A few months later, a company called Peter Tilling Plastics turned up at Lesmahagow High School, looking for apprentices.
Muirhead signed up for a four-year apprenticeship as a die-setter, which he finished in three years, before moving off the shop floor.
In that time the company was sold to Sweden's Rosti and the former Tilling factory began making mobile phone shells for Nokia, Motorola and Ericsson and components for NCR cash machines.
Through Rosti, Muirhead was introduced to more automation, and he went on the become a production engineer.
Then Rosti went through a restructuring. Some staff were made redundant, but Muirhead stayed on.
By then the company was dealing with some big projects, so that meant he was picking up experience at a young age.
Then, a few years into his career and to his parents' horror, he quit.
Then came the decision to head for New Zealand to play rugby for year, ending up at the Pukekohe Rugby Club.
"I wasn't very good but I had a lot of fun and met a lot of people," he says.
Muirhead enjoyed life in the Franklin area and decided to stay on.
Through an old Rosti contact he secured a job with Brendan Lindsay's Sistema in 2004, working on the shop floor as a die-setter.
These days Muirhead has risen to become SIstema's chief executive, but back then taking a job with the company was a bit of a comedown, given that he had gone on to project management back in Scotland.
At the time, Sistema - which makes plastic food containers and drink bottles - was a relatively simple prospect.
"You could walk around the place with a mallet, a hammer and a screwdriver, and fix pretty much anything.
"It was like going back in time 10 years."
Before long he was getting in owner Lindsay's ear about the need for automation.
"We should do this. We should do that. I was full of ideas and I had seen all this stuff in the UK that we could do.
"It took a while but he eventually let me buy one robot, and we went from 10 per cent rejects to zero."
Once Lindsay saw flawless products rolling off the assembly line, he was hooked.
"That's when it all started. We ordered several more robots and everything snowballed from there."
As Sistema blossomed, so did Muirhead's career. "I went from die-setter to technical manager, then factory manager, general manager and then chief operating officer," he says.
"At the same time we were experiencing tremendous growth.
"It just got very, very busy."
Five sites
By that stage Sistema had a lot of balls in the air and the factory was spread over five sites.
"It was bursting at the seams. We knew that we could do things so much better."
Lindsay wanted to take the business to a new level and set it up for the future.
The first step was to build new premises. Muirhead, Lindsay and six other executives set off on a world quest in search of good ideas to set up a factory from scratch.
They went through as many facilities as they could, visiting Lego in Denmark, a distribution centre in Spain for clothing giant Zara, and heavy machinery maker Caterpillar in the US.
"We all came back with different ideas about how to set up a factory of our own, but we were all on the same page."
Muirhead and Lindsay then spent a year with the architects designing the factory. The result was a state-of-the-art factory at Mangere, big enough to accommodate 10 Airbus A380 passenger jets.
"Our competitors can do big volume but they often have old machines. Others have got cool stuff but not the scale," says Muirhead. "We have got the scale, the size, the technology and the innovation.
"We are doing it all here - that's what has given us the edge - and we are keeping it all here in New Zealand."
Lindsay, who started the business in a half-built garage in Cambridge three decades ago, sold Sistema to US company Newell Brands for $660m late in 2016, much to the chagrin of the local investment community.
The purchase by Newell - a US Fortune 500 company, listed on the New York Stock Exchange - ranked as one of the one of the biggest so-called "trade" sales the market has seen for a while.
At the purchase price Sistema would have ranked as a top 50 company if had listed on the NZX, where it would have been a welcome addition, particularly for KiwiSaver funds with money to invest.
Sistema is all about making food storage and hydration: lunch boxes and drink bottles.
Part of the deal with Newell - which has the Rubbermaid brand - involves Sistema making Rubbermaid products, re-branding them as Sistema and exporting them to the rest of the world outside the US.
The Icahn connection
Newell itself went through a rough patch last year, coming to the attention of legendary corporate raider Carl Icahn of RJR Nabisco fame, who pushed for a breakup of the conglomerate.
