aring for Finance - Mathematics ck to Assignment tempts: Average: 12 3. Percentages and changes of base The percentage change methodology can be applied when comparing two values to each other. Consider two competing bike shops: Spin Cyde with sales of 2,000 bikes this year and Bike World with sales of 2,200 bikes. Which shop has the most sales and by how much? The first question is easy, as Bike World clearly sold more bikes this year. The second question depends on your perspective (or base value). Look at how these two measurements of percentage change can offer different results: %A = (2,200 -2,000) / 2,000 - 10.00% %A - (2,000 - 2,200) / 2,200 - 9.09% In the first calculation, Spin Cycle's sales are used as the base value. The first calculation is interpreted as: Bike World has 10% higher sales than Spin Cycle. In the second calculation, Bike World's sales are used as the base value. The second calculation is interpreted as: Spin Cycle has 9.09% lower sales than Bike World Both statements are correct and describe the same event, but they do so from different perspectives. When comparing values, the base value used is important to understanding the percentage comparison Paradox of Percentage Stock Returns reparing for Finance - Mathematics than Bike World. Both statements are correct and describe the same event, but they do so from different perspectives. When comparing values, the base value used is important to understanding the percentage comparison. Paradox of Percentage Stock Returns The importance of changes in base can be illustrated by looking at percentage stock retums. Suppose a stock's price is $100 today and increases by 10% in each of the next two years. At first glance, you might expect the stock's price to be $120 after two years, since 10% + 10% - 20%. However, this is not correct. It is wrong because the base value is changing. Time Stock Return Stock Price $100 0 1 10% 2 10% Now, suppose a different stock's price is $100 today, increases by 20% this year, and decreases by 20% next year. At first glance, you might expect the stock price after two years to be back at $100. This isn't the case because the base value is changing, Stock Return Stock Price Time 0 $100 1 20% 2 -20%