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MST-12-S2-02 ~45 min ⚡ +75 XP available

Buying Shares: Brokerage, Total Cost and Choosing an Investment

The price on the screen is not what you pay. A broker takes a fee at both ends, so the share has to rise before you are even back to square one. Then the harder question: given a sum of money, where should it go at all?

Today's hook, A broker charges "the greater of $\$29.95$ or $0.10\%$ of the trade". On a small parcel you pay the $\$29.95$. On a large one you pay the percentage. There is exactly one trade value where the two cost the same, and knowing it tells you which rule you are about to be charged under before you place the order. What is it?
0/4QUESTS

Get oriented

Meet the two ways brokerage is quoted and settle the key terms.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any question in this focus area.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any question
01
Recall, your gut answer first
+5 XP warm-up

You buy $\$3500$ worth of shares and pay $\$19.95$ brokerage. The share price does not move at all. You sell the next day and pay $\$19.95$ brokerage again.

Without calculating write down whether you break even, and by how much you are up or down.

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02
Brokerage, and the two ways it is quoted
+5 XP to read

You cannot buy shares directly. A broker places the order and charges a fee, called brokerage, on the way in and again on the way out. It is quoted in one of two ways, and most brokers use both at once.

A flat fee, or a percentage, whichever is larger. A typical quote reads "the greater of $\$29.95$ or $0.10\%$ of the trade value". Small trades pay the flat fee; large ones pay the percentage.

Total cost is the trade plus the fee. When you buy, brokerage is added. When you sell, it is subtracted from what you receive. Same fee, opposite sign, and it is that sign change that catches people.

total cost $=$ shares $\times$ price $+$ brokerage
BUYING
Total cost $=$ trade value $+$ brokerage. You hand over more than the shares are worth.
SELLING
Net proceeds $=$ trade value $-$ brokerage. You receive less than the shares are worth.
THE ROUND TRIP
Buy and sell and you have paid brokerage twice. The price must rise by more than both fees before you make a cent.
03
What you'll master
Know

Key facts

  • Total cost of buying $=$ trade value $+$ brokerage
  • Net proceeds of selling $=$ trade value $-$ brokerage
  • "The greater of $\$F$ or $p\%$" means take whichever is larger
  • A round trip pays brokerage twice
Understand

Concepts

  • Why brokerage matters far more on a small parcel than a large one
  • Where the break-even trade value between the two rules sits, and why
  • Why a profit calculated from prices alone is always too optimistic
  • How return, risk, liquidity and cost separate the four investment types
Can do

Skills

  • Find the brokerage under a "greater of" rule and the total cost
  • Find the true profit on a completed buy-and-sell
  • Find the trade value at which the two brokerage rules cost the same
  • Compare savings accounts, term deposits, shares and property for a stated goal
04
Key terms
BrokerageThe fee a broker charges to place a trade, paid on both the buy and the sell. Like this: buying $\$6200$ of shares with a flat $\$19.95$ fee costs $\$6219.95$ all up.
Trade valueNumber of shares $\times$ price per share, before any fee. Like this: $500$ shares at $\$12.40$ is a trade value of $\$6200$, and the brokerage sits on top of that.
Total costWhat actually leaves your account when you buy. Like this: trade value $\$42\,300$ plus brokerage $\$46.53$ gives a total cost of $\$42\,346.53$.
Net proceedsWhat actually arrives in your account when you sell, after the fee. Like this: selling $\$4080$ of shares with a $\$19.95$ fee returns $\$4060.05$, not $\$4080$.
LiquidityHow quickly an investment can be turned back into cash. Like this: shares sell in a day, a term deposit is locked for its term, and a property can take months, which is why liquidity separates the four options as much as return does.

Apply the greater-of rule

Work out which brokerage applies, and find where the two ways switch over.

