Problem
Metropolitan Bank has an obligation of $1,648,000 at the end of the second year and $1,795,000 at the end of the five years. It also has $3,000,000 to invest and can choose between a zero-coupon bond or a coupon bond. The coupon bond matures in five years, pays an annual coupon of $120,000 and has a balloon payment of $3,000,000. The zero-coupon bond has a balloon payment of approximately $3,650,000 at the end of the fifth year. The default-free yield on a one-year bond is 4%, and the annualized yield on a five-year bond is also 4%.
Assuming that this is only part of the bank's balance sheet, what is the present value of the bank's equity?
What will be the present value of the bank's equity if the central bank increases the overnight rate by 75 basis points?