Discounts and Markups
What this domain tests
Trade discounts reduce list price along a distribution channel; cash discounts reward early payment; markups and markdowns set and adjust retail prices. Expect series-discount net prices, equivalent single discounts, and markup-on-cost versus markup-on-selling-price problems.
Core rules
- Single trade discount: net price = list × (1 − d); discount amount = list × d.
- Series discounts such as 20/10/5 are applied in sequence, never added. Net price = list × (1 − d₁)(1 − d₂)(1 − d₃); the product of the complements is the net price factor.
- Equivalent single discount = 1 − net price factor.
- Cash discount terms: 2/10, n/30 means 2% off if paid within 10 days, with the net amount due in 30 days.
- Markup = selling price − cost. On cost: SP = cost × (1 + markup rate). On selling price: SP = cost ÷ (1 − markup rate).
- Markdown = original price − reduced price, usually stated as a percent of the original selling price.
- Gross margin compares gross profit to net sales.
Worked example
A wholesaler lists an item at $500 with a series discount of 20/10. Find the net price and the equivalent single discount. Net price factor = 0.80 × 0.90 = 0.72, so net price = 500 × 0.72 = $360. Equivalent single discount = 1 − 0.72 = 28%. If the retailer's cost is $360 and it wants a 40% markup on selling price: SP = 360 ÷ 0.60 = $600. The same 40% taken on cost would give 360 × 1.40 = $504, a very different price.
Traps that cost marks
- Adding series discounts (20 + 10 = 30%); the correct equivalent, 28%, is smaller.
- Applying a markup on selling price as though it were on cost.
- Taking a cash discount after the discount period has expired.
- Computing a markdown rate on the reduced price instead of the original price.
- Confusing the discount period with the credit period in terms like 2/10, n/30.
Depreciation and Net Worth
What this domain tests
Depreciation allocates the cost of a long-lived asset over its useful life; net worth (owner's equity) is what remains after liabilities are subtracted from assets. Items ask for annual depreciation, book value, and net worth statements for a person or a small business.
Core rules
- Straight-line: (cost − salvage value) ÷ useful life in years. The charge is equal every year.
- Double-declining balance: rate = 2 × (1 ÷ life), applied each year to the beginning book value. Salvage is not subtracted up front, but book value is never depreciated below salvage.
- Sum-of-the-years'-digits: depreciable base × (remaining life ÷ sum of the years' digits). Accelerated, like declining balance.
- Units-of-production: (cost − salvage) ÷ total estimated units, then × units used in the period.
- Book value = cost − accumulated depreciation. Book value is an accounting figure, not market value.
- Net worth = total assets − total liabilities. Assets are listed at fair market value and include cash, investments, property, and receivables.
Worked example
A $28,000 delivery truck has a $4,000 salvage value and a 5-year life. Find the first two years of depreciation under double-declining balance. Straight-line rate = 1 ÷ 5 = 20%, so the DDB rate = 40%. Year 1: 28,000 × 0.40 = $11,200; book value = $16,800. Year 2: 16,800 × 0.40 = $6,720; book value = $10,080. Total depreciation over the life can never exceed 28,000 − 4,000 = $24,000.
Traps that cost marks
- Applying the DDB rate to original cost every year instead of to declining book value.
- Subtracting salvage value in the DDB base - that is straight-line thinking.
- Depreciating an asset below its salvage value.
- Treating book value as resale value in a net worth statement.
- Double-counting a liability that was already netted against an asset.
Corporate Securities, Distribution of Ownership, Stock and Asset Turnover
What this domain tests
This area covers the instruments a corporation issues, who owns what share of the firm, and the efficiency ratios analysts use. Expect par-value dividend calculations, percentage-of-ownership items, earnings per share, and inventory (stock) and asset turnover.
Core rules
- Common stock carries voting rights and a residual claim on earnings; dividends are declared at the board's discretion.
- Preferred stock normally has no vote but pays a fixed dividend stated as a percent of par value. Cumulative preferred must be paid all arrears before common shareholders receive anything.
- Ownership percentage = shares held ÷ total shares outstanding. Use outstanding shares (issued minus treasury), not authorized shares.
- Earnings per share (EPS) = net income ÷ shares of common stock outstanding.
- Preferred dividend per share = par value × stated rate.
- Stock (inventory) turnover = cost of goods sold ÷ average inventory; it counts how many times inventory is sold and replaced in a period.
- Asset turnover = net sales ÷ average total assets; it measures sales generated per dollar of assets.
- Bonds are debt: a fixed interest rate on face value and a maturity date, with priority over stockholders in liquidation.
Worked example
A firm has 250,000 shares outstanding and net income of $500,000. An investor owns 5,000 shares. Ownership = 5,000 ÷ 250,000 = 2%. EPS = 500,000 ÷ 250,000 = $2.00 per share. If net sales are $3,000,000 and average total assets are $1,500,000, asset turnover = 3,000,000 ÷ 1,500,000 = 2.0, meaning $2 of sales per $1 of assets. A 6% preferred issue with $50 par pays 50 × 0.06 = $3.00 per share annually.
Traps that cost marks
- Computing preferred dividends on market price instead of par value.
- Using authorized or issued shares rather than outstanding shares.
- Using year-end inventory instead of average inventory in turnover.
- Comparing turnover ratios across industries, where capital-intensive firms naturally show lower asset turnover.
- Mixing up dividends with interest, which belongs to bondholders.