If I raise (or lower) the price of my product by a small amount (say 5%), then how much will my units sales increase or decrease?

The elasticity number epsilon is defines so that, if you raise your price by 5%, then the  unit sales increase by epsilon * 5%.

Elasticity models usually assume that

1. Transactions are sufficiently numerous that price-units relationships do not depend on a few purchase decisions.
2. The number of units sold varies continuously with price over some price range (allowing for some random noise in the data).
3. Other non-price conditions of sale are fairly uniform across the market.

If  your situation does not match these conditions, then you probably need to do case-by case analysis of each purchase decision, instead of using an analytical price elasticity model.

If  your situation does match these conditions, then you can use some standard price elasticity models to estimate the change in unit sales and revenue if you change your price.

Here are three useful extensions of textbook models of price elasticity.

1. Non-constant elasticity Textbook models of elasticity usually assume that the relationship between price and sales units a straight line (on a log-log plot). Therefore they cannot predict price(s) that optimized revenue or profit. To detect maxima, you need a model that treats the
   relationship between price and sales units a quadratic curve (on a log-logplot).
2. Interacting products Generally, sales units of one product are affected by prices of interacting products.  (For example, if the price of Pepsi goes up, that is likely to increase the sales of close substitutes like Coca Cola.)  If this is the case, then you probably want to model these cross effects to get results that are useful for decision-making.
3. Estimating profit (in addition to revenue and sale units) If you provide product cost data, then slight extensions of price elasticity models also predict profit margins (as well as revenue and sales units) at any price (or prices for several products).

Below are links to some free and paid spreadsheets that implement elasticity models with some or all of the extras described above. Each one also contains a brief description of the theory and computations.

• Price elasticity model for one product: http://templates.modelsheetsoft.com/modelsheettemplates/product-price-elasticity-templates.aspx
• Price elasticity model for several products: http://templates.modelsheetsoft.com/modelsheettemplates/price-elasticity-templates.aspx

• The patient model tracks patients and the medical procedures they receive.
  • The model tracks populations of new and continuing patients. You can specify an average procedure regimen for new patients for a period of time, and an average frequency of procedures for continuing patients.
  • You can specify your medical procedures and procedure families.
  • For each procedure, you can specify the number of hours of staff time by job type, and the amount of time that relevant medical equipment is utilized.
• The revenue model is based on fee for services: revenue = procedures x fee for each procedure.
  • The model also tracks grant revenue that is not tied to procedures.
• Cost of services includes medical staff time, equipment time, and direct supplies.
  • You can specify medical job types with different specialties and compensation levels.
  • The model tracks medical staff headcount, available hours, applied hours, billed hours, and utilization, by job type. Includes benefits, payroll taxes, bonuses.
  • You can include various types of medical equipment that are leased, and the lease cost of the equipment.
  • The model computes staff and equipment cost per hour and per procedure, and utilization rates for medical staff and medical equipment.

It also contains the key features in a general financial plan for a business: financial statements and backup detail for many parts of the model. See the post on Financial Plan for a Business for more information.

This is our fourth type of financial plan for a business:

1. Financial Plan for a Business (for product businesses)
   blog article
   overview and customizer
2. Financial Plan for Professional Services Businesses
   overview and customizer
3. Financial Plan for a Small Business
   overview and customizer
4. Financial Plan for Medical Services Businesses
   case study
   overview and customizer

A “customizable spreadsheet solution” is a spreadsheet model that you customize by filling in a simple web form in plain English, then download as a conventional Excel workbook. Each solution is feature-rich; you choose the features you want, and the size of the model in terms of time series and dimensions (lists of products, departments and so forth). You can see a list of our customizable spreadsheet solutions with descriptions at http://templates.modelsheetsoft.com//browser/browse.aspx . We welcome your suggestions for new features in this and other customziable spreadsheet solutions.

