Mathematics Standard • Year 12 • Investment and Loans • Lesson 15
Brokerage in Context, the Round Trip
Run a complete buy and sell, then price the difference between what the prices suggest and what the investor actually made. This is where brokerage stops being a rounding error.
1. A completed trade
Asha buys 900 shares at $4.20 and later sells them all at $5.10. Brokerage is a flat $19.95 each way. 7 marks total
Q1.1 Find her outlay.
Q1.2 Find her net proceeds.
Q1.3 Find her profit, and her percentage return on outlay to 2 decimal places.
2. What the prices alone would have said
3 marks
Q2.1 Calculate the profit from the price difference alone, then find the gap between that and your answer to Q1.3. Explain the size of the gap exactly.
3. Why parcel size matters
3 marks
Q3.1 A second investor makes the same round trip on only 40 shares, buying at $4.20 and selling at $5.10, with the same $19.95 fees. Find their profit, and comment on what brokerage did to this trade compared with Asha's.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1
Buying adds the fee: 900 × $4.20 + $19.95 = $3780.00 + $19.95 = $3799.95 [2].
Q1.2
Selling subtracts it: 900 × $5.10 − $19.95 = $4590.00 − $19.95 = $4570.05 [2].
Q1.3
Profit = $4570.05 − $3799.95 = $770.10 [2]. Return = 770.10 ÷ 3799.95 × 100% = 20.27% [1]. The return is measured against the outlay, the money actually committed.
Q2.1
Price-only profit = 900 × ($5.10 − $4.20) = 900 × $0.90 = $810.00 [1]. Gap = $810.00 − $770.10 = $39.90 [1]. That is exactly 2 × $19.95: the two brokerage fees, one on each leg. The gap is never a mystery, and it never depends on the prices [1].
Q3.1
Outlay = 40 × $4.20 + $19.95 = $168.00 + $19.95 = $187.95. Proceeds = 40 × $5.10 − $19.95 = $204.00 − $19.95 = $184.05. Profit = −$3.90, a LOSS [2]. The share rose 21.43% and the investor still lost money, because the same $39.90 of fees is trivial against Asha's $3780 trade and larger than the entire gain on a $168 one [1].