1. GEK2507 Compound & Prosper GEK2507 Frederick H. Willeboordse frederik@chaos.nus.edu.sg

2. GEK2507 Lecture 6 Dynamics of Break-Even Analysis

3. GEK2507 Fixed versus Variable Costs Break Even Analysis Today’s Lecture

4. GEK2507 An important part of running a company is the determination of how the company should be financed and how the prices of the products the company sells should be set. Clearly, in order to do this properly a sound financial analysis is necessary. Break-Even Analysis

5. GEK2507 It is essential to realize that there are two basic types of costs a company incurs. Variable Costs Fixed Costs Variable costs are roughly proportional to a company’s sales. I.e. the cost per unit remains roughly constant. Fixed costs remain roughly the same regardless of sales. I.e. the cost per unit is inversely proportional to sales. Types of Costs

6. GEK2507 Time Position Dynamics is roughly the term used to describe the time evolution of a system. Dynamics This could e.g. describe where a car drove.

7. GEK2507 Total Costs Variable Costs Fixed Costs Sales Sales Value A simple graph but important to understand! Types of Costs

8. GEK2507 Commonly, the Break-even point is defined to be the level of sales where: Revenues = Expenses Let us have a look at a simple example. Aunt Petunia opens a flower shop. Break-Even Analysis

9. GEK2507 Fixed Costs: Rent: 5,000 Utilities: 300 Helper: 1,500 Variable Costs: Flowers: 40% of selling price So we know that: Selling price – cost of flowers – rent – utilities – helper = 0 when she breaks even Break-Even Analysis

10. GEK2507 Let’s enter the last line into the spread sheet It’s good to put the assumptions separately. =E6*$H$7 But!!!?? I’m not a Mathematician! How am I going to find the value for E6 so that E11 = 0? =E6-E7-E8-E9-E10 Break-Even Analysis

11. GEK2507 Piece of cake! Trial and error! Oops! Not as easy as I thought. Especially if H7 is not a nice number like 40%. Is there a better way? Break-Even Analysis

12. GEK2507 We could cave and write down the equation. That would, in fact not be such a bad idea since equations are really not as difficult to understand when one knows what they are supposed to mean. But *** RELIEF *** we can use the previously discussed solver. That was close …. The Solver

13. GEK2507 Lets use the Solver! Incredible! Like this anyone can do Math! The break even point is 11,333 Break-Even Analysis

14. GEK2507 The Solver is a fabulous tool, but really in business it is beneficial to at least be open-minded about equations. Let’s give it a try! We know that: E11=E6-E7-E8-E9-E10 (Income = Sales – Cost – Rent – Utilities – Helper) At the break even point, Net Income = 0 and hence E11 = 0 Inserting this we obtain: 0 = E6-E7-E8-E9-E10 An Equation …

15. GEK2507 We want to change E6 such that 0 = E6-E7-E8-E9-E10 is true. Ah, if we just set E6 to the other values together the above equation is true. Or, E6 = E7+E8+E9+E10 is the solution to our problem. Let’s try it and go back to the situation before we used the solver: An Equation …

16. GEK2507 Let’s fill the equation into cell E6 Oops! What went wrong? =E7+E8+E9+E10 Break-Even Analysis

17. GEK2507 May be Math isn’t as easy as I thought… But wait, doesn’t E7 depend on E6? Yes indeed, we have defined E7 = E6 * H7 (cost of product). Let’s put this into our equation: E6 = E7+E8+E9+E10 => E6 = E6*H7+E8+E9+E10 Or: E6 - E6*H7 = E8+E9+E10 E6 * (1 - H7) = E8+E9+E10 E6 = (E8+E9+E10) / (1 - H7) An Equation …

18. GEK2507 Yosh! Let’s try that again. Yatta! It works After all, this was quite easy wasn’t it? And now we can change H7 to play out scenarios. Very useful indeed! (E8+E9+E10) / (1 - H7) Break-Even Analysis

19. GEK2507 If Aunt Petunia raises the price so that the cost is only 30% of sales …. … she can break even already at 9714. Of course now she may be so expensive that no one wants to buy her flowers anymore. Break-Even Analysis

20. GEK2507 There may be times when it is better to turn things around. Just now, Aunt Petunia found how much she needs to sell in order to break even given certain cost as percentage of sales. This is in general a good idea since for many products the profits are more or less set. In order to see how feasible a business is one could also enter an expected sales amount and then see how much the cost of the product can be in order to break even. The Other Way Around

21. GEK2507 With our nice equation, it’s fairly easy to accomplish this: E6 * (1 - H7) = E8+E9+E10 (1 – H7) = (E8+E9+E10)/E6 H7 = 1 - (E8+E9+E10)/E6 Cool! And I thought that Financial Analysis is only for … others Break-Even Analysis

22. GEK2507 The Solver is a great tool But Math can be very useful as well There are two types of costs: –Variable Costs –Fixed Costs Break Even Analysis is a snap with Excel Key Points of the Day