• Financial Plan for a Small Business
• Sales Plan for a Small Startup
• Cash Flow for a Small Startup
• Cash Requirements for a Small Startup

These models provide a level of detail that is helpful for small startup companies, with a minimum of complexity. The first three applications are cut-down versions of ModelSheet spreadsheet applications for larger businesses. The last three are extensions of spreadsheet templates designed by SCORE for use in small startups. These models assume that the company does not have much historical data. For example, the Sales Plan for a Small Startup does not use historical sales data in the sales planning process, which the larger Sales Plan Spreadsheet Application does.

In all the models that contain time (everything except the Cash Requirements model), you can specify the time range and time grain (days, weeks, months, quarters, years) that you want in your spreadsheet.

Financial Plan for a Small Business

This spreadsheet application integrates the four main financial statements: income statement, balance sheet, cash flow statement, and ratio report. It is a very simplified version of the Financial Plan for a Business spreadsheet application. It is the largest of the spreadsheet applications designed for startups, since it includes its own sales plan, cash flow analysis, and backup detail worksheets as part of the plan. The background worksheets provide detail for income statement items (sales, cost of goods and gross margin, operating expense, financial and tax expense) and balance sheet items (assets, liabilities, equity) and valuation.  

You can learn more at http://templates.modelsheetsoft.com/modelsheettemplates/financial-plan-small-templates.aspx .

Sales Plan for a Small Startup

This spreadsheet application organizes your estimates of sales for the first few years. You can specify a product line with several products. You can specify several sales channels. You can specify prices and sales units for each product and sales channel. (If you want to specify revenue directly, just set prices equal to 1 and enter your revenue as the sales units.) You can specify which time periods contain plan data, and which contain actual results.

This model contains an optional section where you can enter sales history data. If you have such data, it is helpful to compare your plans with history as a test of your assumptions.

You can learn more at http://templates.modelsheetsoft.com/modelsheettemplates/sales-plan-startup-templates.aspx .

Cash Flow for a Small Startup

This spreadsheet has a simple structure. You list your cash receipts from sales and other sources, and you list your expenditures for operating expenses and financial and tax expenditures. You can specify which time periods contain plan data, and which contain actual results. The Advanced version also includes a sheet that organizes text assumptions for each part of the analysis.

You can learn more at http://templates.modelsheetsoft.com/modelsheettemplates/cash-flow-startup-templates.aspx .

Cash Requirements for a Small Startup

This spreadsheet application walks you through the common sources and uses of cash in a startup business. For cash sources, it tracks details concerning founders’ investments, equity investments and loans. It tracks the investors, amounts, and collateral (if any). For cash uses, it lists many of the common expenditures of a startup: rent, insurance, deposits and prepaid expenses, initial inventory, furniture, equipment, and many others. The Advanced version also includes a sheet that organizes text assumptions for each part of the analysis.

You can learn more at http://templates.modelsheetsoft.com/modelsheettemplates/cash-requirements-startup-templates.aspx .

Other Applications for Startup Companies

Other ModelSheet spreadsheet applications may also be useful to small businesses, because they do not require any historical data. These include

• Operations Process Flow (learn more at http://templates.modelsheetsoft.com/modelsheettemplates/operations-process-flow-templates.aspx)
• Investment Project Analysis (learn more at http://templates.modelsheetsoft.com/modelsheettemplates/investment-project-templates.aspx)
• Capitalization Table, since startups usually have to analyze startup financing (learn more at http://templates.modelsheetsoft.com/modelsheettemplates/capitalization-table-templates.aspx)
• Employment Candidate Evaluation (learn more at http://templates.modelsheetsoft.com/modelsheettemplates/job-candidates-templates.aspx )

You can download small free static and customized working samples of each model (in fact, for any ModelSheet model) to get a feel for how it can help you. The startup models are priced to be especially affordable for small startups.

Under ordinary competitive market conditions, the primary objectives of pricing policies are to set prices that maximize revenue, or more to the point, to set prices that maximize profits.

This simple statement of objectives hides the full complexity of pricing decisions. Complexities include these issues.

