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 covers $5 million of the withdrawals by selling all its liquid assets at book value. The remaining $4.5 million is covered by selling nonliquid assets. Since nonliquid assets are sold at 80 cents per dollar, the bank needs to sell $4.5 million / 0.8 = $5.625 million in book value of nonliquid assets. The loss on this sale is $5.625 million - $4.5 million = $1.125 million. The total equity reduction is the sum of the liquid assets sold ($5 million) and the loss on the sale of nonliquid assets ($1.125 million), totaling $6.125 million. However, since the question asks how much the bank's equity will fall and not the final equity value, the correct calculation should focus on the loss incurred from selling nonliquid assets at a discount. The initial mistake in calculation led to an incorrect explanation. The correct approach is to calculate the loss directly related to selling nonliquid assets at a discount: $4.5 million needed - $3.6 million raised (90% of $4.5 million) = $0.9 million loss, in addition to the $2.7 million loss from selling at 80% value, not accounting for the initial $5 million liquid assets used. This discrepancy indicates a need to reassess the calculation focusing on the direct impact of the discount on nonliquid assets on the bank's equity.

A Bank Has Book Value of $5 Million in Liquid