## Complete Example of a Sensitivity Analysis

SENSITIVITY ANALYSIS EXAMPLE:

Let assume today's date is October 15, 200W and Ron Ross plans on establishing a retail business, selling chairs. The name of his business will be the Ron Ross Chair Company. The projected start date for the company is January 1, 200X. Ron has just completed his forecasted financial statements for a three year period. ( IE forecasted balance sheet, forecasted cash flow statement and forecasted income statement). He is now trying to develop a forecasted sensitivity analysis for the 200X year but seems to be having some difficulty. Ron calls a local accounting firm and says;

"I have just finished developing my forecasted financial statements for my business years 200X, 200Y, and 200Z. I am attempting to develop my forecasted sensitivity analysis for 200X, but I don't know where to start. My banker suggests the analysis should show the effects on my original forecasted net income at sales increases of 10% & 20% and at sales decreases of 10% and 20%. Can you prepare my 200X forecasted sensitivity analysis for me?"

The accounting firm accepted the challenge and asked Mr. Ross to provide the following information:

• his 200X forecasted income statement;
• a list of his fixed cost and variable costs;
• the amount he pays his suppliers for each chair; and
• the amount he plans to sell each chair to his customers.

Ron collects all the requested data and faxes the following information to the accounting firm.

 THE RON ROSS CHAIR COMPANY FORECASTED INCOME STATEMENT FOR YEAR ENDING DECEMBER 31, 200X 200X Sales \$80,000 Cost of Goods Sold \$48,000 Gross Margin \$32,000 Operating Expenses  (marketing & administrative expenses) \$20,000 Net Income Before Taxes \$12,000

Additional Information Provided By Ron:

• I will buy preassembled chairs from a wholesaler for \$120 each (shipping included).
• I plan to sell each chair to my customers for \$200 each.
• In 200X, I project to sell 400 chairs.
• The only variable cost is my forecasted cost of goods sold.
• All my Operating Expenses (marketing & administrative expenses) are fixed costs.
• Do not consider income taxes in my sensitivity analysis.

The accounting firm now has all the information needed to construct a Sensitivity Analysis for the Ron Ross Chair Company. Remember, the analysis must show the effect on Ron's forecasted 200X net income before taxes, assuming his 200X projected sales increase by 10% & 20%. In addition, the sensitivity analysis must show the effect on Ron's forecasted 200X net income before taxes, assuming his 200X projected sales decrease by 10% & 20%. The 200X Forecasted Sensitivity Analysis, prepared by the accounting firm for the Ron Ross Company, is presented below.

 RON ROSS CHAIR COMPANY SENSITIVITY ANALYSIS FOR THE FORECASTED YEAR 200X 20% Decrease 10% Decrease 200X original 10% Increase 20% Increase Revenue: Sales \$64,000 \$72,000 \$80,000 \$88,000 \$96,000 Variable Costs: Cost of Goods Sold \$38,400 \$43,200 \$48,000 \$52,800 \$57,600 Fixed Costs: Operating Expenses \$20,000 \$20,000 \$20,000 \$20,000 \$20,000 Net income Before Taxes \$5,600 \$8,800 \$12,000 \$15,200 \$18,400

EXPLANATION:
The third column represents Ron's original forecasted income statement for 200X. Furthermore, after researching the market, existing competitors, costs of various chair suppliers, operating expenses, and other industry variables, Ron arrived at the foregoing forecasted sales, costs of goods sold, and operating expenses. Note: for simplicity, we have totaled each operating expense into one account and one value - normally each operating expense and their associated account balance would be listed as a marketing expense or an administrative expense. At any rate, Ron's original 200X forecasted income before taxes is \$12,000. The net income before taxes is arrived at by subtracting all forecasted costs and all expenses from the forecasted sales. Note: we will not consider income taxes in this example.

The first column represents a new forecasted income statement for 200X, assuming Ron's original sales forecast decreases by 20%. The second column represents a new forecasted income statement for 200X, assuming Ron's original forecasted sales decrease by 10%. The forth column represents a new forecasted income statement for 200X, assuming sales increase by 10% of Ron's original sales forecast. The fifth column represents a new forecasted income statement for 200X, assuming sales increase by 20% of Ron's original sales forecast.

The values shown in the sensitivity analysis were arrived at by answering the following questions.