• What are the main factors that determine customer reaction to prices? Such factors can include be sensitivity to quality, reliability of supply, social status (mostly relevant for consumer products), and obviously costs.
• How do your prices interact with competitors’ prices? In efficient commodity markets (where competing products are good substitutes for one another), your revenue can climb rapidly or decline sharply in response to small changes in your prices or competitors’ prices.
• How much does the past history of pricing affect the market response to current prices? For example, how will market reaction to a price of $100 differ if the price in the recent past was $80 or $120?
• How do prices interact with access to distribution channels? In some markets, distribution channels have enough power that the biggest challenge for suppliers is gaining widespread distribution, from which a large market share will follow. 
• How should longer-term strategic factors affect pricing? Some products and services have high growth rates or otherwise have long-term potential that greatly exceeds their current revenue and profits. Prices of such products should be set by a different set of strategic principles.

The approach we shall take  encompasses the first four issues in a broad pricing framework. The strategic issues in the last bullet cannot be resolved by simple market testing and quantitative analysis, and we plan to discuss them in another article.

Assumptions Behind the Models

ModelSheet’ offers two price testing and price elasticity spreadsheet applications that address these questions in a wide range of situations. The first application answers these questions for one product in isolation, and the second one answers these questions for dozens of interacting products in the same market.

Our approach to pricing decisions is based on several assumptions.

• Revenues and unit sales for one product vary in a smooth fashion over a range of prices. The relationship is smooth but need not be a straight line.
• More generally, revenue and sales units for related products vary in a smooth fashion over a range of prices for all the related products.
• Your products can compete with one another, and with competitors’ products, as good substitutes or marginal substitutes for one another.
• You know the sales units for each product in a broad market at one set of prices for the products. (In the application, these are referred to as reference prices and reference sales units.)
• You can test different prices in different sub-markets in a way that enables you can deduce reaction of the entire market to price changes.  Many factors can complicate the situation so it may not fit our simple interpretation. Examples: People may be able to get different prices in nearly towns, and if the price difference is great enough to cause people to tell their friends and to travel a short distance to get lower prices. Participants may know that the price changes are temporary (for example if they know that a price test is being conducted), which may change their behavior. Different test markets may have sharply different reactions  to prices (for example, very affluent and poor neighborhoods), which means you cannot treat the responses to price changes in submarkets as representative of the whole market.

If your situation fits these assumptions reasonably well, then you can probably apply our pricing models and get reasonable estimates of optimal prices.

The Pricing Analysis Procedure

Under these assumptions, the pricing analysis process is relatively simple to implement. Just follow these steps.

1. Measure the sales units (called the reference sales units) in the larger market at a know reference prices under normal market conditions.
2. Define sub-markets that each have behavior that approximates that of the entire market, and avoid the problems discussed above that can complicate interpretation of test results. If you are testing price interactions of N products, you need at least N * (N + 3)/2 test markets, and preferably twice that number. Record the number of sales units in each of the test markets at the reference price under normal market conditions.
3. Choose test prices for the related products in each test market. The test prices should be higher and lower than the reference price for each product in some test markets, and the changes in prices for each product should be independent of one another in at least a few of the test markets.
4. Run the pricing tests and record the sales units in each test market.
5. Choose a price range for each product over which you want to predict sales units and revenue for each product in the total market.
6. Enter into the ModelSheet spreadsheet application: (a) the reference price for each product, (b) reference sales units for each product for the total market, (c) sales units for each product in each test market at reference prices, (d) sales units for each product in each test market at test prices, and (e) the price range over which you want sales predictions (and the specific prices at which you want predictions).

The Price Testing and Price Elasticity model will return predictions of sales units and revenue for the prices at which you requested predictions. You will not necessarily get a price that maximizes revenues. For example if you test prices between $100 and $150, and the revenue keeps increasing up to a price of $200, then the analysis will not include the price that maximizes revenue.

