Why Units Matter in Ratio Analysis
A ratio is only meaningful when its inputs are measured on compatible bases. Financial statements may show one amount in dollars, another in thousands, and a foreign subsidiary’s figures in a different currency. Share-based calculations add another possible mismatch: earnings may be reported in millions of dollars while shares are stated as thousands of shares. The arithmetic can still produce a number in each case, but the number is useful only if the units have been handled correctly.
Before dividing, identify the unit attached to each input. Check the currency, the scale (such as dollars versus thousands of dollars), and, for per-share calculations, the scale and type of share count. Convert incompatible inputs before calculating. If the inputs share the same currency and scale, the common factor may cancel in a ratio, but that cancellation should be understood rather than assumed.
Scale Labels and Cancellation
A statement heading such as “$ in thousands” means that a displayed amount of 4,650 represents $4,650,000. A heading such as “$ in millions” means that 18.6 represents $18,600,000. The displayed figures are not dollar amounts by themselves; their scale label is part of the data.
If numerator and denominator use the same currency and scale, the shared scale factor cancels. For instance, dividing 18.6 million dollars by 4.65 million dollars gives the same result as dividing 18.6 by 4.65. The ratio is 4.0, with dollars canceling. But if one amount is in millions and the other is in thousands, dividing the displayed values directly omits a factor of 1,000.
Not every ratio is dimensionless. In a ratio of a flow measured over a period to a balance measured at a date, the currencies may cancel while a time basis remains. The earlier material on matching measurement periods and reporting dates addresses that issue. This tutorial focuses on getting the measurement units themselves aligned.
Worked Example: Mixing Millions and Thousands
A hypothetical retailer reports current assets of $18.6 million and current liabilities of $4,650 thousand. It also reports annual sales of $72 million and average total assets of $24,000 thousand. Calculate the current ratio and sales-to-average-assets ratio. State the units and identify the mistake avoided.
Method. Convert each pair to the same scale before dividing. The method avoids treating the displayed figures as if they had identical scale labels.
Current ratio. Current assets are already stated in millions. Convert current liabilities from thousands to millions:
Now divide amounts on the same basis:
The dollars and the million-dollar scale cancel. The ratio is 4.0, or 4.0 times if expressed as a multiple.
Sales-to-average-assets ratio. Convert average assets to millions:
Then calculate:
The result is 3.0, with the monetary units canceling. As a check, the retailer’s sales amount is three times the stated average-assets amount. A direct calculation using the displayed values, such as \(18.6/4{,}650\), would give 0.004 and miss the factor of 1,000.
Currency Must Also Match
Amounts in different currencies cannot be added or compared as if they shared a unit. Convert them to one currency using an exchange rate that is stated for the calculation. If the exchange rate is given as 1 U.S. dollar = 1.35 Canadian dollars, then a U.S.-dollar amount is multiplied by 1.35 to express it in Canadian dollars. To convert Canadian dollars to U.S. dollars, divide by 1.35.
For a ratio whose numerator and denominator are both in the same foreign currency, conversion to another currency is usually unnecessary because the currency units cancel. Conversion is required if the inputs use different currencies, or if the result must be presented in a specified reporting currency. When converting balance-sheet items, use the exchange rate specified for the calculation; do not silently substitute a rate for a different date or purpose.
Worked Example: Combining Two Currencies on a Balance Sheet
A hypothetical insurer’s balance sheet lists cash of 9.0 million Canadian dollars, receivables of 4.0 million U.S. dollars, and current liabilities of 10.0 million Canadian dollars. For this calculation, use the exchange rate 1 U.S. dollar = 1.35 Canadian dollars. Calculate the current ratio in Canadian dollars.
Method. Convert the receivables to Canadian dollars, add them to cash, and divide by liabilities already stated in Canadian dollars. This avoids adding unlike currencies directly.
Convert the receivables:
The U.S.-dollar unit cancels in the conversion. Add the Canadian-dollar assets:
Now calculate the ratio:
The answer is 1.44. The currency and scale cancel in the final division. As a check, the converted current assets exceed current liabilities by 4.4 million Canadian dollars, and \(14.4/10.0\) is 1.44. Dividing the original mixed-currency asset figures by Canadian-dollar liabilities would not produce a valid ratio.
