Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson, which is from the unit "Maths in the Workplace." In this series of lessons, we're exploring how maths is used in different careers.

Let's get started.

In today's lesson, you're going to look at some of the ways that maths is used by independent business owners.

Now, we've got some keywords on the screen, and you may want to pause the video to have a read through and familiarise yourself with these definitions.

If you wish to do that, please pause the video now.

Our lesson today is broken into two parts, and we're going to begin by looking at profit and percentages.

Alex and Izzy have opened their first business, a cafe.

Here are their first three years of results.

So, you can see a table with gross profit and revenue for the three years that their business has been running.

Now, let's just go through what some of these words mean.

Revenue is the income into the business.

In other words, it's the money that goes into the till from the sales.

If customers buy 300 coffees a week at three pound each, then that's 900 pounds in revenue.

Gross profit is the total revenue minus the cost of the goods that were sold.

So, for example, if the milk and beans used to make a cup of coffee cost a pound, and we sell that cup of coffee for three pounds, then that's a gross profit of two pounds per cup.

Now, gross profit only considers the cost of the goods, which are the variable costs.

In other words, as the number of cups of coffee varies, the amount of beans and milk needed also varies.

Gross profit does not include fixed costs like buildings and bills.

So, is Alex and Izzy's business doing well? What do you think? Well, both gross profit and revenue are going up, so it looks like the business is indeed going well.

Is that what you said? However, proportion does play an important part in understanding if a business is doing well, if it's being efficient.

So, let's consider that.

To get from 60,000 pounds in revenue to 120,000 pounds, Alex and Izzy had to be twice as active.

So, they would've had to have made twice as many coffees, cakes, and sandwiches, they may have had to employ more people or invest in bigger kitchen equipment.

But let's look at what happened to their gross profit.

This doubling of effort only resulted in a 25% increase in profit.

So, if you were in a part-time job and your employer said to you, "I'll pay you 25% more if you work twice as hard," I suspect you'd politely decline.

So, to understand their efficiency between revenue and profit, businesses often add a third column to results like these, which is the gross profit margin column.

It's calculated using a formula.

So, the gross profit margin as a percentage is your gross profit divided by your sales revenue and then multiplied by 100.

So, for year one, for Izzy and Alex, what's their gross profit margin? Well, that's 24,000 divided by 60,000, then multiply by 100.

So, that's a gross profit margin of 40%.

For year two, though, it's a gross profit margin of 35%, and for year three, the gross profit margin is only 25%.

Oh, that doesn't look quite as good as we thought it might.

So, in the first year of trading, 40% of their revenue was gross profit, but by the third year of trading, only 25% of their revenue was gross profit.

If this pattern continues, margins might become so tight that their business is no longer viable.

Let's check; you've got that.

Here are the results for year four and year five.

Please calculate the gross profit margin for both years.

If you need it, there's a formula at the bottom of the screen that will help you.

Pause the video and do this now.

Welcome back.

Let's check your answers.

So, for year four, you should have 30%, and year five, well, I've got 33.

3 because I've rounded to one decimal place, but you might just have 33, or you might have said 33.

33, 33 1/3.

They're all valid answers.

What we can see, of course, is that Alex and Izzy's business looks like it's starting to turn around.

So, to ensure their profit margin at the end of the year is healthy, businesses set prices on individual items with a desired profit margin in mind.

So, Alex says, "I didn't get our pricing right in the first three years, Izzy.

I dropped our prices, and we sold more, but it eroded our profit margin." Izzy said, "That's not a problem, Alex.

We know now, so, from here on, we won't sell any individual item for less than a 40% profit margin." Now, the gross profit margin per item can be calculated using a formula.

In order to work out the gross profit margin for a particular item, we can take the item selling price, subtract the cost price, and then divide by the selling price of that item.

Once we've done that, we multiply by 100 to give this as a percentage.

Alex and Izzy sell a cheese and tomato sandwich for four pounds, and the ingredients, remember, the variable costs, are two pounds 20.

So, in order to calculate the gross profit margin, I'll take four pounds and subtract two pounds 20.