Prices that Maximize Profits

For simplicity, we omitted above the steps in the analysis needed to determine prices that optimize profits. To do this, you must enter into the model the reference cost of the reference sales units for each product, and a cost elasticity factor for each product. (If costs increase in direct proportion to sales units, then cost elasticity equals 1. If cost is fixed regardless of sales units, then cost elasticity is zero. Cost elasticity is usually a number between 0.5 and 1.0.) The model will then predict contribution margins (revenue less costs) for each product at each combination of product prices at which you requested a prediction.

If you include competing products in the analysis, you can specify which products are yours and which are not. The model will produce sales and profit predictions for all products in the analysis, and for your products alone.

In Summary

The Price Testing and Price Elasticity models reduce a very complex process to a quantitative analysis that is easy to use and that can help you to make better pricing decisions. Your real-world situation may contain other, subtle factors that require expert guidance to take into account in your pricing study. As always when using analytical methods in business, listen carefully to experienced field experts who are not analysts; they may know about some factors that the analysis does not take into account.

For more information about the Price Testing and Price Elasticity models, see

• For one product: http://templates.modelsheetsoft.com/modelsheettemplates/product-price-elasticity-templates.aspx
• For several interacting products: http://templates.modelsheetsoft.com/modelsheettemplates/price-elasticity-templates.aspx

Appendix: How the Pricing Models Works

This section is more technical, and you can skip it if you like. 

The models answer the question, “If I raise (lower) prices by x%, by what percentage will sales units change?” The answer to this question is known in economics as “price elasticity”, or more precisely the “elasticity of sales units with respect to price”. The technical description of price elasticity is:

elasticity of sales units with respect to price = (change in units/ reference units) / (change in price / reference price) = (percentage change in sales units) / percentage change in price)

You can also define elasticity of revenue with respect to price, which equals 1+ elasticity of sales units with respect to price. We will not use this in the analysis.

Use notations:

• Q = ln(sales units/reference sales units), where “ln” is the natural logarithm base ‘e‘
• P = ln(price/reference price)
• ε (Greek epsilon) = elasticity of sales units with respect to price.

The defining equation of price elasticity is

ε = d ln(Q) / d ln(P)

where ‘d’ means take the derivative (as in calculus). The textbook case assumes that ε is a constant, so that Q and P have a linear relationship.

Q = ε * P

This is a serious limitation, because you can’t do a good job of identifying prices that yield maxima of revenue or profit with a relationship that is (log-) linear. So our models allow ε to change linearly with P, so that the basic relationship is

Q = ε[1] * P + ε[2] * P^2

so:  ε = ε[1] + 2 * ε[2] * P

This yields a (log-) quadratic relationship between sales units and price, so the model is much more effective at solving for the prices that maximize revenue or profit.

If you are studying just one product, then this is the end of the story. If you are studying the market interactions of N products (N>1), then Q and P become vectors with one component for each product, and ε becomes a matrix that describes the effect of changes in the price of product j on the sales units of product i.

Q[i] = ε[1, i] * P[i] + ε[2, i, j] * P[j]^2 (sum over j = 1, …, N)

ε[i] = ε[1, i] + 2 * ε[2, i , j] * P[j] (sum over j = 1, …, N)

The model uses quadratic regressions (generalizations of linear regressions) to compute the best estimates of the elasticity coefficients ε[1, i] and ε[2, i , j] (where i and j = 1, …, N).

ModelSheet’s Cash Flow Analysis model focuses on liquidity – that is, managing cash so that you can meet all obligations without running out.  It contains everything you need to analyze cash flows and line of credit in a small to medium-sized business. It helps a business owner or manager to know in advance when there will be a cash shortfall or excess cash.

The cash flow model tracks the following sources of cash.

1. Trade receivables are tracked by receivable account. You have the option of listing receipts from each account as a time series, or tracking each sales invoice. If you track each invoice, you get a more detailed planned payment schedule for each invoice from each customer, and more insight into credit risks (and an aging report).
2. Non-trade receivables are tracked by receivable account.
3. Bank checking account float (optional).  You can track checking account float to the level of clearing of individual checks. This part of the model draws information from an Excel database of checking account records that are easy to provide from conventional sources of bank information.
4. See the financing options below, which are also sources of cash.

