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.

By the end of today's lesson, you are going to look at some of the ways that maths is used in sales and marketing.

Now we're gonna be using the word "profit" today.

And profit is a business's financial gain.

The difference between the revenue and the cost, a simple formula for the total annual profit is the total revenue, subtract the total costs, and this gives us our yearly profit.

Our lesson's broken into two parts today.

We're gonna begin by looking at Maths in marketing.

If you study business, you'll find many different definitions of marketing.

One simple way to understand it is to think of your customers as your market and the process of marketing as the way in which you get them interested in buying your product or service.

One way to get people interested in a product or service is through advertising.

In the UK, firms spend approximately 40 billion pounds per year on advertising.

That's a lot of zeros.

Now, advertising has changed a lot through the years.

120 years ago, you might have advertised by printing adverts in newspapers, magazines, and on billboards in towns and cities.

100 years ago, radio advertising began.

80 years ago, TV advertising.

Now these forms dominated until roughly 20 years ago when digital online advertising began.

Companies in the UK spend more on online advertising than any other form.

Sam runs a clothing company called Sam's Sleepwear specialising in really comfortable bedtime clothing.

They sell exclusively online, so driving traffic, people, to their website is fundamental to their business' success.

Sam says, "I use Google Analytics to understand which advertising is the most effective.

It gives me so much good data." This is Sam's website traffic data for their first trading year.

Sam says, "Can you guess when I invested some money in online advertising?" Pause the video and see if you can work out when that might have been.

What did you go for? I suspect you noticed that sudden rise in the graph.

Sam invested in online advertising in September, which generated 2,000 more site visits.

Let's do a quick check.

This is Sam's website traffic data for their second trading year.

When did Sam spend money on advertising? And approximately how many extra site visits did this generate? Pause the video while you work this out now.

Welcome back.

So when did Sam spend money on advertising? Well, it looks like there was some investment in April and it generated approximately 3,000 more site visits, but there was also some investment in November, which generated approximately 5,000 more site visits.

Well done if you spotted both of these.

Sam says, "Google Analytics tells me where these extra 5,000 November visitors to my site came from." Well, that's handy.

We've got a pie chart here showing where these visitors came from.

So YouTube advertising generated roughly 2,500 visits.

Facebook advertising generated 1,500 and direct email campaign generated 1,000.

Let's do a quick check.

These are the extra 3,000 April visitors.

Can you work out how many came from each media? Pause the video and work this out now.

Welcome back.

Let's start with YouTube.

That was 1,830 visits.

Facebook gave us 840 visits and an Insta advert gave us 330.

Well done if you've got those right.

So let's go back and look at the November visitors again.

Sam's pointing out, "Well, YouTube did generate 2,500 visits to a website, but it's really expensive to advertise on YouTube." It actually costs Sam 625 pounds.

To advertise on Facebook costs 270 and the direct email campaign cost 140.

What we can do is work out is, it worth it, and how do we do that? Well, let's take our cost and divide by the number of visits.

So in other words, in order to get one extra visitor, I had to spend 25 pence.

Can we work out if Facebook or email were better value? Pause the video and have a go at working this out now.

Welcome back.

Let's start with Facebook.

I spent 270 pounds and that generated 1,500 visits.

This means that I spent 18 pence to generate each visitor when I advertise on Facebook.

For the direct email however, it was even cheaper.

It was only 14 pence in that case.

So in other words, both Facebook and the direct email campaign were better value for money.

Google Analytics also tells Sam where people go upon visiting the website.

So it says that one in 50 visitors go on to make a purchase.

Sam makes an average of 12 pounds profit with every sale.

So let's start with a direct email.

In order to generate those extra 50 visitors, I spent 7.

00 pounds, but I make a 12.

00 pound profit.

That means I actually made a resultant 5.

00 pounds of profit when I get rid of how much I spent on advertising.

So Sam still maintains a profit when they advertise through a direct email campaign.

Does Sam still maintain a profit when advertising through Facebook and YouTube? Pause the video and work this out now.

Welcome back.

Let's look at Facebook first.

Or to generate those 50 visitors, Sam had to spend 9.

00 pounds.

So their 12 pound profit goes down, but they're still making a 3.

