Question

Early the next day, the bank invests $\backslash (35$million of its excess reserves in commercial loans. Later that day, terrible news hits the mortgage markets, and mortgage rates jump to $13\%$, implying a present value of Oldhat’s current mortgage holdings of \)$99838$ per mortgage. Bank regulators force Oldhat to sell its mortgages to recognize the fair market value. What does Oldhat’s balance sheet look like? How do these events affect its capital position?

Short answer

Represent the table showing the Financial's balance sheet as follow:

Oldhat Financial
Assets		Liabilities
Reserves		Checkable deposits	$130,000,000
Required	$10,400,000	Bank Capital	$16,040,400
Excess	$ 3,600,000
Loans
Commercial	$75,000,000
Mortgage	$24,959,600
	$113,959,600		$113,959,600

Bank regulators need to inject an additional $ $2,436,360$to increase Financials' capital ratio to $10\%$

Step-by-step solution

Given Information that

The bank invests $\$35$million of its excess reserves in commercial loans. Mortgage rates jump to $13\%$, implying a present value of Oldhat’s current mortgage holdings of $$99838$per mortgage.

Explanation

Represents the table showing the Financial's balance sheet as follow

Oldhat Financial
Assets		Liabilities
Reserves		Checkable deposits	$\$130,000,000$
Required	$\$10,400,000$	Bank Capital	$\$16,040,400$
Excess	$\$3,600,000$
Loans
Commercial	$\$75,000,000$
Mortgage	$\$24,959,600$
	$\$113,959,600$		$\$113,959,600$

Explanation

Suppose regulators decide to provide the bank with $ 25 million in bank capital, while $ 30 million in deposits is withdrawn. This changes the balance sheet as follows:

Oldhat Financial
Assets		Liabilities
Reserves		Checkable deposits	$\$100,000,000$
Required	$\$10,400,000$	Bank Capital	$\$8,959,600$
Excess	$\$3,600,000$
Loans
Commercial	$\$75,000,000$
Mortgage	$\$24,959,600$
	$\$113,959,600$		$\$108,959,600$

Final Answer

Write the formula to calculate the capital ratio as follows:

$\text{Capital ratio}=\frac{\text{Bank capital}}{\text{Total assets}}$

To have a capital ratio of $10\%$, we can solve the equation as follows to find the amount of additional capital injection (x) that is required as follows:

$\begin{array}{rl}\frac{\mathrm{\$}8,959,600+x}{\mathrm{\$}113,959,600}& =0.10\\ \mathrm{\$}8,959,600+x& =\mathrm{\$}11,395,960\\ x& =\mathrm{\$}2,436,360\end{array}$

Bank regulators need to inject an additional $\$2,436,360$to increase Financials' capital ratio to$10\%$.