1. Spreadsheets in Finance and Forecasting Presentation 8: Problem Solving

2. Objectives After studying the materials for week 8, you will be able to: Set up “what-if” scenarios and summaries Use goal-seek to find the solution to specific problems Use solver to find the solution to more general problems

3. Working Methods You should work through each section of this presentation either in groups, or individually, taking notes. Read through the details of each section carefully, then when you come to the blue “Action point” sticker, carry out the tasks that you are asked to do. If you have difficulties, go back and re-read the section Only move on to the next section when you have completed the task successfully

4. Presentation Sections Click on the button to view the section Introduction Scenarios Goal Seeking Solver

5. Introduction

6. Problem Solving Excel provides many features to help managers solve problems and to make decisions. These include: Creating Scenarios: Using “What if?” situations to look at several different options Goal Seeking: Finding a value of a particular variable to meet specific conditions Solver: Finding solutions to complex problems by imposing sets of conditions on groups of cells.

7. Problem Solving During this lecture, we will look at each one of these in turn. In order to help you understand each of these features, we will look at one situation: Loan Payment

8. Loan Payments Before you open the spreadsheet, look at the next few slides carefully. Examine the various items and make sure that you understand what the spreadsheet is, and what it does. The three cells at G5, G7 and G9 are labelled as “interest”, “borrowed” and “payment”.

9. Loan Payments This shows the following situation : The interest rate is 7.5% per annum We borrowed £20000 Payments are £250 per month The loan was taken out in 2002 The loan will be paid off some time during 2012. The negative amount means that if the payments continue, the amount owing would be negative, i.e. the lender would owe you money!

10. Loan Payments Note that the final amount runs into the negative region. Pressing the “Graph Balance” button runs a macro which shows a chart illustrating the level of the balance outstanding at the end of each year.

11. Activity You should now open up the Loan Payments spreadsheet. Experiment with the amounts in the cells G5, G7 & G9, and with the Graph Ensure that you fully understand what the spreadsheet is doing before you carry on. Action Point ! Return to Menu

12. Scenarios

13. Your small business is doing well You decide to expand, and ask the bank for a loan. You need at least £30 000, and the bank offers you up to £50 000. The bank will charge you 6.5% interest You can only afford £400 per month. Is this sufficient to pay off the loan?

14. Scenario 1 Let’s start with the smallest amount needed, £30 000 The bank will charge you interest of 6.5% Set your monthly payments to £400. Is this sufficient to pay off the loan?

15. Scenario 1 The amount is £30 000 The interest is 6.5% Monthly payments are £400. Enter the details into the correct boxes in the Loan Payments Spreadsheet Action Point ! Now, Can we pay off the loan?

16. Scenario 1 You should have entered these amounts into the boxes. So, when will the loan be paid off?

17. Scenario 1 The amount outstanding is: £1280.96 (positive) in 2010, £3435.78 (negative) in 2011 This means that the loan would be paid off some time during 2011

18. Saving a Scenario This is the first of our “what if?” scenarios. Excel allows us to store these scenarios for future reference, and compare them one with another. Over the next few slides, this method will be explained.

19. Creating a Scenario Click on Tools, then Scenarios, then Add In Scenario Name, put “Small Amount” Then click here; Now click on cell G7 Click OK Click OK again on the next box Then Close on the last box Action Point !

20. What exactly is a Scenario? A scenario simply is a description of a particular situation, defined by particular values of certain variables Excel stores these Scenarios, and you can return to them

21. Scenario 2 Let’s move on to the a larger amount. Suppose we borrow £40 000 The bank will still charge you interest of 6.5% The monthly payments are still £400. Is this sufficient to pay off the loan? Action Point !

22. Changing the Scenario In this scenario we change the amount of the loan to £40 000, but the payments remain constant. The period of the loan new extends to 2015.

23. Changing the Scenario Create a New Scenario, and call it “Medium Amount” Action Point !

24. Final Scenario Change the amount of the loan to £50 000 Store this Scenario as “Large Amount” Action Point !

25. Comparing Scenarios We can re-examine the scenarios once we have stored them by clicking on Tools - Scenarios, and then selecting the particular Scenario: Small, Medium or Large Amounts Then click OK. When will the loan be paid off in each case?

26. Deleting Scenarios Select Tools- Scenario Delete Each of the three Scenarios in turn. Action Point !

27. Scenario Challenge Now Create three different scenarios, in which the Loan is £40000, and the payments are £450 per month In scenario A (low interest) the interest is 4% In scenario B (medium interest) the interest is 7% In scenario C (high interest) the interest is 10% What amount of the loan is remaining in 2010 in each case? Action Point !

28. Scenario Challenge In scenario A (low interest) £4,985.94 is left in 2010 In scenario B (medium interest) £13,324.51 is left in 2010 In scenario C (high interest) £23,989.76 is left in 2010

29. Scenario Summaries Click on Tools – Scenario and Summary Select Scenario Summary use as “results cell” the amount owing in 2010 (Cell I22) Click OK Action Point !

