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Equipment, people and a price rise can all grow profit; compare them on the change in monthly profit, find how many customers a price rise can lose before it stops paying, and weigh what each choice risks if its assumptions are wrong.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will compute the change in monthly profit from equipment, a hire and a price rise, choose the best on the figures, find how many customers a price rise can lose, write the price-rise rule, and work what happens when more customers leave than expected.
You can find a constraint, compare ways to relieve it, and plan the cash a step needs. The three commonest steps — equipment, people and price — can now be compared on one measure, using the contribution arithmetic from the costing course.
| Term | What it means |
|---|---|
| Change in monthly profit | How much a choice adds to, or takes from, each month's profit. |
| Equipment lever | A machine or space that adds capacity and a monthly cost. |
| People lever | A hire that adds capacity and a wage, plus the owner's time to train. |
| Price lever | A higher price that earns more on each unit kept and loses the contribution of any customers who leave. |
| Price-rise limit | The most units a rise can lose before it stops adding profit. |
Northside Repairs does 150 repairs a month at 25 dollars of contribution each. Three choices:
$$\text{price rise} = d (v - l) - l m$$
On these figures the price rise is the best, and it needs no cash up front and adds no fixed cost. Owners often reach for equipment first, because it feels like growth; the price lever is the one most often left untried. Every figure here rests on stated assumptions about volume, price and cost. It says what follows if those assumptions hold; it is not a prediction, and it is not advice about what any real business should do.
Another way: table
Northside Repairs' three levers.
| Choice | Change in monthly profit |
|---|---|
| Second stand | 100 |
| Apprentice | 200 |
| Price rise | 310 |
Another way: steps
Use the same measure for each lever. The change in monthly profit, worked from the contribution a unit, the units each lever adds or loses, and its monthly cost.
For equipment and people, cap the extra units. A stand or an apprentice adds capacity, but only the units customers want count, and only up to the next constraint.
For price, count both sides. Every unit still sold earns the rise; every unit lost takes away its whole contribution. The limit — how many units the rise can lose before it stops paying — is the rise times the units, divided by the rise plus the contribution.
Weigh the risks, then test. Each lever rests on an assumption that could be wrong.
Check each figure by sense. A price rise that loses no customers must add the rise times every unit; one that loses exactly its limit must add zero. An equipment option whose extra units are capped must never be credited with more than the unmet demand.
The figures rest on assumptions, and each lever fails in its own way:
Doing nothing has a risk too: rivals that grow while the business stands still, and an owner who stays the constraint.
The limit turns the riskiest assumption into a single figure. Northside Repairs raising its price by 4 dollars can lose up to 4 × 150 ÷ (4 + 25), about 20 repairs a month, before the rise stops paying. If the owner's evidence — customers who have mentioned price, rivals' prices, what happened after the last rise — suggests far fewer than 20 would leave, the rise is a sound bet. If it suggests something close to 20, the rise is a gamble.
The limit is larger when the contribution a unit is small compared with the rise, which is why businesses with thin margins gain the most from small price rises, and why a business charging too little has room to raise its prices a long way before losing money.
When the business is at its capacity limit, a price rise is often the cheapest way to grow profit, because customers who leave free up time for others who will pay more. A workshop with a two-week waiting list that raises its price and loses ten repairs has not lost ten repairs at all: it has shortened the waiting list, and the next customers in line take the freed slots at the higher price. When the business has spare capacity, the calculation is less generous, because lost customers leave empty slots behind.
The levers are not exclusive. A common sequence is a price rise first, because it needs no cash and tests how much customers value the service; then, if demand holds, the extra profit funds equipment or a hire to serve the customers who stayed. Taken in that order, each step is paid for by the one before, and the business never takes on a fixed cost without evidence that the demand will cover it.
Every lever's figure rests on a guess, and the guesses are not equally good. The cost of a repair stand is a quote from a supplier: firm. The wage of an apprentice is set by the owner: firm. But the extra repairs each would bring, and the number of customers a price rise would lose, are estimates about how customers will behave. Those are the figures to question hardest.
