Numbers English Contest #18

Using the English and data from Contest #17, what is the percent profit margin change based on production?

Calculate this margin for initial and final conditions.

Solution to Contest #17

The first step is to calculate the profit at the initial conditions, based on 200 units of sales.

Total costs = Fixed + variable = $234,200 + $137 x 200 = $261,600

Profit = Sales - Total Costs = $1490 x 200 - 261,600 = $36,400

Profit per Unit (Margin) = $36,400 / 200 = $182 per unit.


Using the same equations, we now calculate the margin with the changes:

Total costs = Fixed + variable = $(234,200+12,500) + $151 x 200 = $276,900

Profit = Sales - Total Costs = $1490 x 200 - 276,900 = $21,100

Profit per Unit (Margin) = $21,100 / 200 = $105.50 per unit.


Now we calculate the % change in margin for the increased expenses:

% Change = (Final Margin - Initial Margin) / Initial Margin x 100% = (105.50-182.00)/182.00 x 100% = -42% 


These fairly small decreases in costs (5.3% in fixed and 10.2% in variable) reduced margin by 42%. This concept is called leveraging.

Numbers English Contest #17

West Electronics is a specialty instrumentation manufacturer for water treatment plants. They have developed a loyal following in North America for a line of their sensors that sells for $1490. 

Fixed expenses are $234,200 per month. Variable expenses are $137 per unit.

If fixed costs rise by $12,500 and variable costs jump to $151, what is the change in the per unit margin (based on monthly sales of 200 units) expressed in percentage points? The selling price stays the same.

Please note that this short passage of English text requires at least six sets of calculations to get the right answer. Can you translate this English to frame the calculations properly? 

Solution to Contest #16

How much will it cost to run this test advertising campaign?

Each viewing of the ad will be seen by 5,784 (240,000 x 0.0241) people.

To get at least half million impression, it will need to be shown 87 times (500,000 / 5,784 and rounded up)

Total cost is $27,405 (87 x $315).

If the manufacturer's profit is $825 per car sold, how many cars must be sold just to pay for this advertising campaign?   

The manufacturer needs to sell at least  34 cars ($27,405 / $825 and rounded up) more than its usual sales to pay for this advertising campaign.

 

Numbers English Contest #16

A car manufacturer is testing out an advertising campaign by using a local TV station. It has identified a particular evening TV show it feels will reach its target audience. The car manufacturer wants to run a half million impressions in the next month to see how this campaign affects sales in this area. If the campaign is successful, it will expand this campaign nationally.

The area serves 240,000 people. The ratings for this TV show are 2.41% of the total population. TV commercials for that show run for $315 for a 30-second spot. How much will it cost to run this test advertising campaign? If the manufacturer's profit is $825 per car sold, how many cars must be sold just to pay for this advertising campaign?   

Solution to Contest #15

First, we take a look at what the questions is asking for.

Which campaign is most effective for Dave, based on a cost per 1000 impressions?

Note that the question did not ask for cost per click.

Next we calculate the cost per 1000 impressions for Campaign #1.

$31.00 / 40,134 x 1000 = $0.772 per thousand impressions.

Next, we do some calculations for Campaign #2. We must think a little to use the information relating to "clicks" appropriately.

Cost = $31.00 x 2.1 = $63.00

Clicks = 158

Click Through Rate = 0.92% = 0.0092

Impressions = 158/0.0092=17,174

Cost per 1000 impressions = $63.00 / 17,174 x 1000 = $3.67 per thousand impressions.

Next, we do some calculations for Campaign #3. 

Cost = $31.00 - $12.25 = $18.75

Clicks = 158 * (1-0.115) = 140

Click Through Rate = 0.92% + 0.54% = 1.46% = 0.0146

Impressions = 140/0.0146 = 9,589

Cost per 1000 impressions = $18.75 / 9,589 x 1000 = $1.96 per thousand impressions. 

Campaign #1 is the most effective campaign, based on cost per thousand impressions. 

Contest #15

Dave is evaluating the effectiveness of his Google ad campaigns for his business English program. Although he is paying on a cost per click basis, he is looking to see which campaign is giving him the most impressions for the least money.

Last month, Campaign #1 cost $31.00. It had 105 clicks and 40,134 impressions.

Campaign #2 cost two point one times as #1. It had 158 clicks and had a click-through rate of zero point nine two percent.

Campaign #3 cost $12.25 less than campaign #1. It had 11.5% fewer clicks than Campaign #1, but had a higher click-through rate than Campaign #2 by zero point five four percentage points. 

Which campaign is most effective for Dave, based on a cost per 1000 impressions?