Mathematics Standard • Year 12 • Investment and Loans • Lesson 14
Shares and Yield, Reasoning
Work backwards, compare two shares that disagree about which is better, and diagnose a solution that is wrong for a reason worth naming.
1. Working backwards
Q1.1 A share pays a dividend of 51 cents and yields 6.00%. Find its price, then state what happens to that yield if the price rises to $10.20 while the dividend is unchanged.
2. Two shares that disagree
Share P: bought $3.00, now $3.90, dividend 12 cents. Share Q: bought $20.00, now $20.60, dividend 96 cents. 7 marks total
Q2.1 Find the capital growth of each, correct to 2 decimal places.
Q2.2 Find the dividend yield of each, correct to 2 decimal places.
Q2.3 A retiree living on investment income and a 25-year-old building wealth ask you which share was better. Give each a different answer and justify both.
3. Diagnose the solution
A student is asked for the dividend yield on a share trading at $7.50 that pays a dividend of 30 cents, held in a parcel of 400. 3 marks
Q3.1 The student writes: "yield = 400 × 30 ÷ 7.50 = 1600%". Name the two errors and give the correct answer.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1
Price = 0.51 ÷ 0.06 = $8.50 [1]. At $10.20 the yield becomes 0.51 ÷ 10.20 = 5.00% [1]. It falls, because the dividend is fixed and the price is the denominator; the holder is better off by $1.70 a share despite the smaller percentage [1].
Q2.1
P: (3.90 − 3.00) ÷ 3.00 = 30.00% [1]. Q: (20.60 − 20.00) ÷ 20.00 = 3.00% [1].
Q2.2
P: 0.12 ÷ 3.90 = 3.08% [1]. Q: 0.96 ÷ 20.60 = 4.66% [1].
Q2.3
The retiree: Q. They spend the income, and Q yields 4.66% against P's 3.08%, so every dollar invested pays more cash each year [1]. The 25-year-old: P. They do not need the income and have decades for growth to compound, and P grew 30.00% against Q's 3.00%, ten times as fast [1]. Neither share is better in the abstract; the question is only answerable once a goal is named, which is why the marks are for the justification and not the choice [1].
Q3.1
Error 1: the number of shares is in the calculation. Yield is a per-share percentage and cannot depend on parcel size [1]. Error 2: cents divided by dollars. 30 cents must become $0.30 before dividing by 7.50 [1]. Correct: 0.30 ÷ 7.50 × 100% = 4.00% [1]. A sense check kills 1600% on sight: no share yields more than its own price.