Question $14$

Consider the following two banks:

$$ Bank $1$ has assets composed solely of a $12-$year, $7$ percent coupon, $$1$ million loan with a $7$ percent yield to maturity. It is financed with a $12-$year, $5\mathrm{.}5$ percent coupon, $$1$ million CD with a $5\mathrm{.}5$ percent yield to maturity.

$$ Bank $2$ has assets composed solely of a $6-$year, $10$ percent, zero$-$coupon bond with a current value of $$564,473\mathrm{.}93$ and a maturity value of $$1,000,000.$ It is financed with a $12-$year, $7\mathrm{.}25$ percent coupon, $$1,000,000$ face value CD with a yield to maturity of $9$ percent.

All securities except the zero$-$coupon bond pay interest annually.

If interest rates rise by $1$ percent $(100$ basis points$),$ what is the difference in the value of the assets and liabilities of each bank?

Institution Initial Assets Initial Liabilities

Bank $1$ $$1,000,000$ $$1,000,000$

Bank $2$ $$564,473\mathrm{.}93$ Solve for this...

Asset Value Difference Bank $1$: $

Liability Value Difference Bank $1$: $

Asset Value Difference Bank $2$: $

Liability Value Difference Bank $2$: $