05
The "greater of" rule, and where it switches over
core concept

A quote of "the greater of $\$29.95$ or $0.10\%$" is two rules with a switch between them. Work out both and take the larger:

brokerage $= \max\left(F,\; \dfrac{p}{100} \times V\right)$   ($V$ the trade value)
buying: $\quad$ total cost $= V + \text{brokerage}$
selling: $\quad$ net proceeds $= V - \text{brokerage}$

The switch happens where the two are equal, and you can find it exactly. Set $\dfrac{p}{100} \times V = F$ and solve for $V$. With $F = \$29.95$ and $p = 0.10$, that gives $V = 29.95 \div 0.001 = \$29\,950$. Below that the flat fee is larger and you pay it; above it the percentage takes over.

Why this matters more on a small parcel. A $\$19.95$ fee on a $\$500$ trade is $4\%$ of what you invested, and the share has to rise $8\%$ before a round trip breaks even. The same fee on a $\$20\,000$ trade is $0.1\%$. Brokerage is the reason small, frequent trades lose money even when the picks are good.

Brokerage is the greater of a flat fee $F$ and a percentage $p\%$ of the trade value $V$. Buying costs $V + $ brokerage; selling returns $V - $ brokerage. A round trip pays brokerage twice, so the true profit is always less than the price difference suggests. The two rules cost the same at $V = F \div (p/100)$.

Pause, copy the "greater of" rule, both the buying and selling forms, and the break-even calculation, into your book.

Quick check: Brokerage is the greater of $\$29.95$ or $0.10\%$ of the trade value. What is the brokerage on a trade of $\$22\,000$?

Work the brokerage examples

Follow total cost, total proceeds and the comparison of two purchases.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · A FLAT FEE

Nadia buys $500$ shares at $\$12.40$ each. Her broker charges a flat fee of $\$19.95$. Find the total cost, and express the brokerage as a percentage of the trade value.

1
$V = 500 \times \$12.40 = \$6200.00$
Trade value first, before any fee. This is the number the percentage rules would be applied to, and it is not what she pays.
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PROBLEM 2 · THE GREATER OF TWO RULES

Theo buys $1800$ shares at $\$23.50$ each. His broker charges the greater of $\$29.95$ or $0.11\%$ of the trade value. Find the total cost.

1
$V = 1800 \times \$23.50 = \$42\,300.00$
Trade value first, again. You cannot apply a percentage rule until you have the thing it is a percentage of.
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PROBLEM 3 · THE ROUND TRIP, WHERE THE FEE BITES TWICE

Sam buys $400$ shares at $\$8.75$ and sells them later at $\$10.20$. Brokerage is a flat $\$19.95$ each way. Find the true profit and the return on his outlay.

1
outlay $= 400 \times 8.75 + 19.95 = \$3500 + \$19.95 = \$3519.95$
Buying, so the fee is added. This is the money that actually left his account.
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True or false: If a share price does not move at all, a buy followed by a sell leaves you exactly where you started.

Avoid the brokerage traps

Fix the slips that leave brokerage out of the total cost.

Common errors · the 3 traps that cost marks

Trap 01
Adding brokerage on the sale
The fee always costs you, which means it is added when buying and subtracted when selling. Adding it both times inflates the proceeds and overstates the profit by twice the fee, and the answer still looks plausible.
Trap 02
Taking the smaller of the two brokerage figures
"The greater of $\$29.95$ or $0.10\%$" means exactly that. Work out both and take the larger. A question that gives you two numbers where only one is needed is testing whether you read the rule, and picking the friendlier one is not an accident the marker forgives.
Trap 03
Calculating the return on the trade value instead of the outlay
Your return is measured against what you actually committed, which includes the buying fee. Dividing by the trade value flatters the result every time, and it is the same class of error as using the price you paid where a dividend yield wants the price today.

Drill it and revisit

Run the drill, then return to your opening answer and name what has changed.

Quick-fire practice · 5 calculations

1

Buy $250$ shares at $\$6.80$ with a flat brokerage of $\$19.95$. Find the total cost.

2

Buy $12\,000$ shares at $\$4.15$ with brokerage of $0.12\%$ of the trade value. Find the brokerage and the total cost.