Asset sales worth US$5 billion and board changes ensued.
One year later, Newell has made progress on its turnaround plan, but the company's share price has yet to recapture recent highs.
Last month, Newell's interim chief executive Chris Peterson said its first-half results were showing the "first green shoots of progress".
"While still early in the organisation's turnaround, we believe our decisive and strategic actions to strengthen our performance will drive further improvement going forward, as we work to transform Newell Brands into a leading next-generation consumer products company," he said.
Muirhead says Newell has been "very supportive" since the acquisition, during which time Sistema's revenue shot up by 20.4 per cent.
"We have been very much left alone," he says. "They are conscious of the growth of the Sistema brand and the presence that we have now in 110 countries.
"They knew that we were doing something quite extraordinary and did not really want to change it."
But it hasn't all been plain sailing.
Sistema hit the headlines last year when some staff went on strike over pay and conditions.
"It was a challenging time," says Muirhead, who describes the relationship with the E Tu union as "fine now".
Next year will be a big one for the company as it ramps up investment in new products, and Muirhead says the plant is constantly evolving.
He says Sistema is heavily involved in "Industry 4.0" - the so-called fourth industrial revolution that involves digital technology.
Internet of things
Sistema has shifted from a regime of preventative maintenance - when machine parts are replaced at set intervals - to one where electronic sensors can detect when a machine is under stress and report back to a central computer, in real time.
About 93 per cent of Sistema's machines are now fully electric, moving away from older hydraulic-based technology.
Muirhead, now 39, was just 37 when he became CEO at Sistema in 2017.
"It was quite frightening I must admit. It's a beast."
The transition involved a crash course in accounting, but he says the key has been having good people around him.
So how did a die-setter - with no experience in sales, marketing or finance, go from the shop floor to being in charge of a multimillion-dollar operation?
That's a question he asks himself.
"It's been quite incredible. I think about it often: How did I end up here?
"I didn't have a plan. It's really been quite surreal."
"I come to work and I work hard. I give it my all, every day, and I try to make a difference.
"If I take personalities and egos out of the picture, and I'm doing the right thing for the business every single day, then I don't think I can go far wrong."
Muirhead says he feels a responsibility to keep the company on the trajectory Lindsay set it on. "So far it's been going very well."
And dreams of farming?
Muirhead, with wife Claire and two children, have 50 head of cattle on 28 hectares at their home at Karaka.
"I'll go home and drive my tractor around," he says. "That's me."
Swimming against the tide
New Zealand manufacturers have long complained about the difficulties of dealing with a floating exchange rate and the tyranny of distance from their key markets.
Mass production of plastic products for sale in 110 countries seems to run counter to the run of play for manufacturing exporters.
But as far as the currency goes, Sistema has a natural hedge.
Its main input - polypropylene - is imported from South Korea and paid for in US dollars.
The finished product - plastic food containers and drink bottles - is sold mostly in US dollars.
While the New Zealand dollar cost of inputs rises when the Kiwi dollar is weak, so too will the company's export receipts when it comes to repatriating US dollars.
A strong New Zealand dollar can mean fewer Kiwi dollars coming in, but equally, lower input costs in Kiwi dollar terms provide an offset.
Even so, mass production of plastics in New Zealand is no small feat.
"We really are swimming against the tide, when you think about what we are doing," says chief executive Drew Muirhead.
"The raw material is from Korea. We ship it here, manufacture, mould it, and ship it back to Korea, and put it on the shelves in their home town."
Muirhead says new products have been vital. Since the Newell takeover, Sistema introduced 20 new lines.
Drink bottles are Sistema's fastest growing line, and he says "we'll be introducing new product next year which we feel will take Sistema to the next level."
For Muirhead, the trick is constantly coming up with new products and colours as retailers are very conscious of "stale" looking products on their shelves.
"It's a tough market. We fight for everything," he says.
"There are lots of private labels coming onto the scene and lots of copycats," he says, adding that Sistema spends a lot on protecting its intellectual property.