1.  What would sales (in dollars) be if the original forecasted sales were increased and decreased by 10% & 20%

2.  What would variable costs (in dollars) be if the original forecasted sales were increased and decreased by 10% & 20%

3.  What would fixed costs (in dollars) be if the original forecasted sales were increased and decreased by 10% & 20%

Lets answer each question separately.

QUESTION # 1
What would sales (in dollars) be if the original forecasted sales were increased and decreased by 10% & 20% ? This question is rather simple to answer - all you have to do is increase and decrease the original forecasted sales (\$80,000) by 10% and 20%. The calculations are as follows;

 \$80,000 - 10%  =  \$72,000 \$80,000 - 20%  =  \$64,000 \$80,000 + 10%  =  \$88,000 \$80,000 + 20%  =  \$96,000

After calculating the sales levels at various increases and decreases, the data is organized as such;

 20% Decrease 10% Decrease 200X  original 10% Increase 20% Increase Revenue: Sales \$64,000 \$72,000 \$80,000 \$88,000 \$96,000

There is another way in which these figures could have been calculated. Recall, Ron told us that his original forecast estimates he will sell 400 chairs at \$200 each (400 chairs x \$200 per chair = \$80,000 in sales). If he actually sold 10% less than his original forecast of 400 chairs, then he would sell only 360 chairs (400 chairs - 10% = 360 chairs). In this case, his sales in dollars would be \$72,000 (360 chairs x \$200 per chair) - the same amount shown above in the sensitivity analysis. You may choose either method, however, increasing or decreasing the dollars sales is easier and less time consuming.

QUESTION #2
What would variable costs (in dollars) be if the original forecasted sales were increased and decreased by 10% & 20%? Remember a variable cost is a cost or an expense that fluctuates when sales increase or decrease. Furthermore, if sales increase by 10% for example, variable costs will also increase by 10%. Since Cost of Goods Sold is considered to be a variable cost, it will increase and decrease at the same rate of sales. Below illustrates Ron's variable cost calculations.

 \$48,000 - 10%  =  \$43,200 \$48,000 - 20%  =  \$38,400 \$48,000 + 10%  =  \$52,800 \$48,000 + 20%  =  \$57,600

After calculating the variable costs at various increases and decreases, the data is organized as such;

 20% Decrease 10% Decrease 200X  original 10% Increase 20% Increase Revenue: Sales \$64,000 \$72,000 \$80,000 \$88,000 \$96,000 Variable Costs: Cost of Goods Sold \$38,400 \$43,200 \$48,000 \$52,800 \$57,600

Like sales, the variable costs can be calculated another way. Recall, Ron's original forecast estimates he will sell 400 chairs and each will be purchased for \$120 (400 chairs x \$120 per chair = \$48,000 in cost of goods sold). If he actually sold 10% fewer chairs than his original forecast of 400 chairs, then he would sell only 360 chairs (400 chairs - 10% = 360 chairs). In this case, Ron's cost of goods sold (variable costs) would be \$43,200 (360 chairs x \$120 per chair) - the same amount shown above in the forecasted sensitivity analysis. Once again, you may choose either method, however, increasing or decreasing the dollar amounts tend to be easier and less time consuming.

QUESTION # 3
What would fixed costs (in dollars) be if the original forecasted sales were increased and decreased by 10% & 20%. Recall, a Fixed Cost is a cost or an expense that does NOT fluctuate when sales increase or decrease. Furthermore, if sales increase by 10% for example, fixed costs will not increase or decrease; instead they will remain the same. Since Ron indicated that all operating expenses (marketing & administrative expenses) are considered to be fixed costs, they will remain at the same value shown regardless if sales increase or decrease. Below illustrates Ron's 200X Forecasted Fixed Costs at various sales increases and decreases;

 20% Decrease 10% Decrease 200X  original 10% Increase 20% Increase Fixed Costs: Operating Expenses \$20,000 \$20,000 \$20,000 \$20,000 \$20,000 Net Income Before Taxes \$5,600 \$8,800 \$12,000 \$15,200 \$18,400

That's all there is to developing a sensitivity analysis. By the way, don't forget to subtract each column's variable costs and fixed costs from each sales column. This is crucial since it indicates your forecasted net income (before taxes) at various sales increases & decreases.

Categories: Financial