Understadion Ratio structure

CFA Level I FRA
#1

Can anyone help me understand this basic concept on Ratios:

“…since the ratio is less than one, the percentage change of the numerator is greater than the percentage change of the denominator, so the ratio will increase…” -this come from the below question

What would be the impact on a firm’s return on assets ratio (ROA) of the following independent transactions, assuming ROA is less than one?

Transaction #1 – A firm owned investment securities that were classified as available-for-sale and there was a recent decrease in the fair value of these securities.

Transaction #2 – A firm owned investment securities that were classified as trading securities and there was recent increase in the fair value of the securities.

Transaction #1 Transaction #2

A) Higher Higher B) Higher Lower C) Lower Higher

Your answer: B was incorrect. The correct answer was A) Higher Higher

Available-for-sale securities are reported on the balance sheet at fair value and any unrealized gains and losses bypass the income statement and are reported as an adjustment to equity. Thus, a decrease in fair value will result in a higher ROA ratio (lower assets). Trading securities are also reported on the balance sheet at fair value; however, the unrealized gains and losses are recognized in the income statement. Therefore, an increase in fair value will result in higher ROA. In this case, both the numerator and denominator are higher; however, since the ratio is less than one, the percentage change of the numerator is greater than the percentage change of the denominator, so the ratio will increase.

#2

Gekko11, I would always recommed doing a brief simulation. In an exam, just use your calculator to compute somthing like this:

Imagine a company has:

Assets = 100 (including some investment securities), and

Income (Return) = 25

and thus ROA of 25/100 = 0.25 which is less than 1.

If the investment securities are:

  1. classified as available-for-sale and their value decreases, e.g. by 5, the asset value will fall to 95 (100-5), but there will be no impact on income (seeing as AFS investments are revalued via equity and not income), so the adjusted ROA is 25/95 = 0.263 which is HIGHER than before

  2. classified as trading securities and their value increases, e.g. by 5. the asset value will go up to 105 (100 + 5), and there will be an equal impact on income (as trading securities are revalued via income), which will rise to 30 (25 + 5). This results in a new ROA of 30/105 = 0.286 which is HIGHER than before

In the exam, just run a simluation with any numbers that come to your head and you will get the correct result. I think this approach is better than learning the rules by heart.

#3

ratio < 1

take a fraction e.g. 39/100 = 39%

add the same number to the numerator and denominator

e.g. 49/110 (10 add to numerator and denominator)

49/11- = 44.5% -> ratio increased

now say same number was removed from numerator and denominator - e.g. 30/91 = 32.96% - ratio decreased