3

Brokerage is the greater of $\$29.95$ or $0.10\%$. Find the brokerage and total cost on a trade of $\$22\,000$, and say which rule applied.

4

Same rule. Find the brokerage and total cost on a trade of $\$45\,000$, and say which rule applied this time.

5

For that same rule, find the trade value at which the flat fee and the percentage cost exactly the same.

Match each investment to the feature that most sets it apart:

  • Savings account
  • Term deposit
  • Shares
  • Property
  • Sells within a day, but the price can fall as fast as it rises
  • Large entry costs and months to sell, with rent as income
  • Cash available any time, at the lowest return of the four
  • A guaranteed rate, on condition the money stays locked for the term
10
Comparing the four investment strategies

Lesson 11 compared savings accounts and term deposits on return, risk and liquidity. Shares and property complete the set, and the four separate on four measures, not one.

InvestmentTypical returnRisk to capitalLiquidityCost to enter
Savings accountLowestNoneImmediateNone
Term depositLow, guaranteedNoneLocked for the termNone
SharesHigher, not guaranteedReal, can fallDaysBrokerage, both ways
PropertyGrowth plus rentReal, and undiversifiedMonthsLarge, stamp duty and fees

No column ranks them on its own. A saver with a house deposit needed in eighteen months and a saver investing for retirement in forty years should choose differently from this same table, and an exam question naming a time frame or a goal is telling you which column to weigh.

The four investments separate on return, risk to capital, liquidity and cost to enter. Savings accounts and term deposits carry no capital risk and the lowest returns; shares and property carry real risk, higher potential returns, and entry costs that savings products do not have. The right choice depends on the investor's time frame and purpose, not on the return column alone.

11
Revisit your thinking

Back to the hook, and to the Think First. Under "the greater of $\$29.95$ or $0.10\%$", setting $0.001V = 29.95$ gives $V = \mathbf{\$29\,950}$. Below that you pay the flat fee, above it the percentage.

And the Think First: buy $\$3500$ of shares, pay $\$19.95$, sell at the same price, pay $\$19.95$ again. You are down $\$39.90$ having done nothing wrong. The price had to rise about $1.14\%$ just to get you back to level.

Brokerage is not a rounding error on a small parcel. It is the reason the first question about any trade is how much you are trading, not what you are trading.

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Practise buying shares

Answer the question bank, then write full short-answer responses.

01
Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next.

Q1. Buying $500$ shares at $\$12.40$ with flat brokerage of $\$19.95$ costs:

Q2. Brokerage is the greater of $\$29.95$ or $0.10\%$. On a trade of $\$45\,000$ the brokerage is:

Q3. Selling $\$4080$ of shares with a flat brokerage of $\$19.95$ gives net proceeds of:

Q4. Under "the greater of $\$29.95$ or $0.10\%$", the two rules cost the same at a trade value of:

Q5. A saver needs their money back with certainty in exactly $12$ months. The most appropriate of the four is:

02
Short answer
ApplyBand 33 marks

SA 1. Ingrid buys $600$ shares at $\$14.25$ each with a flat brokerage of $\$19.95$.
(a) Find the total cost. (2 marks)
(b) Express the brokerage as a percentage of the trade value, correct to 2 decimal places. (1 mark)

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ApplyBand 44 marks

SA 2. Jonas buys $800$ shares at $\$6.50$ and later sells them all at $\$7.80$. Brokerage on each trade is the greater of $\$19.95$ or $0.12\%$ of the trade value.
(a) Show that the flat fee applies on both trades. (1 mark)
(b) Find his outlay, his net proceeds and his profit. (2 marks)
(c) Find his percentage return on outlay, correct to 2 decimal places. (1 mark)

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AnalyseBand 55 marks

SA 3. Mel has $\$50\,000$ and will not need it for $5$ years. She is choosing between a savings account at $4.2\%$ p.a. compounded annually, a $5$-year term deposit at $4.8\%$ p.a. compounded annually, shares, and an investment property.
(a) Find the value of the savings account and the term deposit after $5$ years. (2 marks)
(b) Find the difference between them. (1 mark)
(c) Mel says "the term deposit wins, so shares and property are not worth considering". Evaluate that statement with reference to return, risk, liquidity and cost to enter. (2 marks)

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📖 Comprehensive answers (click to reveal)

MC 1, B: $V = 500 \times 12.40 = \$6200$, and buying adds the fee: $\$6219.95$. Option C subtracts it, which is the selling rule.

