MBA Quantitative Methods PC-Exercises Introductory Examples

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1 MBA Quantitative Methods PC-Exercises Introductory Examples intro.xls intro_with_output.xls intro.doc For all Examples you need the file intro.xls. The file intro_with_output.xls is the file with the results of the introductory examples. In this file are the examples with propositions for a complete solution. Remarks: There is not the one and only way, there are always more ways to solve problems. Try to separate data and formulas in spreadsheets. Example 1: Production planning model for boats In this example we will get to know some basic excel-functions and principles. Calculating Profit 1. Calculate the total profit in cell B4 by summing the profit per unit multiplied by the associated production quantity. Start with the spreadsheet boat in the file intro.xls. Go to cell B4. Enter the formula =C2*C3+D2*D3 Cell A4, type Total profit As general rules: - Data should never be typed directly in a formula (separation of data and formulas). If the profit per unit changes, the formula still holds true. - Always test formulas after entering them. Test the formula: Type 1 into cell C2 total profit should be 1,200 Type 1 into cell D2 total profit should rise to 2, Calculate the total usage of materials in cells B8 to B10 by summing the required quantity per product by the associated production quantities Go to cell B8. Enter the formula =C$2*C8+D$2*D8. The $-signs before the row numbers indicate an absolute reference that allows the formula to be copied in cells B9:B10. Copy the formula: select cell B8; place the cursor over the small black square in the lower right corner of the cell, drag down to B10. Go to cell B7 and label it Used. intro.pdf Page 1

2 3. Making sure the model is scalable: You could insert a column in the worksheet for a new boat type with the insert column command, then profit and requirement data could be entered. But if you did so, all the formulas would need to be modified! It is likely to introduce errors into the model. Better: use the SUMPRODUCT-Formula. Go to cell B4. Replace the formula =C2*C3+D2*D3 by =SUMPRODUCT(C2:D2,C3:D3). same calculation but SUMPRODUCT includes automatically additional columns inserted between C and D. Go to cells B8:B10 and replace the formulas by SUMPRODUCT-formulas. Don t forget the $ signs on the arguments $C$2:$D$2 so you can copy the formula correctly. Hint: toggle the <F4> key while editing the formula to apply the $ signs to the correct arguments. 4. Feasibility Checking: The materials on hand are limited. As we experiment with various production figures, we must check that they are feasible. That is, we must not consume more raw materials than we have on hand. Use logical formulas to compare the raw materials with the materials on hand. Go to cell F8. Enter the formula =E8>=B8. This formula return the logical value TRUE, if E8 >= B8 and FALSE otherwise. Copy cell F8 to F9:F10. Enter the label Feasible in cell F7. intro.pdf Page 2

3 5. What If Analysis: Data Tables Given a spreadsheet model, you can experiment with the inputs by hand. This is known as what if analysis. Start by setting both boat production quantities to zero. Now how many sailboats can you produce? You can try different numbers. But we will apply a more analytical approach: Data Tables A data table allows you to repeatedly evaluate a particular formula within the model while systematically varying one or two input cells on which the formula depends. Set up a Data Table that calculates the total profit for all feasible combinations of production quantities of both types of boats from 0 to 150 in steps of 5 units. Data Table a. Entering the Formula that has to be evaluated for different variations of inputs. The result/formula is the total profit but only if the quantities are feasible. Go to B4. Divide the total profit by 1000 to express the profit in thousands (that will make results smaller and need less space). =SUMPRODUCT(C2:D2;C3:D3)/1000 We must only print the profit value if the production quantities are feasible, that is, if all the cells F8:F10 are TRUE in Excel: AND(F8:F10) must be TRUE. The formula that drives the table Go to cell G6. Enter a formula that returns the total profit in thousands if the combination of production quantities is feasible, otherwise, it will return blank. Enter =IF(AND(F8:F10);B4; ) Remark: Syntax of the IF-Statement: =IF(logical_test; value_if_true; value_if_false) Test the formula by changing production quantities in cells C2 and D2. b. Specifying the Quantities to Evaluate Sailboats: row 6 from column H (H6), numbers from 0 to 150 in increments of 5 Motorboats: column G from row 7 (G7), numbers from 150 to 0 in decrements of 5. Profit Formula c. Using the Data Table Command Select the entire table (G6:AL37) Go to the menue bar, choose Data > Table The Data Table dialog appears Row input: C2 (production quantity of sailboats Column Input: D2 (production quantity of motorboats) Click OK, and the entire table will fill in. intro.pdf Page 3

