A bank has book value of $5 million in liquid assets and $95 million in nonliquid assets. Large depositors unexpectedly withdraw $9.5 million in deposits. To cover the withdrawals the bank sells all of its liquid assets at book value. To raise the additional funds needed the bank sells the necessary amount of nonliquid assets at 80 cents per dollar of book value. As a result, the bank's equity will _____________.

Question

Quizplus · Accepted Answer

The bank initially had $100 million in assets ($5 million in liquid assets + $95 million in nonliquid assets). After the withdrawal of $9.5 million in deposits, the bank sold all of its $5 million in liquid assets at book value to cover the withdrawals. This leaves the bank with $90.5 million in assets ($95 million in nonliquid assets - $4.5 million from selling liquid assets). To raise the additional $4.5 million needed to cover the withdrawal, the bank sells nonliquid assets at 80 cents per dollar of book value, yielding $3.6 million ($4.5 million x 0.8 = $3.6 million). This means that the bank's equity, which was originally $5 million, is now reduced by the total amount needed to cover the withdrawal, which is $9.5 million minus the $5 million in liquid assets sold, plus the $3.6 million received from selling nonliquid assets, or a total reduction of $1.9 million. Therefore, the bank's equity falls by $1.9 million, leaving it with $3.1 million in equity ($5 million original equity - $1.9 million reduction).

A Bank Has Book Value of $5 Million in Liquid