MC 2, D: $0.10\%$ of $\$45\,000$ is $\$45.00$, which is greater than $\$29.95$, so the percentage applies. Option A takes the smaller; option C misplaces a decimal.

MC 3, A: Selling subtracts the fee: $\$4080 - \$19.95 = \$4060.05$. Option B adds it, the single most common error in this topic.

MC 4, C: Set $0.001V = 29.95$, so $V = 29.95 \div 0.001 = \$29\,950$. Below it the flat fee is larger, above it the percentage is.

MC 5, B: A known term and a guaranteed rate match a known date and a need for certainty. Shares and property both carry real capital risk over a period that short, and option D ignores risk entirely.

SA 1 (3 marks): (a) $V = 600 \times \$14.25 = \$8550.00$ [1]; total cost $= \$8550.00 + \$19.95 = \mathbf{\$8569.95}$ [1]. (b) $19.95 \div 8550 \times 100\% = \mathbf{0.23\%}$ [1].

SA 2 (4 marks): (a) Buy: $0.12\%$ of $\$5200 = \$6.24$, which is less than $\$19.95$. Sell: $0.12\%$ of $\$6240 = \$7.49$, also less than $\$19.95$. So the flat fee applies to both [1]. (b) Outlay $= \$5200 + \$19.95 = \mathbf{\$5219.95}$; proceeds $= \$6240 - \$19.95 = \mathbf{\$6220.05}$; profit $= \mathbf{\$1000.10}$ [2]. (c) $1000.10 \div 5219.95 \times 100\% = \mathbf{19.16\%}$ [1]. Note the price-only profit would be $800 \times \$1.30 = \$1040$, overstating it by exactly the two fees.

SA 3 (5 marks): (a) Savings: $50\,000 \times 1.042^5 = \mathbf{\$61\,419.83}$ [1]. Term deposit: $50\,000 \times 1.048^5 = \mathbf{\$63\,208.64}$ [1]. (b) Difference $= \mathbf{\$1788.81}$ [1]. (c) The statement is too strong, and the marks are for saying why on the stated measures [2]. Return: the term deposit beats the savings account, but shares and property have historically returned more over five-year periods, so it does not follow that it beats everything. Risk: the term deposit is guaranteed and the other two are not, which genuinely favours it if Mel cannot tolerate a fall. Liquidity: the term deposit is locked for the full five years, so it is actually the least liquid of the four bar property, which cuts against Mel's claim rather than for it. Cost to enter: the term deposit has none, while shares cost brokerage twice and property carries stamp duty and fees, which is a real point in the term deposit's favour. A complete answer concludes that the term deposit is a defensible choice for a five-year horizon with no tolerance for loss, but that "not worth considering" overstates it.

Drills: 1. $V = \$1700$, total $= \mathbf{\$1719.95}$  ·  2. $V = \$49\,800$, brokerage $= 0.0012 \times 49\,800 = \mathbf{\$59.76}$, total $= \mathbf{\$49\,859.76}$  ·  3. $0.10\%$ of $\$22\,000 = \$22.00 < \$29.95$, so the flat fee applies; total $= \mathbf{\$22\,029.95}$  ·  4. $0.10\%$ of $\$45\,000 = \$45.00 > \$29.95$, so the percentage applies; total $= \mathbf{\$45\,045.00}$  ·  5. $V = 29.95 \div 0.001 = \mathbf{\$29\,950}$.