4 Blank cells denote infeasible combinations. This table provides a lot of information. Among other things it shows that a profit of 198,000 is possible by producing 65 sailboats and 120 motor boats. Notice that this occurs at a corner of the area of feasible production figures. Save the file in your directory. 6. Experimenting with the assumptions of the model a. Suppose the number of engines available were only 100 units. What would be the maximum profit, and for what production quantities would it occur? b. Return the number of engines back to 120. Now reduce the profit per unit of motor boats below 800 until the maximum profit occurs in multiple cells. What is the profit, and in how many cells does it appear? Continue reducing the profit per unit of motor boats. In how many cells does the optimal profit appear? intro.pdf Page 4

5 Example 2: Time Value of Money Calculations In this example we will get to know some excel-functions for time value of money calculations. We use the following xls-functions: Future value = FV(rate,nper,pmt,pv) Present value = PV(rate,nper,pmt,fv) Discount rate = RATE(nper,pmt,pv,fv) Number of periods = NPER(rate,pmt,pv,fv) where pv fv rate pmt nper = present value = future value = Interest rate (as a decimal) = regular payment (each period) = number of periods Remarks: To solve for the rate or the number of periods, you have to put a negative sign on either the pv or the fv. To solve for the pv: either put a negative sign on the fv or get a negative result. The same holds true for fv. Calculating the Future Value 1. You have 10,000 EUR to invest. You will need the money in 5 years and you expect to earn 8% per year. How much will you have in 5 years? Go to the spreadsheet Time Value of Money in the file intro.xls. Cell C4: 10,000 PV Cell C5: 5 Number of Periods Cell C6: 0.08 Rate Cell C8: =-FV(C6;C5;0;C4) Notice that there is a sign convention in the spreadsheet with positive inflows and negative outflows. A negative sign was placed before the FV formula to make the result positive. Note that this problem does not include a payment, so it was entered as 0. Calculating the Present Value 2. You need 150,000 EUR in 18 years for your daughter's education. If you can earn 6% per year, how much do you need to invest today? Go to cell C15 Cell C15: 150,000 FV Cell C16: 18 Number of Periods Cell C17: 0.06 Rate Cell C19: =-PV(C17;C16;0;C15) intro.pdf Page 5

6 Calculating the Rate 3. You have 30,000 EUR to invest and you need 45,000 EUR for a down payment and closing costs on a house. If you want to buy the house in 2 years, what rate of interest do you need to earn? Go to cell C26 Cell C26: 30,000 PV Cell C27: 45,000 FV Cell C28: 2 Number of Periods Cell C30: =-PV(C17;C16;0;C15) Note that the rate will display as a whole percent, you need to format the cell to see the decimal places. Note a negative sign was entered before the cell reference for the FV to maintain the sign convention. Calculating the Number of Periods 4. You have 15,000 EUR to invest right now and you figure you will need 25,000 EUR to buy a new car. If you can earn 9% per year, how long before you can buy the car? Go to cell C Cell C38: 15,000 PV Cell C39: 25,000 FV Cell C40: 0.09 Rate Cell C42: =-NPER(C17;C16;0;C15) intro.pdf Page 6

7 Example 3: Valuation of Cash Flows 1. Future Value of an uneven cash flow Consider the cash flows presented in the table below. What is the value of the cash flows in year 5? Assume that the interest rate is 15%. Year Cash Flow 1 1, , , , ,000 Go to the spreadsheet Valuation of Cash Flows in the file intro.xls. : Cell B5: 15% Rate Cell B6: 5 Valuation Point of Time Cells C9:C13: the cash Flows Cell B9: =$B$6-$A9 Compounding Periods Copy the formula to cells B10:B13 Cell D9: = FV($B$5,B9,0,C9) Copy the formula to cells D10:D13 Comments The negative sign before the FV formula makes the result positive. The dollar signs around B5 and B6 make the rate and time an absolute reference so that the formulas may be entered once and then copied down. The FV-formula asks for a payment between number of periods and present value, hence this is Present Value of an annuity What is the present value of 50,000 per year for 15 years if the interest rate is 7%? Assume that the payments occur at the end of the periods. Variables: Cell B21: Cell B22: 0.07 Cell B23: 15 Payment (PMT) Rate Number per periods Cell B25: = PV(B22;B23;B21) Note: The negative sign in the formula makes the result positive. You could also put a negative sign before the PMT inside the parentheses. Finding the payments You are borrowing 10,000 on a 10 month loan with an annual interest rate of 8 percent. What will your monthly payments be? Variables: Cell B32: Cell B33: 0.08/12 Cell B34: 10 Presernt Value Rate Number per periods Cell B36: = PMT(B33;B34;B32) intro.pdf Page 7