Problem 2
By calculating some ratios based on the average of opening and closing balances, we make the implicit assumption that changes in these accounts occurred uniformly throughout the year. Sometimes, however, the actual change occurs unevenly, perhaps due to an acquisition. In such cases, ratios based on averages will be distorted. Discuss how you would calculate the return on assets ratio if the growth in assets occurred: (i) At the beginning of the year (ii) At the end of the first quarter (iii) At the end of the second quarter (iv) At the end of the fourth quarter
Answers:

Since the assumption in using average of opening and closing balance is that changes occurs evenly throughout the year, our goal is to minimize the impact of uneven distribution of asset growth;

At the beginning of the year:

Use the usual computation average of beginning and ending assets in the denominator or,

Use the average of end of year and end of first quarter assets in denominator.
Example:

Given

Since the increase in Assets is in the beginning of the year, we will assume that these assets will be carried though to all of the year’s balances. But assuming that the beginning balance is way too different compare to the ending balances of each quarter. Use the below computation;

New given:

This way, you have eliminated the effect of the beginning inventories and considered the normal asset level thought the year.

At the end of the first quarter increase:

Use weighted average: .25 x opening assets + .75 closing assets; this matches the numerator that reflects a return on the additional assets for 3/4 of the year. Alternatively, use end of first quarter assets.

Given:

In giving the beginning balance 25% of average assets, you have given more weight to the inventory level of assets carried at most time of the year (75%).

Here