Robert Zimmer Room 6, 25 St James Lecture 2 Robert Zimmer Room 6, 25 St James

This course is about building models and making decisions It is about organising information It is about being able to ask what-if questions It is about applying powerful mathematical models (I might try to teach you some maths when you aren’t looking but that is incidental)

Example of a decision: should I have another beer? Organising Information: How much money I have How much money a beer costs How drunk am I? Do I have to drive? How fat am I? How much do I like the people in the pub? How much do I like the people at home?

Another Question What is the most money I am prepared to pay for this drink? That is at what price does the pleasure of the drink become less than its price?

Some more questions What is the geometric shape of all the points at which the pleasure of the beer exactly matches the pain of the payment? How will my pleasure, my weight, and my mental state compare if instead of a beer I have chips? or do my Java coursework?

Spreadsheet modeling is the process of entering the inputs and decision variables into a spreadsheet and then relating them appropriately, by means of formulas, to obtain the outputs. Once a model is created there are several directions in which to proceed. Sensitivity analysis to see how one or more outputs change as selected inputs or decision variables change. Finding the value of a decision variable that maximizes or minimizes a particular output. Create graphs to show graphically how certain parameters of the model are related.

Good spreadsheet modeling practices are essential. Spreadsheet models should be designed with readability in mind. Several features that improve readability include: A clear logical layout to the overall model Separation of different parts of a model Clear headings for different sections of the model Liberal use of range names Liberal use of formatting features Liberal use of cell comments Liberal use of text boxes for assumptions, lists or explanations

Example 2.1 – Building a Model Randy Kitchell is a NCAA t-shirt vendor. The fixed cost of any order is $750, the variable cost is $6 per shirt. Randy’s selling price is $10 per shirt, until a week after the tournament when it will drop to $4 apiece. The expected demand at full price is 1500 shirts. He wants to build a spreadsheet model that will let him experiment with the uncertain demand and his order quantity.

In this model the profit is calculated with the formula Profit = Revenue – Cost and the Cost = 750 + 6*B4

Revenue Case 1: Demand outstrips order (B3 > B4) In that case everything gets sold for 10 dollars Revenue is then simply 10*B4 (since B4 is the number ordered)

Revenue Case 2:You have ordered too many. That is order (B3) is less than peak demand Then you can only sell B3 at 10 dollars and the rest (B4-B3) at 4 dollars Revenue = 10*B3+4*(B4-B3)

Revenue Formula Revenue = IF(B3>B4,10*B4,10*B3+4*(B4-B3))

Profit Formula Profit = IF(B3>B4,10*B4,10*B3+4*(B4-B3)) –

Adding Flexibility We add flexibility by allowing more things to vary

Ex. 2.1(cont’d) - Building a Model The formula can be rewritten to be more flexible. =-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8)) It can be made more readable by using range names. The formula would then read =-Fixed_order_cost-Variable_cost*Order + IF(Demand > Order, Selling_price*Order, 10*Demand+Salvage_value* (Order-Demand)

Ex. 2.1(cont’d) - Building a Model We might like to have profit broken down into various costs and revenues, rather one single profit cell. The profit formula would be = -(B12+B13)+(B15+B16). Range names could be used for these intermediate output cells, but it is probably more work than it is worth. Labels and/or color coding can help a lot with readability.

Ex. 2.1(cont’d) - Building a Model Data tables could be used to see how sensitive profit is to the inputs, the demand, and the order quantity, and charts to show any numerical results graphically.

Example 2.2 – Cost Projections The company knows that wood prices and labor costs are likely to increase in the future, and it would like to project its costs of manufacturing the bookshelves into the future. The data can be found in Table 2.1. Build a spreadsheet model that allows the company to experiment with the growth rates in wood and labor costs so that a manager can see, both numerically and graphically, how the costs of the bookshelves will vary in the next few years.

Ex. 2.2(cont’d) - Planning the Model The reasoning behind the model is straightforward. First project the unit costs for wood and labor into the future. Then for any year, multiply the unit costs by the required numbers of board-feet and labor hours per bookshelf. Finally, add the wood ad labor costs to obtain the total cost of a bookshelf.

Ex. 2.2(cont’d) – The Model

Ex. 2.2(cont’d) – Developing the Model Develop the model with the following steps. Inputs: Enter the inputs into the upper left corner of a worksheet. These can be referred to later with Excel formulas. Design output table: You need to think ahead of time how you want to structure your outputs. The important point is that you should have some logical design in mind before diving in. Projected unit costs of wood: It is important to have a strategy in mind before you enter the formulas. You should design your spreadsheet so that you can enter a single formula and then copy it whenever possible.

Ex. 2.2(cont’d) – Developing the Model For example: enter the formula =B9 in cell B19 and copy it to cell C19. Then enter the general formula =B19*(1+B$10) in cell B20 and copy it to the range B20:C25. Projected unit labor costs: To calculate projected hourly labor costs, enter the formula =B13 in cell D19. Then enter the formula =D19*(1+B$14) in cell D20 and copy it down to column D. Projected bookshelf costs: With careful use of absolute and relative addresses, enter a single formula for these costs – for all years and for both types of wood. To do this, enter the formula =B$5*B19+B$6*$D19 in cell E19 and copy it to the range E19:F25.