The cash flow model tracsk the following uses of cash.

1.  Employee disbursements for salaried and hourly employees. You can list employees at any level of detail, from individuals to groups. Accounts include compensation, benefits, payroll taxes, and allocations for travel & entertainment. You can specify payroll schedules for salaried and hourly employees separately, in terms of payroll frequency and start dates. (It can accommodate companies that stagger paying hourly and salaried employees to smooth the cash flow.) The model reads the employee data from two Excel databases that included in the model, and that are easy to populate from your data sources.
2. Disbursement accounts for which you track payments by time period for each vendor or account.
3. Disbursement accounts for which you track payments by your purchase invoice. This gives you finer insight into your payment policies, along with an aging report to help you manage payments.

 The cash flow model incorporates several financing options that serve as sources of cash.

1. You can specify a “line of credit” arrangement whereby you can borrow money from a bank on favorable terms. The amount you can borrow is determined by your “borrowing base”, which is determined by the level of qualified inventories and accounts receivable. You can specify many of the policy parameters in the line of credit. The model enables you to track cash flows to and from the creditor, financing expenses, and your outstanding loan balance.
2. You can factor receivables and get up-front cash and cash at time of customer payment. You can specify the term of the factor loan and fees. The model handles the case in which you bear the risk of customer default, and the case in which the “factor” bears this risk.

You have the option to segment the cash flow by business units or other entities. It also provides optional variance analysis of actual and planned cash flows.

The model includes these features because they are the most common features requested by customers.

You can learn more about the cash flow model at http://templates.modelsheetsoft.com/modelsheettemplates/cash-flow-templates.aspx .

We also offer a simpler cash flow analysis for small startups at http://templates.modelsheetsoft.com/modelsheettemplates/cash-flow-startup-templates.aspx .

If you want to alter or add additional features to the cash flow model to suite your needs, please contact us at info@modelsheetsoft.com .

ModelSheet Software is excited to bring you our new web-based product, the Template Customizer. It enables you to create expressive and easy-to-use spreadsheet templates customized to suit your needs in minutes! Manually customizing a comparable spreadsheet template can take hours or even days.

To try the Template Customizer, please visit our website at http://templates.modelsheetsoft.com. You can browse our selection of 20 prebuilt customizable models. Each model has four versions – light, standard, advanced and advanced, extra-large. The customizable models are:

Finance
* Activity-Base Budgets
* Financial Plan for a Professional Services Business
* Financial Plan for a Business
* Capitalization table
* Investment Project Analysis
* Cash Flow Analysis
* Cash Flow for a Small Start-up
* Cash Requirements for a Small Start-up

Marketing and Sales
* Sales Plan
* Sales Plan for a Small Start-up
* Product Profitability
* Price Testing and Price Elasticity
* Marketing Program Effectiveness

Economics and Stochastic Modeling
* Macroeconomic Model of an Economy
* Monte Carlo Simulation of an Economy

Other Models
* Decision Support
* Operations Process Flow
* School Grade book
* Employment Candidate Evaluation
* Job Opportunities

To customize a model:

1. Select a model of your choice from the Model Browser.
2. Fill out the simple web forms presented to you.
3. Your spreadsheet template is ready for download in minutes!

If you don’t find a model that meets your needs, please contact us at info@modelsheetsoft.com to learn about our Consulting Services. We can build customizable models that suit your needs, and deliver them on the Template Customizer. You may customize them as many times as you wish as your specific needs change. Our technology enables us to offer you unprecedented value.

We’d be delighted to hear from you if you have any questions or feedback about our products or services so that we may serve you better.

Thank you!

Sincerely,

Krishnan Badrinarayanan
Marketing Manager | ModelSheet Software LLC
email: krishnanb@modelsheetsoft.com

ModelSheet has a customizable Activity-Based Budget model that has the main features needed to apply this powerful budgeting method. The model  accommodates numerous cost centers; each cost center can have numerous expense accounts; each expense account can be driven by numerous activities; and each activity driver can drive any number of expense accounts.

