Bank A has a leverage ratio of 10, while Bank B has a leverage ratio of 20. Similar losses on bank loans at the two banks cause the value of their assets to fall by 7 percent. Which bank shows a larger change in bank capital? Does either bank remain solvent? Explain.
Bank A has a leverage ratio of 10, which means that its assets are 10 times its capital. If the value of the assets falls by 7%, it implies the value of bank A's assets declines by 0.07 * 10 * bank A's capital = 0.7 * bank A's capital.
Bank B has a leverage ratio of 20, which means that its assets are 20 times its capital. If the value of the assets falls by 7%, it implies the value of bank B's assets declines by 0.07 * 20 * bank B's capital = 1.4 * bank B's capital.
Since 1.4 (Bank B) > 0.7 (Bank A), Bank B shows a larger change in bank capital.
To determine if either bank remains solvent, we need to see if their capital is still positive after the decline in the value of their assets.
For Bank A:
New Capital = Old Capital - Change in Capital
New Capital = Old Capital - 0.7 * Old Capital
New Capital = 0.3 * Old Capital
Since the new capital (0.3 * Old Capital) is still positive, Bank A remains solvent.
For Bank B:
New Capital = Old Capital - Change in Capital
New Capital = Old Capital - 1.4 * Old Capital
New Capital = - 0.4 * Old Capital
Since the new capital (-0.4 * Old Capital) is negative, Bank B becomes insolvent.
In conclusion, Bank B shows a larger change in bank capital, and it becomes insolvent, whereas Bank A remains solvent.
To determine which bank shows a larger change in bank capital, we need to calculate the change in bank capital for both Bank A and Bank B.
The change in bank capital can be calculated using the leverage ratio and the change in the value of assets.
For Bank A:
Change in bank capital = Leverage ratio * Change in assets
Change in bank capital = 10 * (-7%) = -0.7
For Bank B:
Change in bank capital = Leverage ratio * Change in assets
Change in bank capital = 20 * (-7%) = -1.4
From the calculations above, we can see that Bank B shows a larger change in bank capital compared to Bank A.
Now, to determine if either bank remains solvent, we need to consider whether their capital is positive or negative after the change.
For Bank A:
Initial bank capital was not provided in the question, so we cannot determine if it remains solvent based on the given information.
For Bank B:
If the initial bank capital of Bank B is positive, say $X, then after the change, the new bank capital would be X + (-1.4). If this value remains positive, Bank B remains solvent.
In summary, Bank B shows a larger change in bank capital compared to Bank A, but based on the given information, we cannot determine if either bank remains solvent without knowing their initial bank capital values.
To determine which bank shows a larger change in bank capital, we need to calculate the change in bank capital for each bank.
The leverage ratio is calculated as the ratio of total assets to bank capital. In this case, Bank A has a leverage ratio of 10, which means its total assets are 10 times its bank capital. Bank B, on the other hand, has a leverage ratio of 20, meaning its total assets are 20 times its bank capital.
If the value of the assets in both banks falls by 7 percent, we can calculate the change in bank capital as follows:
For Bank A:
Change in Bank Capital_A = (Change in Assets_A) / Leverage Ratio_A
Change in Bank Capital_A = (-7%) / 10 = -0.7%
For Bank B:
Change in Bank Capital_B = (Change in Assets_B) / Leverage Ratio_B
Change in Bank Capital_B = (-7%) / 20 = -0.35%
From the calculations, we can see that Bank A shows a larger change in bank capital compared to Bank B. Bank A has a change in bank capital of -0.7%, while Bank B has a change in bank capital of -0.35%.
To determine if either bank remains solvent, we need to look at their resulting bank capital after the change.
If the change in bank capital is negative, it means the bank's capital has decreased. In this scenario, both banks have a decrease in bank capital. However, to determine solvency, we need to compare the resulting bank capital to any regulatory requirements or capital adequacy ratios.
Without additional information about the specific regulatory requirements or capital adequacy ratios, we cannot definitively determine if either bank remains solvent. Typically, banks are required to maintain a certain capital ratio to ensure solvency. If the resulting bank capital after the change remains above the required ratio, the bank would generally be considered solvent. Conversely, if the resulting bank capital falls below the required ratio, it may raise concerns about solvency.
It is important to note that this analysis is a simplified explanation, and in practice, the determination of solvency involves more complex factors and considerations.