Developing the Model -- continued Chart: Highlight the range E19:F25 and click on Excel’s Chart Wizard button. This leads you through a sequence of steps. You should experiment with the possibilities. The model can be used to answer any what-if questions Woodworks might want to ask. The model has been built in such a way that a manager can enter any desired values in the input cells, and all of the outputs , including the chart, will update automatically. Burying input numbers inside Excel formulas is bad practice.

2.4 Breakeven Analysis Many business problems require us to find the appropriate level of some activity. This might be the level that maximizes profit, or it might be the level that allows a company to break even – no profit, no loss.

Example 2.3 - Breakeven Analysis The Great Threads Company is planning to print a brochure of its products and undertake a direct mail campaign. The cost of printing the brochure is $20,000 plus $0.10 a catalog. The cost of mailing each catalog is $0.15. In addition, the company will include direct reply envelopes in it’s mailings. It incurs $0.20 in extra cost for each direct mail envelope that is used by a respondent. The average size of a customer order is $40, and the company’s variable cost per order averages around 80% of the order’s value.

Ex. 2.3(cont’d) - Breakeven Analysis The company plans to mail 100,000 catalogs. It wants to develop a spreadsheet model to answer the following questions: How does a change in the response rate affect profit? For what response rate does a company break even? If the company estimates a response rate of 3%, should it proceed with the mailing? How does the presence of uncertainty affect the usefulness of the model?

Ex. 2.3(cont’d) - Planning the Model A single “bottom line” output variable, in this case profit, is of most concern. The logic for converting inputs and the decision variable into outputs is quite straightforward. Then it must be investigated how the response rate affects the profit with a sensitivity analysis.

Ex. 2.3(cont’d) - Developing the Model To create this model, proceed through the following steps. Heading and range names: Be cautious not to go overboard with range names. Enter input values: Some of the values have been combined in the statement of the problem. To document this process, enter comments in a few cells. Inserting comments in cells is a great way to document your spreadsheet models without making it too cluttered. Model the responses: Enter any reasonable value, such as 8%, in the Respone_rate cell. =Number_mailed*Response_rate in cell E5

Ex. 2.3(cont’d) - Developing the Model Model the revenues, costs and profits: Enter the formula =Number_of_responses*Average_order in the in cell E8. Enter the formula =Fixed_cost_of_printing, =Variable_cost_of_printing_mailing*Number_mailed and =Number_of_responses*Variable_cost_per_order in cells E9, E10, and E11. Enter the formula =SUM(E9:E11) in the cell E12, and enter the formula =Total_revenue-Total_cost in the cell E13.

Ex. 2.3(cont’d) - Data Table A a one-way data table is formed to show how profit varies with the response rate. Data tables are called “what-if” tables. They illustrate what happens to selected outputs if selected inputs change. From the data table it can be seen that profit changes from negative to positive when the response rate is somewhere between 5% and 6%. This could be found by trial and error, but it is easier to find with Excel’s Goal Seek tool.

Ex. 2.3(cont’d) - Goal Seek Goal seek is useful for solving a single equation in a single unknown. The unknown is called the changing cell because it is allowed to be changed to make the equation true. Select the Tools/Goal Seek menu item and fill in the resulting dialog box. If the response rate is 5.77%, Great Threads breaks even.

Ex. 2.3(cont’d) - Limitations of the Model Question 3 asks whether the company should proceed with the mailing if the response rate is only 3%. The apparent answer is “no” because profit is negative. This reasoning is taking the short-term view. To consider the long term impact of our decisions the model must incorporate the long term explicitly into the model. To do this a more complex model must be built.

Ex. 2.3(cont’d) - Limitations of the Model Question 4 asks about the impact of uncertainty in the model. It makes more sense to talk about the probability that profit will have a certain value or the probability that the company will break even.

2.6 Decisions Involving the Time Value of Money Cash flows are received at different points in time, and a company must determine a course of action that maximizes the “value” of cash flows. The later a dollar is received, the less valuable the dollar is. This is useful in making decisions. $1.00 X 1/(1+r) now = $1.00 a year from now The value 1/(1+r) in the above equation is called the discount factor.

The quantity on the left is called the present value of $1 The quantity on the left is called the present value of $1.00 received a year from now. If money can be invested at annual rate r compounded each year, then $1 received t years from now has the same value as 1/(1+r)t dollars received today – that is, the $1 is discounted by the discount factor raised to the t power. By multiplying a cash flow received t years from now by 1/(1+r)t (its present value), then the total value of all cash flows over all years is called the net present value (NPV) of our cash flows.

The rate r (usually called the discount rate) used by major corporations generally comes from some version of the capital asset pricing model. The discount factor is 1 divided by 1 plus the discount rate. The NPV is the sum of all discounted cash flows.