# A table showing her income at R5 per cupcake would look like this: Cupcakes Income in R

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1 Break-even functions When working with break- even problems, we typically have to compare two situations: for example, two car rental companies, two cell phone packages, flat- rate versus prepaid electricity. The term break- even, however, is more specific to income and cost. When your income exceeds your cost, you make a profit. When your cost exceeds your income, you make a loss. But when your income equals your cost, you break even, meaning that at that specific point you do not make a profit OR a loss. Ashley bakes cupcakes at a cost of R3 each. She sells each cupcake for R5. Her fixed cost per month is R1 for renting the stall from which she sells her cupcakes. A table showing her income at R5 per cupcake would look like this: Cupcakes Income in R A formula for her income would therefore be: Income = (5 the number of cupcakes) or y = 5x Where y is the amounts in Rand and x is the number of cupcakes A table showing her total cost at R3 per cupcake added to the R1 fixed cost per month would look like this: Cupcakes Total cost in R A formula for her total cost would therefore be: Total cost = 1 + (3 the number of cupcakes) or y = 1 + 3x Where y is the amounts in Rand and x is the number of cupcakes R number of cupcakes Income in R Total cost in R The graph: From the tables it should be clear that Ashley s income and total cost is the same when she sells 5 cupcakes that are worth R25. The coordinates for the break- even point is (5 ; 25). Identify these coordinates on the graph and make sure that you are comfortable plotting graphs like this one.

2 If she sells more than 5 cupcakes, she makes a profit and if she sells less than 5 cupcakes, she makes a loss. Typical context of break- even problems P Comparing car rental P Comparing a contract phone package to a pay- as- you- go phone P Finding the break- even point when working with cost and income P Comparing prepaid electricity to flat- rate electricity Activity 3: Luxury car rental p.4.2 Robert wants to hire a Mercedes SLK cabriolet for his matric farewell, but he is not sure if it will fit his budget. He does an internet search and finds the following two packages which he can compare: v Package 1: Adventure Car Hire charges R1 per day including insurance and free mileage for a Mercedes SLK 2 Cabriolet. v Package 2: Exclusive Cape Cars charges R9 per day including insurance but mileage is charged at R,8 a kilometre for the same car. Robert used the following two formulae to work out which package is cheaper: Formula 1: y = R1 Formula 2: y = R9 + R,8x 1. Which company is represented by the formula y = R1? 2. Complete the table below: Kilometres Amount (R) Plot the values in the table on the graph. 4. G Why is the graph a horizontal line? 5. How far must Robert drive for both car rental companies to charge the same? 6. How much does Robert have to pay for driving 2 km with Exclusive Cape Cars?

3 7. If the route Robert chose is about 2 km, a. Which company is the cheaper option? b. How much money will Robert save 8. How far did Robert drive if he spends R95 at Exclusive Cape Cars? 9. G If Robert was charged R5 insurance because he is only 18 years of age, explain how this would change the graph you plotted? Activity 31: BlackBerry contracts Nosi was offered a bursary to study Film and Multimedia Studies at City Varsity in Cape Town after her Grade 12 year. Since she does not have a personal computer, she will need a cell phone that can browse the internet to do research for projects that she will have to complete. According to her research, a BlackBerry with its unlimited web- browsing seems like the best option. She finds the following two deals from Vodacom: v R2 5 cash for the phone, and R5 per month for the internet and connectivity on prepaid v R169 per month over 24 months on a Weekend Every Day contract with internet and connectivity included On prepaid Nosi will have to buy pay-as-you-go airtime vouchers since it is not included in the phone price or the R5 per month. On the Weekend Every Day contract Nosi receives 12 off-peak minutes and is charged at contract rates for her calls for which she receives itemised billing every month. The fixed cost is not dependant on the amount of months for which you have the contract, It is a once off amount. 1. What is Nosi s fixed cost on the prepaid option? 2. What is Nosi s variable cost on the prepaid option? The variable cost is dependent on the amount of months for which you have the contract. 3. Write down a formula to represent Nosi s total monthly cost, excluding calls, on the prepaid option. 4. Write down a formula to represent Nosi s total monthly cost, excluding calls, on the Weekend Everyday contract option. 5. Complete the following table to show Nosi s accumulative (total) payments to Vodacom: Months Pre- paid: Contract: x x