00 pound profit.

What about for YouTube though? Well, to generate 50 visitors, Sam spends 12.

50 pounds.

Hang on, that means they're not making a profit anymore.

That's actually a loss! Suddenly, YouTube advertising doesn't seem to be as good as it initially looked.

So expensive advertising formats diminish profit.

However, they can help improve brand recognition and repeat sales.

Businesses need to balance the risk and reward of such investments.

In other words, it might be worth doing that just once to improve brand recognition and then you might not advertise that way again in the future.

It's time for your first task.

Question one.

Sam's Sleepwear is now well established in the bedwear marketplace.

On three occasions in this year, Sam spent just under 5,000 pounds on online advertising campaigns.

When were those campaigns? Which one was the most effective? And how do you know? Pause the video while you work this out now.

Question two, Sam's Sleepwear is now well established in the bedwear marketplace.

They spend the below on advertising and generate 14,000 extra visitors to their website.

They now make a sale from one in 40 visitors and an average of 14 pounds per sale.

I'd like you please to calculate which form of media is the most profitable and advise Sam as to where to spend their next advertising budget.

Pause the video and work this out now.

Welcome back.

Let's go through our answers.

So when were those advertising campaigns? Well, you might have said the advertising campaigns happened in March, August and November.

That's where we can see the rise in our graph.

Now we know that November campaign was the most effective because it resulted in the greatest spike or increase in site visits.

Question two, I asked you to calculate which form of media is the most profitable and advise Sam as to where to spend their next advertising budget.

So let's work this out for each of the different places we could have advertised.

For YouTube, it's costing us roughly 28 pence per visit.

You'll notice that I haven't rounded here.

I'm gonna be keeping that exact value on my calculator so I can make future calculations and be as accurate as possible.

I'm making a profit of approximately 2.

78 pounds, and that's from my YouTube advertising.

What about Facebook though? Well, it's costing me roughly 22 pence per visit, which means that through Facebook advertising, I'm getting approximately 5.

07 pounds profit.

What about direct email? Well, that's 13 pence it's costing me per visit, giving us a result of approximately 8.

44 pounds in profit.

What about Google? Well, that's costing me 46 pence per visit, which actually means I'm making for each sale, a 4.

80 pound loss.

So what would you advise Sam? Well, you might have said, "Google's expensive and currently unprofitable for a business of your size." You might have also said that "Direct email campaigns remain the most profitable form of advertising for your business.

You spent more than seven times 350 pounds of advertising on Google.

Perhaps redirect that money and do more direct email campaigns." For YouTube and Facebook, you might have said, "They are both more expensive and less profitable than direct email, but they are still making a profit and they do give your brand or business good exposure.

So perhaps you should continue to invest in advertising this way." Well done if you said anything like that.

It's now time to look at Maths in Sales.

Jacob and Izzy ran a business selling high quality frying pans in the catering industry.

Last year, The business sold 200,000 units at a price of 30 pounds each.

Jacob is the sales director and makes a proposal at a board meeting.

"Market research shows that if we halve our price, we can double our sales.

That would make us the market leader.

I think we should do it." Do you think that sounds like a good idea? Pause the video and have a discussion now.

Welcome back.

So do you think it's a good idea? Well, this proposal's a curious one.

I'm selling 200,000 units at 30 pounds each.

Now, I was told that if I halved the price, in other words 30 becomes 15, I'll double the number sold.

Well, hang on a second.

If I'm currently selling 200,000 units at a price of 30 pounds each, that's 6 million pounds in revenue.

But halving the price of 15 pounds and selling 400,000 units will give me the exact same revenue.

Hmm? But Jacob was saying, "Well more people will know about us.

So maybe that's better in the long run.

We'll be those market leaders.

Biggest sales in the company's history!" Hmm? Thankfully, Izzy is a commercial accountant and she understands the difference between revenue and profit.

Revenue is the income into our business.

In other words, the total money that goes in the till from our sales.

Profit is our financial gain.

It's the difference between our revenue and the cost to make the goods.

We currently sell 200,000 units at a price of 30 pounds each.

Now each of those units costs us 20 pounds to manufacture, package, and distribute.