For equipment and people, the key question is whether the extra capacity will be used. A second stand only adds repairs if customers are being turned away now, or if the waiting list is long enough that some give up. If the workshop has idle hours already, the stand adds cost and nothing else. The evidence to look for is the work turned away: phone calls that could not be booked, customers who left when told the wait, a waiting list that keeps growing.
For price, the key question is how many customers would leave. The evidence is different: what rivals charge for the same work, how often customers mention price, what happened the last time prices rose, and how many customers come back because of the quality rather than the cost. A business whose customers compare prices online before every purchase will lose more to a rise than one whose customers come for a trusted name.
Where the evidence is thin, the lever with the smallest downside is the one to try first. A price rise can be reversed next month if customers leave; a lease or a hire cannot be undone so cheaply.
A bike repair shop with two mechanics had a three-week waiting list every spring and assumed the answer was a third mechanic, at about 3,800 dollars a month. The shop did about 320 repairs a month at an average contribution of 32 dollars.
The owner worked all three levers. A third mechanic would add about 110 repairs a month if the waiting list filled them: 110 × 32 − 3,800 = −280, a loss, once training time and slower first months were counted. A second repair stand, at 250 a month, would let the two mechanics work faster on busy days and add about 25 repairs: 25 × 32 − 250 = 550. A price rise of 8 dollars on the standard service had a limit of 8 × 320 ÷ 40 = 64 repairs; the owner expected perhaps 15 customers to go elsewhere, and the waiting list would refill their slots.
She raised the price in March and added the stand in April. The waiting list shrank to ten days, about 12 customers a month went elsewhere and were replaced from the list, and monthly profit rose by about 3,000 over the spring. When the waiting list grew back to three weeks the following year, she hired the third mechanic — by then at a price that made the hire pay.
People who study business finance often point out that a small price rise usually does more for profit than the same percentage rise in volume or fall in cost, because the whole rise reaches the profit line. The price-rise limit in this lesson is the small-business version of that point, with the risk made explicit.
Growth means more equipment or more staff. A price rise is a growth lever too.
Any lost customer makes a price rise a mistake. It can still pay, up to its limit.
The option adding most units is best. Compare the change in profit.
A lost customer only costs the rise. It costs the whole contribution of the unit.
The figures settle it. Weigh each option's risk too.
A price rise must keep every customer. It pays as long as fewer leave than its limit, and the limit is often larger than owners expect.
A hire costs only the wage. Count the owner's hours spent training, the slower first months and the payroll taxes and benefits on top of the wage.
Equipment always adds capacity. It only adds units if the work is waiting; with idle hours already, it adds a fixed cost and nothing else.
The best lever on paper is the one to commit to. The figures rank the levers only as well as their guesses allow. When two levers are close, prefer the one whose key guess can be tested cheaply and whose cost can be undone. A price rise tried on one service for a month tells the owner more about customers than any estimate, and costs little if it has to be reversed; a three-year lease on a second stand is a bet that cannot be taken back.
Read the business.
$160 \text{ cleans at } 40 \text{ contribution}$
A month.
Work a second van.
$20 \times 40 - 880 = -80$
Extra cleans less the van's cost.
Work a 5-dollar price rise losing 8 cleans.
$5 \times 152 - 8 \times 40 = 440$
The rise on cleans kept, less those lost.
Find the price-rise limit.
$5 \times 160 \div (5 + 40) \approx 17.8$
About 17 cleans could go.
Decide and test.
$\text{raise the price for new customers first}$
The number and the risk together.
Work the stand.
$20 \times 25 - 400 = 100$
Extra repairs less its cost.
Work the apprentice.
$40 \times 25 - 800 = 200$
Extra repairs less the wage.
Work the price rise.
$4 \times 140 - 10 \times 25 = 310$
The best on the figures.
Find the price-rise limit.
$4 \times 150 \div 29 \approx 20.7$
About 20 repairs could go.
Compare with the expected 10.
$10 < 20$
A comfortable margin.
Plan the order.
$\text{price first; the apprentice if the queue returns}$
Each step funded by the one before.
Read the business.
$300 \text{ mugs at } 20; \text{ a waiting list of } 40$
She is at capacity.
Work a 5-dollar rise losing 20 buyers.
$5 \times 280 - 20 \times 20 = 1000$
If the lost mugs are simply lost.
Fill the freed slots from the waiting list.