The key inputs to an activity-based budget are the cost-per-activity-count, and the budgeted activity counts in the budget time range. The ModelSheet model allows the user to specify both numbers by time period. The model  starts by suggesting cost-per-activity-count coefficients based on historical data for expenses and activity counts. You can use these values as the budget inputs, or use them as historical benchmarks and override the suggested numbers. You can also separate out fixed costs that are not driven by activity counts and add the fixed costs into the final budget.

One of the key benefits of activity-based budgets is the ways you can analyze variances from plan. An expense variance can be due to either higher-than-planned activity counts, or higher-than-planned cost per activity count. These types of variances have quite different causes and remedies. The ModelSheet template enables you to include actual activity counts and actual expenses, from which it can report both types of variance for each activity and for each expense account in each cost center.

In the customizable templates, you can specify the activity drivers, cost centers, expense accounts in each cost center, the activities that drive each expense account, the expense-per-activity-count coefficients, the history time range, the budget time range, and the time grain (day, week, month, etc.). The current versions can handle up to 500 expense accounts that are driven by up to 100 activity counts. We can raise these limits for special projects.

This tool is designed to help people who already use activity-base budgeting by providing a customized tool at low prices, and to help people to experiment with the method without having to manually build spreadsheet tools. You can access the template on our website at http://templates.modelsheetsoft.com/modelsheettemplates/activity-based-budget-templates.aspx . You can customize and download a small free working sample to get an idea how it works before buying one. [Note: If you want this model before February 15, 2010, please contact us directly for more information. After that date, the model will be publicly available at the URL listed above.]

The Next Step in the Evolution of Spreadsheets?

Spreadsheets wildly succeeded because they enable domain experts to self-serve with less dependence on programmers. Spreadsheets are so successful that they are now used in complex applications where their strengths are weaknesses, because spreadsheets strip out basic program structures.

MIT-alumni founders of ModelSheet Software will present two applications of technology that promises to revolutionize spreadsheets.

ModelSheet Authoring is a SaaS environment for authoring and maintaining models that

• retains what is best about spreadsheets: use of sheet layout to present model logic during authoring, an easy-to-learn modeling paradigm, and a flexible and familiar UI.
• adds the program structures needed to effectively author complex models: named variables, dimensions, time series, readable symbolic formulas (and far fewer formulas), variable data types.
• automates many manual cell-level operations needed to build spreadsheets.
• delivers models  as conventional spreadsheets.

ModelSheet customized templates enable spreadsheet users to customize spreadsheets by filling in a simple web form, without editing a spreadsheet or its formulas. Some simple examples are:

• specify a time line, including time range and multiple time grains

• specify number, names and hierarchy of items in a dimension (such as products and product families)

• include or exclude major features.

While the focus will be on applications, the presenters are prepared to discuss the advanced software technology underlying ModelSheet.

Come and see if you agree that ModelSheet is the next step in the evolution of spreadsheets.

URL: http://www.modelsheetsoft.com

Founders: Howard Cannon (MIT Computer Science),  Richard Petti (MIT Mathematics)

• The capability to make one worksheet per cost center will be a standard option in a new Activity-Based Budgeting template to be published in the first quarter of 2010. This capability will show up on other templates over time, and we can apply this feature to templates of your choice on a case by case basis.
• We have developed the capability to automate generating one workbook per cost center for ABB, and for any dimension in a model. We can apply this capability for you in just about any model or template , but we nave not included this capability as standard feature in any published models at this time.

These features save you the time and effort of making similar worksheets and workbooks for different items in a list. The biggest advantage of these features appears when you want to change the number if items in a dimension; with ModelSheet, the number of worksheets or workbooks just changes automatically with no intervention on your part.

This is the way spreadsheets should work for you. That (and some customer requests) is why we added these features to ModelSheet Authoring and ModelSheet Customizable Templates.