So, remember that selling price, subtract cost price.

So, once I've worked that out, I've got one pound 80.

I then divide that by the selling price, divide by four, and then multiply by 100.

This gives us a gross profit margin of 45%.

Remember, one pound 80 is the cash gross profit they make from each sandwich, and the 45% is what proportion of the selling price this is.

It's now your turn.

What I'd like you to do is, for each of the items, so the flapjack, the coffee, and the goat's cheese sandwich, calculate the gross profit margin, then advise Alex and Izzy of any items that aren't making their 40% gross profit margin target.

Pause the video while you work this out now.

Welcome back.

Let's see how you got on.

So, let's start with the flapjack.

You should have found that the flapjack has a gross profit margin of 55%; for the coffee, the gross profit margin is 90%.

Wow, that's really good.

Coffee has an especially high profit margin; Alex and Izzy want to sell more coffee than any other product.

But what about our goat's cheese sandwich? Well, that has a gross profit margin of 33 1/3%, or 33.

3 to one decimal place.

Those goat's cheese sandwiches are not meeting the 40% profit margin.

Alex and Izzy need to either increase their price, find a way to reduce their cost price, or stop selling the sandwiches.

Percentage calculations enable small businesses to determine how to price their products.

So, for example, if I want a profit margin of 40%, then the cost has to be 60% of the selling price.

So, our goat's cheese sandwich, for example, if the cost price was three pounds, then the selling price multiplied by 0.

6 has to equal three.

That means, therefore, that the selling price can be calculated by doing three divided by 0.

6, which means I have to sell a goat's cheese sandwich for five pounds; that therefore leads to a profit margin of 40% or two pounds.

Alex and Izzy have to make a minimum 40% gross profit margin on these items. So, let's calculate the minimum price that they must sell each item for.

Pause the video while you work this out now.

Welcome back.

How did you get on? So, for the chicken mayo sandwich, we have to sell for at least four pounds.

For the croissants, we have to sell them for at least two pounds 50, and the shakes, one pound 92.

Alex wants to make a minimum 75% gross profit margin on cakes.

Calculate the minimum selling price for these cakes.

Pause and do this now.

Welcome back.

We know that the cost price has to be 25% of the selling price.

So, dividing by 0.

25 gives us a selling price of one pound 20 for the lemon drizzle and one pound 80 for the carrot cake.

Izzy says, "I do love maths, but we sell almost 100 products.

Calculating minimum pricing is gonna take hours!" She's got a point.

Alex says, "Well, that's why most small businesses use spreadsheets.

We should too." So, they start by making a list of products and their respective cost prices, and you can see that here in our spreadsheet.

Now, they can write a formula to calculate all of the minimum selling prices automatically.

So, because we want 40% gross profit, we know that we're going to be dividing by 0.

6 for all of these.

So, we write the formula: B3 divided by 0.

6.

We're dividing whatever value is in the B column by 0.

6 to get the value for the C column in the same respective row, which means that we need to sell for 50p.

They type the formula rather than the individual calculation because that way it can be copied down to the other cells.

And you see we've done that here.

Dragging the formula down means it's replicated in every row, and it updates.

So, B3 in the next row would be B4, B5, et cetera.

They can delete any row they don't need and then click format, number, and currency, and the results appear in a currency format.

Much easier to read.

However, did you spot it's not 40% all the way down? For the pastries, we want a minimum gross profit at 50%.

So, we need to tweak the formula here.

So, we're gonna be dividing by 0.

5 rather than 0.

6.

There we go.

That's now fixed.

In a matter of minutes, Alex and Izzy can calculate the minimum selling price across a wide variety of goods using spreadsheets and formulas.

Now, a small business is not going to sell all of their products for the minimum price calculated.

They'll look at the market to understand what their competitors charge and what customers are willing to pay before they decide a selling price.

So, for example, a cappuccino, they're not gonna sell it for 50p.

The going rate's about three pounds, so they're gonna go for that.

So after they decide their selling prices, another formula can be written in the gross profit percentage column to automatically calculate that for each product.