$20 \times 25 = 500$
Twenty mugs at the new contribution.
Add the refill to the gain.
$1000 + 500 = 1500$
The freed slots earn again, at the higher price.
Find the price-rise limit.
$5 \times 300 \div 25 = 60$
Before counting the waiting list at all.
Compare with equipment.
$\text{a second kiln adds nothing: throwing is the limit}$
Price is the only lever that helps now.
Decide on the figures.
$\text{raise the price; review in two months}$
With the waiting list as the measure.
Find the price-rise limit.
$5 \times 300 = 25 l, \text{ so } l = 60$
A 5-dollar rise on 300 mugs at 20.
Work the change if 20 leave.
$5 \times 280 - 20 \times 20 = 1000$
The rise on mugs kept less those lost.
Compare with the limit.
Northside Repairs does $150$ repairs a month, each contributing $25$ dollars. Three ways to grow: a second repair stand, costing $300$ dollars a month, would add $12$ repairs a month; an apprentice, costing $1000$ dollars a month, would add $22$; or it could raise its price by $4$ dollars a repair and expect to lose $10$ repairs a month. Fill in the change in monthly profit for each, in dollars. Write a fall with a minus sign.
| Change in monthly profit, dollars | |
|---|---|
| Second repair stand | |
| Apprentice | |
| Price rise |
Complete the worked solution: Maya sells $625$ mugs a month, each contributing $19$ dollars. She would raise the price by $6$ dollars. Find how many mugs a month she could lose before the rise stops adding profit.
Multiply the rise by every mug sold now.
$6 \times 625 =$ a
What the rise would bring if nobody left.
Add the rise to the contribution.
$6 + 19 =$ b
Each lost mug costs its contribution and the rise it would have paid.
Divide the first by the second.
$(\text{rise on all}) \div (\text{cost a lost mug}) =$ l
Mugs she can lose before the rise stops paying.
Compare with her estimate.
$\text{expected losses below the limit?}$
Then the rise pays.
Plan a test.
$\text{raise the price on one design first}$
The losses are an assumption to check.
Northside Repairs does $150$ repairs a month, each contributing $25$ dollars. Three ways to grow: a second repair stand, costing $400$ dollars a month, would add $30$ repairs a month; an apprentice, costing $1200$ dollars a month, would add $46$; or it could raise its price by $2$ dollars a repair and expect to lose $12$ repairs a month. By how much would the price rise change the monthly profit, in dollars?
Answer:
Northside Repairs does $150$ repairs a month, each contributing $25$ dollars. Three ways to grow: a second repair stand, costing $500$ dollars a month, would add $10$ repairs a month; an apprentice, costing $1200$ dollars a month, would add $39$; or it could raise its price by $6$ dollars a repair and expect to lose $15$ repairs a month. The stand would change the monthly profit by $-250$ dollars, the apprentice by $-225$, and the price rise by $435$. Which is best on these figures?
A hair salon sells $v$ cuts a month, each contributing $m$ dollars. It raises its price by $d$ dollars and expects to lose $l$ cuts a month. Write the change in monthly profit, $g$.
Answer:
Maya sells $145$ mugs a month, each contributing $20$ dollars. She is thinking of raising the price by $5$ dollars. How many mugs a month could she lose before the rise stops adding profit?
Answer:
A hair salon does 240 cuts a month, each contributing 30 dollars. A fourth chair, leased for $400$ a month and worked by the existing stylists in their gaps, would add $45$ cuts; a new stylist at $2200$ a month would add $75$; a price rise of $3$ dollars would lose $15$ cuts. Fill in each change in monthly profit, in dollars.
| Amount | |
|---|---|
| Fourth chair | |
| New stylist | |
| Price rise |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Northside Repairs does 150 repairs a month at 25 dollars of contribution each. It raises its price by $4$ dollars, and $29$ repairs a month leave instead of the handful it expected. What does the rise now do to the monthly profit, in dollars? Write a fall with a minus sign.
Answer:
You can compare very different growth choices on one measure, and know the limit of a price rise. Tell someone why a price rise is a growth lever. Next: using economies of scale.
17. Your turn: Maya without a waiting list, step 3
$20 < 60$
Well inside it.