A bank has $200 reserves, $800 loans, $400 securities, $1200 deposits, and $100 debt.
a) Calculate the bank's capital.
b) Calculate the bank's leverage ratio.
c) Suppose there is a stock market boom, so that the bank's assets increase by 2 percent. What is the percentage change in the bank's capital? What is the change in the bank's capital in dollars?
d) Suppose that, instead of stock market boom, some borrowers default on their debt so that the bank's assets decrease by 2 percent. How much is now the bank's capital?
My answers:
a.) Capital = assets - liabilities = $1400-$1300 = $100
b.) leverage ratio= assets/debt = 1400/100 = 14
I dont understand c and d, please help super urgent
c) To calculate the percentage change in the bank's capital due to a stock market boom, we need to determine the new capital and then compare it to the original capital.
First, let's calculate the new capital after the stock market boom. Since the assets increase by 2 percent, we need to find 2 percent of the total assets and add that to the original capital.
New capital = Original capital + (2% of total assets)
Total assets = reserves + loans + securities = $200 + $800 + $400 = $1,400
2% of total assets = 0.02 * $1,400 = $28
New capital = $100 + $28 = $128
To calculate the percentage change in capital, we use the formula:
Percentage change = (New capital - Original capital) / Original capital * 100
Percentage change = ($128 - $100) / $100 * 100 = 28%
So, the percentage change in the bank's capital due to a stock market boom is 28%.
To calculate the change in the bank's capital in dollars, we simply subtract the original capital from the new capital:
Change in capital = New capital - Original capital
Change in capital = $128 - $100 = $28
So, the change in the bank's capital in dollars due to a stock market boom is $28.
d) To calculate the new capital after some borrowers default on their debt and the bank's assets decrease by 2 percent, we need to determine the new total assets and then subtract liabilities from it.
First, let's calculate the new total assets after the decrease. Since the assets decrease by 2 percent, we need to find 2 percent of the total assets and subtract that from the original total assets.
New total assets = Original total assets - (2% of original total assets)
2% of original total assets = 0.02 * $1,400 = $28
New total assets = $1,400 - $28 = $1,372
Next, let's calculate the new capital:
New capital = New total assets - liabilities
Liabilities = debt = $100
New capital = $1,372 - $100 = $1,272
So, the bank's capital after some borrowers default on their debt and the bank's assets decrease by 2 percent is $1,272.
Sure, let's break down the calculations for parts c and d step-by-step.
c) In this scenario, the bank's assets increase by 2 percent. We need to calculate the percentage change in the bank's capital and the change in the bank's capital in dollars.
Step 1: Calculate the new value of the bank's assets:
Increase in assets = 2% of total assets = 2% of $1400 = $28
New assets = Total assets + Increase in assets = $1400 + $28 = $1428
Step 2: Calculate the new value of the bank's capital:
New capital = New assets - Liabilities = $1428 - $1300 = $128
Percentage change in capital = (New capital - Original capital) / Original capital * 100
= ($128 - $100) / $100 * 100
= 28%
Change in capital in dollars = New capital - Original capital
= $128 - $100
= $28
Therefore, the percentage change in the bank's capital is 28%, and the change in the bank's capital in dollars is $28.
d) In this scenario, the bank's assets decrease by 2 percent. We need to calculate the new value of the bank's capital.
Step 1: Calculate the decrease in the bank's assets:
Decrease in assets = 2% of total assets = 2% of $1400 = $28
New assets = Total assets - Decrease in assets = $1400 - $28 = $1372
Step 2: Calculate the new value of the bank's capital:
New capital = New assets - Liabilities = $1372 - $1300 = $72
Therefore, the new value of the bank's capital is $72.