Question 6.P.6: Washington Group holds total assets of $12 billion and equit...

Alternative Scenario a:

Suppose Washington Group finds its ROA climbing by 50 percent, with assets and equity capital
unchanged. What will happen to its ROE? Why?

R0A increases by 50%, with no change in assets or equity capital.

Therefore, the new ROA = 0.011 * 1.5 = 0.0165 or 1.65%.

New ROE = 1.65% * 10 = 16.50%

This represents a 50% increase in ROE. With no changes in assets or equity, the investors’ funds are more effectively utilized, generating additional income and making the bank more profitable.

Alternative Scenario b:

On the other hand, suppose the bank’s ROA drops by 50 percent. If total assets and equity capital hold their present positions, what change will occur in ROE?

ROA decreases by 50%, with no change in equity or assets.

Therefore, the new ROA = 0.011 * 0.5 = 0.0055 or 0.55%.

New ROE = 0.55% * 10 = 5.50%

This represents a 50% decrease in ROE. The bank’s management has been less efficient, in this case, in managing their lending and/or investing functions or their operating costs.

Alternative Scenario c:

If ROA at Washington Group remains fixed at 0.0076 but both total assets and equity double, how does ROE change? Why?

ROA = .0076 or .76%

Total assets double in size to $24 billion and equity capital doubles in size to $2.4 billion..

Therefore, the equity multiplier (i.e. total assets/equity capital) remains the same (E.M. = $24/$2.4 = 10). As a result, ROE changes from the original situation (i.e.), .76% * 10 = 7.6%).

This represents a decrease in ROE. The bank’s management has been less efficient, in this case, in managing their lending and/or investing functions or their operating costs.

Alternative Scenario d:

How would a decline in total assets and equity by half (with ROA still at 0.0076) affect the bank’s ROE?

This, of course, is just the reverse of scenario 3. Since the changes in both assets and equity capital are the same, the ratio of the two (i.e., the equity multiplier) remains constant. As a result, there is again no change in ROE.

E.M. = Total Assets/Equity Capital = $6/$0.6 = 10.

Therefore, ROE = .76% * 10 = 7.6%.