Remember, your gross profit margin as a percentage is the selling price, subtract the cost price, divide the result by the selling price, and then multiply by 100.

And here's the formula we're going to use.

Can you match that to the columns and see why we've used that particular notation? We can then, of course, copy that formula down.

Alex and Izzy can now understand which of their products are the most profitable.

By far, it's their coffees.

They've got a really high gross profit percentage.

Let's do a quick check.

On this spreadsheet, what formula should be typed into cell C3? In other words, I want to calculate the minimum selling price for some lemon drizzle cake.

Pause and make your choice now.

Welcome back.

You should, of course, have chosen B.

For A, the target GP, remember, is 75%, not 40%.

So we shouldn't be divided by 0.

6.

And then C, all formulas need to start with an equals sign at the beginning.

So, having set selling prices, what formula is typed into cell E3? Pause the video while you make a choice now.

Welcome back.

You should, of course, have gone with A.

The others don't even have the brackets they need to have around the subtraction.

Remember, we need priority of operations.

And C, they're just in the wrong order, as well as not having brackets.

So, double fail there.

With the spreadsheet complete, which product do you think Alex and Izzy will place in the most prominent place in their cafe? Pause the video and make choice now.

Welcome back.

Did you pick the lemon drizzle? It has the highest GP percentage, so definitely the one to go for.

It's now time for your first task.

For question one, fill in the blanks for this small business's first few years of results and comment on how their profit margin is changing.

There's a formula there in case you want to use it.

Pause the video and do this now.

Question two, calculate the gross profit margin for each of these items for this new paddleboard shop.

Once you've done that for parts A to D, for part E, I'd like you to comment on which product is not achieving the 30% gross profit margin target and advise what should happen.

Pause the video and do this now.

Question three: By completing a spreadsheet or otherwise, calculate the minimum selling price and gross profit margins for this bicycle shop's products.

In part B, comment on any products not achieving minimum gross profit margins.

Part C, advise the business as to which products they should place most prominently in their shop.

Pause the video while you do this now.

Time to go through the answers.

So for question one, you should have filled in the table as follows.

Feel free to pause the video while check your work.

So you might have reported whilst revenue increases are slowing, the gross profit margins have increased to a healthy level.

Question two, you had to work out the gross profit margin for each item.

In part A should have 35%, B, 40%, C, 25%, and D, 42.

5%.

Part E, I asked you to comment on which product is not achieving the 30% gross profit margin target.

Well, that's the carbon paddle.

That's only at 25%.

So what should they do? Well, the business needs to either find a cheapest supplier, raise the selling price, or stop selling the product.

Then in question three, I asked you to complete the spreadsheet.

So, you could've either written onto it or created your own spreadsheet and filled these in.

You then had to comment on any products not achieving minimum gross profit margins.

Well, let's see which ones they are.

You should have identified the anti-puncture tyres and the cleated pedals because they're not achieving the minimum GP margins.

What should they place most prominently? Oh, things to do with brakes.

So the pads and the cables, absolutely, 'cause that's where the gross profit margin is the highest.

It's now time for the second part of the lesson, we're gonna look at tracking performance.

Now, most small businesses use spreadsheets to track their performance.

What was this business's greatest revenue in a month in this year? What was their lowest revenue in a month this year? And what's an average month for this business? Pause the video while you discuss this with the people around you.

Welcome back.

So the month that was the best was definitely August.

In August, we had a revenue of 21,300 pounds.

Lowest was January, where it was only 11,000.

And an average month? Well, I calculated the mean average, and that was 13,417 pounds to the nearest pound.

If you did the median average, that was 12,350.

Now, what I've done is just summed these up here so I can see those statistics.

The range of values is 10,300 pounds.

That's easy to calculate because I have the highest and lowest monthly revenue values.

Now, understanding averages and the spread of performance data helps a business to plan.

Every business needs to forecast its sales to ensure they have the stock ready to meet the needs of their customers.

It's time for a quick check.