Share Counts and Per-Share Amounts
A per-share figure has units of currency per share, such as dollars per common share. To calculate one, the numerator must be a monetary amount and the denominator must be the relevant share count. The scale labels on both quantities matter: a numerator in thousands of dollars divided by a denominator in thousands of shares produces dollars per share, because the “thousand” factors cancel.
For earnings per share, the common calculation uses earnings available to common shareholders divided by the weighted-average number of common shares outstanding during the period. If preferred dividends are present, they are deducted from net income to obtain earnings available to common shareholders. The weighted average is used because the number of common shares may change during the reporting period; the calculation must not casually substitute an ending share count.
This formula’s unit follows directly from division. If net income is in dollars and the denominator is in shares, the result is dollars per share. If both are reported in thousands, the scale factors cancel and the result still has units of dollars per share.
Worked Example: Earnings per Share With Amounts in Thousands
A hypothetical manufacturer reports net income of $27,600 thousand, preferred dividends of $1,200 thousand, and weighted-average common shares of 8,800 thousand. Calculate earnings per common share. Name the method and the unit trap it avoids.
Method. First calculate earnings available to common shareholders, then divide by the weighted-average common share count. Keep both figures in thousands until the division so their scale factors cancel.
Earnings available to common shareholders are:
Divide by the weighted-average shares:
The result is $3.00 per common share. To check the scale, the same calculation in unscaled units is $26,400,000 divided by 8,800,000 shares, which also equals $3.00 per share. The calculation avoids mistaking “8,800 thousand shares” for only 8,800 shares.
Why a Common Scale Factor Cancels
The cancellation rule follows from ordinary division. If both monetary amounts are reported in thousands, each displayed amount represents its numerical value multiplied by 1,000 dollars. The common factor appears in both numerator and denominator and therefore cancels. The same reasoning applies to millions, or to thousands of dollars divided by thousands of shares.
The cancellation is valid only when the same factor and compatible units occur on both sides of the division. It does not justify dividing a figure in millions by a figure in thousands as though their displayed numbers used the same scale. Nor does a scale factor convert one currency into another: currency conversion requires an exchange rate.
For each input, record its currency and whether it is in dollars, thousands, or millions. For per-share calculations, record the share-count scale too.
Convert currencies using the stated exchange rate and convert scales when the inputs have different scale labels.
Cancel units only when they genuinely match, then state whether the answer is a multiple, a percentage, or a currency amount per share.
Common Mistakes and Their Corrections
A common error is to treat a statement’s displayed figures as though they all use the same scale. For example, dividing current assets shown as $18.6 million by liabilities shown as $4,650 thousand gives \(18.6/4{,}650=0.004\). That is not the current ratio: the inputs were not on the same scale. Converting liabilities to $4.65 million gives \(18.6/4.65=4.0\).
Another error is to add amounts in different currencies before converting them. A balance sheet amount in U.S. dollars and one in Canadian dollars do not become a common total merely because both are labelled “dollars.” Convert one amount using the specified exchange rate, and show the resulting currency.
A third error is to overlook the share-count scale. Dividing 26,400 thousand dollars by 8,800 thousand shares gives $3 per share, not $3,000 per share: both scale factors cancel. Conversely, if earnings are stated in dollars but shares in millions, the mismatch must be handled explicitly before interpreting the quotient.
Check Your Understanding
For each problem, check the unit labels before calculating.
- A hypothetical lender reports cash of $7.2 million and short-term obligations of $1,800 thousand. Calculate cash divided by short-term obligations. (Answer: 4.0)
- A hypothetical exporter has sales of 50 million euros and operating costs of 32 million euros. Calculate costs as a proportion of sales. Do the amounts need currency conversion? (Answer: 0.64, or 64%; no conversion is needed because both amounts are in euros and use the same scale.)
- A hypothetical fund lists investments of 6.0 million U.S. dollars and 2.0 million Canadian dollars. Use 1 U.S. dollar = 1.25 Canadian dollars to express total investments in Canadian dollars. (Answer: 9.5 million Canadian dollars)
- A hypothetical company reports net income of $15,750 thousand, preferred dividends of $750 thousand, and weighted-average common shares of 5,000 thousand. Calculate earnings per common share. (Answer: $3.00 per share)
- A hypothetical distributor reports annual sales of $45 million and average assets of $15,000 thousand. Calculate sales divided by average assets after aligning scales. (Answer: 3.0)