Investment returns: study guide

Key ideas

Investment questions ask how well money performed or whether a plan pays off. Return on investment, compound annual growth, real return, net present value and break-even each answer a different version of that question.

• Return on investment is the gain over the cost, (final − cost) ÷ cost, shown as a percentage. It ignores how long it took.
• CAGR is the constant yearly rate that gets from the start value to the end value, (end ÷ start)^(1 ÷ years) − 1.
• The real return removes inflation, (1 + nominal) ÷ (1 + inflation) − 1. The rule of 72 estimates the doubling time as 72 ÷ rate in percent.
• NPV discounts each future cash flow by (1 + r)ᵗ and subtracts the initial outlay. Break-even units are fixed costs ÷ (price − variable cost).

Key equations

• ROI = (gain − cost) ÷ cost × 100
• CAGR = (end ÷ start)^(1 ÷ years) − 1
• real = (1 + nominal) ÷ (1 + inflation) − 1
• years to double ≈ 72 ÷ rate in %
• NPV = Σ CFₜ ÷ (1 + r)ᵗ − initial
• break-even = fixed costs ÷ (price − variable cost)

Worked example

An investment that grows from 1000 to 1500 in 4 years has CAGR = 1.5^(1/4) − 1 = 10.67 %. A 7 % return with 3 % inflation is 1.07 ÷ 1.03 − 1 = 3.88 % real. At 8 % money doubles in about 72 ÷ 8 = 9 years. Paying 2000 and ending with 2600 gives ROI = 600 ÷ 2000 = 30 %. Fixed costs of 12 000, a price of 25 and a variable cost of 10 give a break-even of 12 000 ÷ 15 = 800 units. Paying 1000 now for 600 in each of 2 years at 10 % has NPV = 600 ÷ 1.1 + 600 ÷ 1.21 − 1000 = 41.32.

Common mistakes

• Subtracting inflation from the nominal rate instead of dividing, which is only an approximation.
• Comparing a total ROI over different time spans without converting to a yearly rate.
• Using the price instead of the contribution margin, price − variable cost, in the break-even formula.

Practice

Test yourself with practice questions on this topic: Investment returns