I'd like you, please, to calculate the range and average for the year two sales of the same business.

Pause and do this now.

Welcome back.

Let's check that work.

So you should have found that the highest value was 23,500, and the lowest was 11,600.

This gave a range of 11,900 pounds.

The mean average was 14,525 pounds, and the median 13,550 pounds.

Well done if you got those right.

Now, comparing year-on-year averages and spread informs a business owner about the health of their business.

The owner can conclude, "The mean average is higher, "therefore we've sold more in year two." Seems sensible so far.

They could also state, "The range is higher, therefore, monthly sales are more volatile, less predictable." Ah, so the average may have gone up, but so is variability.

Your turn now.

Make two comparisons about the year-on-year performance of this business.

Pause and do this now.

Welcome back.

Now, you might have said, "The mean average is lower, therefore, they're sold less in year two.

The range is lower, therefore, monthly sales are more consistent, so, easier to predict." Well done if you said either of these or something similar.

Now, one benefit of using a spreadsheet is that small business owners can easily produce graphics to more easily spot trends.

So, using the insert or chart function, this owner can see their revenue plotted against the time.

What pattern can you more easily see now? Well, this graphical representation shows us this business experiences seasonal trends.

The company might sell a product which people use most during the summer because their sales went up, and they might gift it at Christmas time.

Your turn.

What pattern can you see from the graph of this small business' sales data? Pause and work this out now.

Welcome back.

Now, you might have said, "A large seasonal variation is seen with higher sales in colder months." Well done if you did.

Now, many small businesses experience seasonal variation.

The volatility in the graph makes it difficult to see if sales are actually improving.

Are these sales going up or down? Can you predict what will happen next? Well, it's quite hard to tell, isn't it? Now, a small business using a spreadsheet to track year-on-year sales in a format like this can benefit from the variety of types of chart that the software can draw.

Here we go.

We've now got a chart where we can see year one revenue, and we could see year two revenue.

We could call this a dual line graph or a comparable line graph.

It clearly shows us that year two revenues are all above year one's.

So, year on year, this business is improving its sales.

Let's do a quick check now.

What patterns do you see year-on-year in the graph of this small business' sales? Pause and work this out now.

Welcome back.

What did you say? You might have said, "There is less seasonal variation in year two." In other words, the line is flatter.

You could also have said, "Winter/autumn sales are higher in year two, whereas summer sales fell." Well done if you said any of that.

It's now time for your final task.

Here are the first three years of sales for a new small business.

For part A, calculate the mean and range for each year and comment on any changes year on year.

Part B, you can open the spreadsheet, highlight this range of data, and click the insert/chart button to graph the sales data year-on-year.

If you don't have access to spreadsheet software, don't worry, 'cause on the next slide, we have got a graph that you can use.

And then in part C, comment on any patterns that you spot in the data.

Pause the video and work this out now.

When you are ready, press play so that you can see the chart, if needed, for part C.

Here's the chart so that you can answer part C.

It's now time to go through our answers.

We're going to start with part A.

So, what I've done is listed year one, year two, and year three, and calculated the range for each and the mean for each.

Now, you might've said, "The mean is increasing, so the business is selling more year-on-year.

The range is also increasing, so the sales are becoming less consistent, which means they're less predictable month-on-month." Well done if you said something like this, and if you've got your values correct.

For part B, this is the graph you should have produced.

Now, remember, if you didn't have access to spreadsheet software, we did give you a copy of this so that you could still answer part C.

So, part C, you might've said, "The graph shows that there is a seasonal peak to the business' sales in November or December.

Their performance is level year-on-year, January to September, but the October, November, December sales are improving with each year." Well done if you said something like that.

Independent business owners use percentage calculations to monitor profit over time, profit on individual items, and to set selling prices.

Spreadsheets are used to help small businesses understand their most profitable products.

Small businesses also use averages, spread, spreadsheets, and graphing technology to monitor performance over time.

Well done.

I hope you've enjoyed seeing how small independent business owners are using maths to help their businesses.

I look forward to seeing you for more math in the future.

Goodbye for now.