30. Scenario Summary This is the Summary Page. The values in cell I22 can now be compared across the three scenarios.

31. Follow-up Activities You should now examine the first section of Formative Activity 8. This challenges you to find a range solutions to particular problems for a Software- producing company Return to Menu

32. Goal Seeking

33. In Goal Seeking, we look at specific Scenarios in which particular cells achieve target values. These are achieved by altering other, named cells.

34. Goal Seeking For example: Suppose we wish to borrow £50,000. The interest rate is fixed at 6.5%, but we would like to pay this back by 2010 at the latest. To do this will mean changing the monthly payments.

35. Goal Seeking Click on Tools – Goal Seek We set cell I22 to zero. (This is the amount owing in 2010) We will make changes to cell G9; this is the value representing the monthly payments. Action Point !

36. Goal Seeking - Solution This box shows that a solution has been found. OK, so where is the solution to the problem?

37. Goal Seeking Solutions In this solution, we borrow £50 000, at 6.5%, and pay the loan back by the end of 2010. In order to achieve this, we changed cell G9. This shows that the payments need to be £684.32

38. Challenge Suppose we borrow money at 4.5% interest and we need to pay back the loan by the end of 2012. We can afford to pay £550 per month. What is the maximum amount of the loan we can afford? Action Point !

39. Solution The Goal Seeker has converged on the amount of £52, 223.94 This is paid off by the end of 2012 Here you needed to set cell I22 to zero by changing cell G7

40. Goal Seeking using a chart Click on Graph Chart, and click on the point for 2008. Wait, then click again. Wait, then click and hold. Now drag this all the way back down to zero. Suppose we want to pay the loan back by 2008

41. Goal Seeking using a chart Suppose we want to pay the loan back by 2008 This box appears. The Set Cell will automatically be filled in; we need to type in “borrowed” in the By Changing cell box.l

42. The Solution found! This shows the new data using the original chart parameters; this means that if you had kept on paying in the same way for the same amount of time, then the loan company would be in debt to you.

43. Follow-up Activities You should now examine the second section of Formative Activity 8. This section uses Goal Seeking to work out the Break-Even Price for products retailed by the software- producing company Return to Menu

44. Solver

45. Solver is an “Add- in” which extends the idea of goal- seeking. Instead of changing one cell, solver changes a number of cells to meet a target criterion.

46. The First Step If your Tools menu does not have “Solver”, you need to select “Add-Ins” and select “Solver Add-in” The Solver will then be part of the Tools menu.

47. The Problem We wish to borrow up to £50 000 We can afford up to £600 per month The interest will be at least 4% We wish to pay off the loan at the latest by the end of 2018

48. Solver parameters You need to add in the parameters of the cells which will change: borrowed, interest, payment (cells G5, G7 and G9) In addition you need to specify the cell value which you need to converge on: in this case, I30, which we will set at Zero. Action Point !

49. Solving the problem We set cell G7 – “borrowed” at less than 50000; We set cell G5 – “interest” at – at least 4% (0.04) We set cell G9 – “payments” at less than £600 The target cell I30, the amount owing in 2018, is set to zero. Use the Add button to add in these constraints

50. Solver Results This box appears when a solution has been found. The options allow you to change he values of the variables to the current solution, or to save it as a scenario. We can also get reports on the Answer, and how close Excel was in finding a solution to the given constraints.

51. Have we found a solution? It is certainly true that: “borrowed” is less than 50000; “interest” is at least 4% (0.04) “payments” is less than £600 the amount owing in 2018, is set to zero

52. Is this what we wanted? Not really. The question should have been: “What is the maximum amount we can borrow at 4%, if we are prepared to pay £600 per month, but want to pay the money off in 2018?”

53. The solver dialogue box The question should have been: “What is the maximum amount we can borrow at 4%, if we are prepared to pay up to £600 per month, but want to pay the money off in 2018?” Here we need to change the amount borrowed to a minimum amount; this will force solver to give us a solution. Use the Change button, to modify the Constraints

54. Three Scenarios The three scenarios all are feasible solutions However if we want force solver to find the maximum we can borrow, we should set the payment to 600

55. Another Feasible Solution Here solver tells us that for payments of £600 per month, we can support a loan of £60 000 and pay it off by 2018, even if the interest rate were to rise to 8.96% However, what is the maximum loan we can take out at 4%, and still pay it off by the deadline?

56. The Solution Here solver tells us that for payments of £600 per month, we can support a loan of £83 896.53 and pay it off by 2018, provided that the interest rate does not rise higher than 4% In fact, we could have found this using Goal Seek!

57. Working with the Tools As you have seen, these spreadsheet tools are quite sophisticated, and therefore require you to ask the right questions in the right manner, before they supply you with the solution to your problem. Asking the wrong question will still lead you to a correct answer – but not to the problem you are trying to solve!

58. Follow-up Activities You should now examine the final three sections of Formative Activity 8. This challenges you to use Solver find a range of solutions to particular problems for the software- producing company Return to Menu