a mechanism for describing their business and computing the most profitable alternatives. Though not described in detail in this short section, it is an analytical method that farmers may want to consider using in their business in the future as they gather more data about their farm operation.

Another consideration -- Availability of Cash

This page emphasizes methodology for assessing the profitability of alternatives. It does not address the availability of cash to pay expenses when they are due. As explained in other steps, profit and cash flow are not the same, and neither can be overlooked. A profitable alternative may still be inappropriate for a firm if the necessary cash resources are not available. Any analysis of profit must be accompanied by a cash flow assessment (as described in other steps of the planning process).

Investing in a Long-Term Asset

The preceding discussion does not address the issue of deciding whether to invest in a long-term asset; that is, a resource that can be used for several years. This question arises because time affects the value of money. The next several paragraphs introduce how the value of money is affected by time.

If someone was to offer a choice between accepting $1 today or $1 a year from now, nearly everyone would take the money today -- it is more valuable now than a year from now. Three factors influence this assessment: 1) risk -- the concern that the person may not be able and willing to pay the dollar one year from now, 2) the opportunity cost that the dollar received today could be invested for a year and earn a return during the 12 months, and 3) inflation that will reduce the purchasing power of the dollar received a year from now.

But if the offer was changed to a choice between $.90 today and $1 a year from now, some will take the $.90 now and some will elect to take a $1 12 months from now. There is no right or wrong answer; the difference is that the individuals, after considering the three factors listed above, accepted different assumptions. The different assumptions led to different decisions.

Based on the preceding example, there must be a procedure to estimate the present value of future revenue.  The extent to which the value of the future payment is reduced is called discounting . A dollar one year from now is (in the opinion of some people) worth $.90 today; these individuals decided that the three factors listed above justify approximately a 10% discount. The 10% rate, in this example, is called the discount rate.

Each individual establishes their own discount rate to reflect their assessment of the 3 factors. Once an individual has their discount rate (i) in mind, they can use it in the following formula to calculate the present value of a future payment. (n is the length of time until the payment is received.)

PV = FV/(1+i)ⁿ

Example.  $1000 to be received one year from now has a present value of $901if the decision maker decides to use a discount rate of 11% [1000/(1.11)¹ = 901]. The discount rate may reflect an anticipated 3% inflation, 4% opportunity cost and 4% premium to compensate for the risk of accepting the delayed payment.

Usually the discount rate is on the basis of one year. The exponent of 1 represents that time period. If the time until the payment will be made is less than one year or more than one year, the exponent can be adjusted to reflect the time period.

Example. Discounting a payment to be received 6 months (.5 years) from now would use a formula of PV = FV/(1+i)^.5 If the payment is to be received 21 months (1.75 years) from now, the formula would be PV = FV/(1+i)^1.75 .

Computer programs (such as a spreadsheet) ease the process of applying the present value formula.

With this analytical procedure, costs and revenues that are expected to occur in different time periods can be discounted to present value and then compared to one another. Without discounting, it is inappropriate to compare the cost of making an investment today to revenue it would generate 5 years in the future.

If some aspects of discounting are confusing, it may be helpful to think of the concept as the opposite of compound interest -- a concept that may be more familiar.

Value of a long-term asset

Discounting has innumerable applications; one application is determining the value of a long-term asset such as land, a building, or equipment.

When acquiring any asset, the price paid should be no more than the present value of the profit the asset will generate during its useful life. For example, buying a tract of land involves

• estimating the revenue that will be generated each year, including the selling price or value in the last year,
• subtracting all costs of operating the land (including opportunity costs for owned assets, but not land costs) for each year,
• discounting the remaining amount (which is the return to owning the land) for each year to its present value, and
• adding all the present values of the revenue that will be earned each year of ownership.
• The total is the maximum that should be paid for the land. This procedure is referred to as capitalization. This analytical procedure can be used for valuing any asset.

The previous example involves many assumptions about inflation, change in commodity prices, change in input costs, change in production technology, and numerous other factors. No one can make these projections with absolute confidence, but these are the factors that should be explicitly considered in deciding how much to pay for a tract of land, a building, or a major piece of equipment.

Changing the size of the business

One way to overcome diminishing marginal productivity is to acquire more of whatever resource is short or limiting. Carried to an extreme, such a strategy will increase the size or scale of operation. But in implementing such a strategy, some resources may take considerable time to acquire; for example, a building. Therefore, a strategy of increasing size or scale is usually considered to take place over the long-run.

But even in the long-run (where more of every asset is acquired if it is found to be limiting), some resource will likely be short or limiting. The challenge is that sometimes the limitation may not be obvious. Inputs such as management skills, capacity to assume risk, and willingness to assume risk are inputs (similar to equipment, seed, feed, and fertilizer). Continuing to increase the size of the business without adding management resources, for example, will eventually lead to diminishing marginal productivity and a condition of less than profit maximizing.

Conclusion

Profit maximizing issues require considerable detailed information. Short-hand methods can ease the analysis because the focus is on only the parts of the business that would be affected by the alternative. These methods indicate the change in profit but not the total profit. Basic ideas to keep in mind include

• diminishing marginal productivity -- additional input will eventually result in decreased rate of production increases
• collecting information about production processes because the production response is different for each business
• opportunity cost -- income that cannot be earned because an asset is put to another use should be treated as a cost
• risk -- increased exposure to risk should be compensated for with additional earnings
• maximum profit is not earned with maximum output
• discounting is used because money today has a different value than money in the future
• the maximum value of an asset is the present value of its future earnings
• management skills, capacity to assume risk, and willingness to assume risk may be limiting factors as the scale of a business is increased.

Last Updated October 31, 2005

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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