7 Remember that the break- even point on the graph has an x and a y coordinate. Now that you know that Xanthi has to sell 1 brownies to break- even, how much money is 1 brownies worth? 1 brownies at R5 each: 5 x 1 = R5 or: R15 + R3,5 for each of the 1 brownies: R15 + 3,5 x 1 = R5 The coordinates for the break- even point are: (1;5) Let s plot the graph without making a table of values: All you need to plot a graph is two sets of coordinates. If you can make two dots on the graph, you can draw a line. It is a good idea to include a third point. If the three points do not make a line, then you made a mistake. The income graph starts at the origon, because if you do not sell any brownies, you do not make any money. The income graph therefore starts at (;). We also know that it cuts through the break- even point: (1;5). Plot these two points on your graph. Your total cost graph will start at R15, because your fixed cost is independent of your cost per brownie. The total cost graph therefore starts at (;15). We also know that it cuts through the break- even point: (1;5). Plot these two points on your graph. Connect the dots and label each line to distinguish between the graphs: R total cost income break- even brownies Do you remember how to write coordinates? First the x, then the y: (x;y) R brownies At what point does it show that Xanthi is making a profit, and at what point is she making a loss? You make a profit when your income exceeds your cost, and you make a loss when your cost exceeds your income. Profit = income cost

8 Where would the profit and loss regions be on your break- even graph? Rand 9 8 profit break- even 4 total cost 3 2 loss income amoount of brownies When the income line is higher than the cost line, it is the profit region. When the cost line is higher than the income line, it is the profit region. For which values of x does Xanthi make a profit? When she sells more than 1 brownies and x is therefore more than 1 brownies or x > 1 For which values of y does Xanthi make a profit? When she makes more than R5 and y is therefore more than R5 or y > 5 For which values of x does Xanthi make a loss? When she sells less than 1 brownies and x is therefore smaller than 1 or x < 1 For which values of y does Xanthi make a loss? When she makes less than R5 and y is therefore smaller than 1 or y < 1

9 Activity 34: Selling Valentine s Day bracelets The Grade 12 s are making bracelets for Valentine s Day. They make the bracelets at a cost of R3 and sell them for R5 each. They also have a fixed amount of expenses of R2, which covers the cost of the petrol used to buy the materials for the bracelets, as well as the printing of posters used to market the bracelets. 1. Write a formula to work out the income (where x is the number of bracelets): 2. Use your formula to complete the following table: Amount of bracelets R 3. Write a formula for total cost (where x is the number of bracelets): 4. Use your formula to complete the following table: Amount of bracelets R 5. Calculate how many bracelets the grade 12 s will have to sell in order to break- even. 6. Use your tables in question 2 and 4 to draw graphs of the income and total cost function on the same set of axes. Distinguish clearly between the two graphs and indicate the break- even point with an arrow Work out the following: a) For which values of x (number of bracelets) would they make a profit? b) For which values of x (number of bracelets) would they make a loss? c) For which values of y (the amount of Rand) would they make a loss? 8. Indicate the profit and loss regions on the graph Calculate the profit (or loss) for selling 4, 16 and 4 bracelets. 1. How many bracelets must they make and sell to make a profit of R1?

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Registered in England Registered Number: 04744238 Registered Address: 62 The Street, Ashtead, Surrey, KT21 1AT Registered with the Chartered Institute of Taxation as a firm of Chartered Tax Advisers Car

### MANAGEMENT ACCOUNTING 2 MODULE CODE: ACCT08004

Business School (Paisley & Hamilton Campus) Session 013-014 Trimester 1 MANAGEMENT ACCOUNTING MODULE CODE: ACCT08004 Date: 1 st January 014 Time: 1000-100 Answer THREE questions Question 1 in Section A,