Have you spotted what the issue is yet? Well done if you have.

If you're not sure, feel free to pause the video, maybe chat to the people around you to see if they've worked out what's the problem here? When you're ready, press play.

Have you all worked out what the problem is? This is a classic example of where mathematics helps businesses with crucial decision making, which could make or break their business.

Let's consider the current situation.

We're selling 200,000 units per year, and the selling price is 30 pounds a unit.

The cost price per unit is 20 pounds, which means the profit per unit is 10 pounds, which means our annual profit is 2 million pounds.

Well, that sounds nice.

Alternative way to look at the same numbers could be to say, well, our revenue is 6 million pounds, but the cost is 4 million pounds.

So the profit, remember, is the total revenue minus the total costs, which is 2 million pounds.

So same answer, just different way of looking at it.

And this might be an easier way to understand profit versus revenue.

We spent 4 million pounds to make 6 million pounds.

That's a profit of 2 million.

This is how an accountant would interpret Jacob's proposal.

Let's considered the new situation.

We're now selling 400,000 units for a selling price of 15 pounds per unit.

The cost price per unit is 20 pounds.

That means the profit per unit is negative five pounds.

Oh, that's.

that's not good, is it? So actually we're gonna lose 2 million pounds every year.

I'm a lot less keen on Jacob's idea now.

I don't know about you.

Now of course, we could look at this a different way.

We could say, well, the total revenue for the year is 6 million pounds.

Total cost to the year is 8 million pounds, which means that our profit is negative 2 million pounds.

In other words, we spent 8 million pounds to make 6 million pounds.

So we lost 2 million.

Well, that's not good, is it? It's clearly not a sensible thing to do.

Businesses use mathematics in the form of commercial accounting to make decisions on pricing.

Let's do a quick check.

Aisha and Alex work for a business that sells archery sets.

Their business currently sells 12,000 units per year at a price of 80 pounds and the cost of producing, packaging and distributing each unit is 50 pounds.

Calculate their annual revenue and their profit.

Pause and do this now.

Welcome back.

Well, their revenue, remember, is the total they make.

So that's 12,000 times the 80 pound per unit gives us 960,000 pounds.

In order to calculate profit though, we need to take away those costs.

Well, the total cost is 600,000 pounds, meaning the profit is 360,000 pounds.

Well done if you got that.

So that's their current situation.

Aisha says, "Customers have told me if we halve our price, they'll buy twice as many sets.

We'd really hit the bullseye with our sales numbers." That is a terrible joke, Aisha.

What I'd like you to do is be the accountant and show why it would be a poor commercial decision to halve their prices.

Pause and do this now.

Welcome back.

Did you approve it? So under the current situation, their profit was 360,000 pounds a year.

For the new situation, we're going to sell twice as many units.

'cause remember, customers said they'll buy double, and the selling price remember, got halved, so it became 40 pounds.

The cost price though hasn't changed, which means that our revenue is 960,000 pounds, which is what it was before, but the costs have increased to 1,200,000 pounds.

This means that our profit is negative 240,000 pounds.

Definitely not good for the business.

The accountants have to consider every decision and sometimes the results are a little unexpected.

So what we can see here is Jacob and Izzy and their current situation with their frying pans.

Izzy says, "Market research shows that if we increase our price by 10%, our sales will go down by 15%.

I think we should do it." What?! Do you think that sounds like a good idea? Pause the video and have a quick chat now.

Welcome back.

Well, if you said "That seems a little suspicious, increasing our price but reducing our sales? That doesn't sound good," I can see why.

But let's look at the numbers and see if they agree.

The intuition says, it doesn't sound good, but accountants are there to help us understand our profitability.

So let's be the accountant and calculate what a 10% rise in price for a 15% loss in sales actually does to our business.

Remember, previously we had a revenue of 6 million, costs of 4 million, and a profit of 2 million pounds.

Let's look at the new situation.

We're gonna have a 15% loss in sales, which means that we're now only selling 170,000 units.

The selling price per unit though, has increased by 10%.

So it's gone from 30 pounds to 33 pounds.

The cost price per unit though, has stayed the same at 20 pounds.

This means that our revenue is now 5,610,000.

