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Chapter 4

Chapter 4. Planning Models. Operations Analysis Using MS Excel. Planning modeling. Chapter Outline: The basic planning problem The basic pricing problem 3. Nonlinear cost and demand functions XP Function Mathematical model of an XY Function Spreadsheet Model of XY Function

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Chapter 4

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  1. Chapter 4 Planning Models Operations Analysis Using MS Excel

  2. Planning modeling • Chapter Outline: • The basic planning problem • The basic pricing problem • 3.Nonlinear cost and demand functions • XP Function • Mathematical model of an XY Function • Spreadsheet Model of XY Function • Approximating the cost with a Cubic Function • Preparing a Five year Plan • The Impact of Pricing

  3. The Basic Planning Problem Down is a skeleton model for a five year projection of profit for a corporation. • Assumption • Selling price is $60 (not change over next five years) • Fixed cost $1500 (grow at constant rate) • Number of units – 80 (grow at a constant rate) • Variable cost $45 per unit (not change over next five years)

  4. The NPV function calculates the net present value based on a series of cash flows. The syntax of this function is =NPV(rate,value1,[value2],[...]) The annual cash flows are the (profit = revenues minus costs) generated from the investment during its lifetime. NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account. These cash flows are discounted or adjusted by incorporating the uncertainty and time value of money. NPV is one of the most robust financial evaluation tools to estimate the value of an investment. NPV > 0 the investment would add value to the firm, so the project may be accepted NPV < 0 the investment would subtract value from the firm, so the project should be rejected NPV = 0 the investment would neither gain nor lose value for the firm, so we should be indifferent in the decision whether to accept or reject the project.

  5. The Basic Planning Problem

  6. The Basic Planning Problem Data table is created to view What-if Analysis on the growth rates for fixed costsandunits sold

  7. The Basic Pricing Problem • The central issue in pricing is determining how quantity sold depends on the price. • Demand in most cases is elastic, that is when the price increases, the demand decreases. • The simplest assumption is that demand is a linearly decreasing function of price. • Organization assumptions or judgments: • At price $70, sales will be 2,400 • One dollarincrease in price = 37 units decrease in the sale • Using the above information to express the number of units sold as a function of price. • PRICE UNIT • (PRICE– 70) = 0 70 2400 • (PRICE – 70) > 0 INCREASE DECREASE • (PRICE – 70) < 0 DECREASE INCREASE • Change in number of units = - 37 * (PRICE - 70) • Using the second assumption, then • Number of unit = 2400 + Change in number of units • Number of units = 2400 - 37 * (PRICE - 70) = 4990 – ( 37 * PRICE )

  8. The Basic Pricing Problem = 4990 – 37 * Price = 50000 + 35 * Quantity = Price * Quantity = Revenue – Total Cost Marketers are interested in a price range of $60 to $100. They expect fixed cost to be $50000, with a unit cost of $35.

  9. Maximum profit occurs around $42,750 at the price $85. More accurate value can be generated by entering more numbers in the column providing the input to the table. However exactness might be misleading because of the uncertainty in the demand function.

  10. Quantity Variable Cost 0 0 50 3000 100 4500 150 4900 Nonlinear Cost and Demand Function • Most applications in real life have nonlinear relationships. They follow a curved, nonlinear XY functions. • EX. • Torrington Corporation, deciding whether they should introduce a new product. • Production prepares a cost estimate for making up to 150 units. (variable cost will not be a linear function of quantity) • Graph is prepared to show the curve representing variable cost • The problem is to develop formulas to give the cost values for any value of the quantity.

  11. Nonlinear Cost and Demand Function Mathematical Models of an XY Functions • Suppose Torrington wishes to determine the cost associated with the quantity 70. • Find the slope of any line segment. Considering the cost at 50 with 3,000; then slope is calculated as; • Slope= (Y2-Y1)/(X2-X1) • = (4,500-3,000)/(100-50) = 30 • Cost = Y1 + Slope ×( X-X1) • Quantity (X) = 70, X1=50, and Cost Y1= 3,000; • Then Cost for X = 3,000 + 30 × (70 – 50) = 3,600

  12. Nonlinear Cost and Demand Function Spreadsheet Models of an XY Functions • Cells A3 to C7 (Number of units, variable cost, slope) contain a lookup table that Excel uses to find the necessary parameters for a given number of units. • Cells B9 to B11 are user-entered data.(Input factors) • Cells B12 to B14 use the lookup table to find required items of data. • Cell B15 computes the variable cost for the number of units entered in cell B10, • Variable cost = UP + ( NUMBER OF UNIT – LEFT ) * SLOPE using the formula =B13 + ( B10-B12)*B14 • Cell B16 computes the total cost by adding the fixed and variable costs using =B11 + B15 • Cell B17 compute revenue using =B9*B10 • Cell B18 profits using =B17-B16

  13. Nonlinear Cost and Demand Function Spreadsheet Models of an XY Functions The table in the left shows the data table comparing number of units with profits Training Exercise Calculate profits against number of units being sold, where number of units start from 0 up to 150 with increment of 10 units. Find the break-even point using Goal seeker?

  14. Nonlinear Cost and Demand Function Approximating the Cost with a Cubic Function • Curves are a good facility for representing nonlinear • functions. Polynomial is a class of functions that are often • satisfactory. • The linear (first-order) function has the following form: • 2 + (10 * X) • Quadratic function assumes the form: • -24 + (56 × X2) • Cubic function assumes the form: • +(5.3 × X2) + ( 21.6 × X3)

  15. Nonlinear Cost and Demand Function Approximating the Cost with a Cubic Function The general approach 1- Try polynomials, quadratic, cubic, and so on, on the spreadsheet representing the situation. 2- Calculate the values for the given curve 3- Calculate the square of the deviations (differences), add them 4- Minimize the sum with Excel Solver by allowing the coefficient of function to be changed.

  16. Nonlinear Cost and Demand Function Approximating the Cost with a Cubic Function • Cell A3 uses the formula “=AVERAGE(A2, A4)”. • Column C calculates the cubic function based on the current coefficients in cells F3 to I3. For example Cell C2 uses the formula • “=$F$3 + ($G$3*A2)+($H$3*A2^2) +($I$3*A2^3)”. • Column D calculates the squared difference between the variable cost and the cube function. For example, cell D2 uses the formula “=(B2-C2)^2”. •  Cell D10 shows the original sum of deviations.

  17. Nonlinear Cost and Demand Function Approximating the Cost with a Cubic Function • The target cell D10 needs to be minimized. There are no constraints. The cells to vary are the cubic coefficient in cells F3 to I3. • The better way to judge how good the approximation is to compare the given curve with the calculated curve. • If the management feels that the approximation is not good enough, a fourth, fifth order polynomial or other type of function can be tried.

  18. Preparing a Five-Year plan • The lookup table is no longer required as cubic equation replaces it • Cell B7 in the cubic model now computes the variable cost using the cubic function = $D$6+($E$6*B5)+($F$6*B5^2)+($G$6*B5^3) • This Modified Model can be used to perform scenario analysis

  19. Growth in Sales Growth in Fixed Cost Best, optimistic 30% 10% Realistic 20% 20% Worst, pessimistic 10% 30% Preparing a Five-Year plan • The management is particularly interested in three scenarios • They are also interested in growth over the next five years

  20. Preparing a Five-Year plan

  21. The Impact of Pricing • Apply the cubic function approach to the analysis of pricing • The Marketing suggests the following pegs to approximate the price versus quantity • The first step is to develop a cubic function for quantity based on price. Price Quantity 20 250 40 150 60 100 80 60

  22. The Impact of Pricing

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