That's not as good as it was before.

But wait.

Our costs have also decreased because we're not selling as many units.

They've gone down to 3.

4 million pounds.

This means that our profit has actually increased.

We went from 2 million to 2,210,000.

That's an increase to our profit of 210,000 pounds.

So despite what we initially thought, this is actually good for our business?! Let's check our understanding.

The year is 2050 and Laura's Lunar Launches charge 250,000 pounds for a day trip to the moon with an included surface walk.

They currently take 600 passengers per year at a cost of business of 225,000 pounds per person.

Laura says, "Market research tells us if we drop our price by 5%, we'll get 30% more passengers.

My sales team want to do it to grow market share.

Should we do it?" Pause the video and work this out now.

Welcome back.

So, should they do it? Well, let's consider the numbers.

With the current situation, the profit to the business is 15 million pounds.

Let's consider the new situation.

So we've got 30% more flights, it means our flights go from 600 to 780, but the same price has a 5% drop.

So it's now gone to 237,500 pounds.

The cost price remains unchanged.

It means that our revenue and our costs have changed and therefore our profit is now 9,750,000 pounds.

So you might have said, "Don't make the change, Laura.

Whilst it will generate more revenue, our profit will decrease by more than 5 million a year." Ouch! It's time for your final task.

Jun is the CEO of a sweet manufacturer that sold 36,000 packets of sweets last year at 1.

80 pound a packet.

Their manufacturing cost is 60 pence per unit.

Part A, calculate Jun's current revenue in profit.

Part B: If Jun could double his sales by halving his price, should he? And then part C: if Jun can increase his sales by a third, by reducing his price by one third, should he? Pause the video while you work this out now.

Welcome back.

Question two.

Andeep is a commercial accountant for a guitar manufacturer that sells 1200 units a year at 600 pounds per unit and costs 480 pounds per unit to make.

Which of the below are good commercial deals? So you've got part A, part B and part C.

Part D: If Andy were to drop his price by 12%, what percentage uplift in sales would he need in order to maintain existing profit? Pause the video while you work through these now.

Welcome back.

Let's go through our answers.

So calculate Jun's current revenue in profit.

Well, you should have found that the current revenue was 64,800 pounds and the current profit was 43,200 pounds.

So if Jun could double his sales by halving his price, should he do that? Well, if he does that, the profit becomes 21,600 pounds.

So you might've said, "While this will increase volume i market share, it halves your profit.

I recommend you don't do this." And then in part C, if you could increase your sales by a third by reducing his price by one third, should he do it? Well, if he does do it, profit becomes 28,800 pounds.

So you might have said, "Whilst this will increase volume in market share, it still reduces profit.

In fact, it reduces it by a third.

So I recommend you don't." Question two, you had to work out for Andeep which of the below were good commercial deals.

So is a 5% uplift in sales for a 10% drop in price worth it? Well, our profit goes from 144,000 pounds per year to 75,600 pounds per year.

That is not worth it.

In part B, what about a 50% uplift in sales for a 15% drop in price? Well profit becomes 54,000 pounds.

Ooh, ouch.

That's still not good, is it? Going from 144,000 pounds per year to only 54,000 pounds per year? Nope.

That's a definite no.

What about part C? We're gonna do a 10% drop in the sales for an increase of 5% in the price.

If I do that, my profit becomes 162,000 pounds.

Oh, that's a win.

My profit's gone up.

Brilliant deal.

In part D, if Andeep were to drop his price by 12%, what percentage uplift in sales would he need to see to maintain the existing profit? Well, the current total profit is 144,000 pounds.

So if we drop our price by 12%, the new profit per unit is 48 pounds.

This means I need to sell 3000 units.

So I need 150% increase in sales if I want to see the same profit.

Well done if you got that all right.

It's now time to sum up what we've learned today.

In marketing, we can use data from systems like Google Analytics to identify which types of advertising are most profitable for our business.

In sales, we know that the sales team will always want to reduce the price to increase the volume of their sales, but the accountants can do the maths to help understand if that decision would be a profitable one or not.

Well done today.

I hope you've enjoyed learning some of the different ways that maths is used in sales and marketing.

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

Goodbye for now.