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Brief Principles of Macroeconomics...

8th Edition
N. Gregory Mankiw
ISBN: 9781337091985

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BuyFindarrow_forward

Brief Principles of Macroeconomics...

8th Edition
N. Gregory Mankiw
ISBN: 9781337091985
Textbook Problem

A bank has capital of $200 and a leverage ratio of 5. If the value of the bank’s assets declines by 10 percent, then its capital will be reduced to

a. $100.

b. $150.

c. $180.

d. $185.

To determine

The leverage ratio and the asset of the bank.

Explanation

The leverage ratio is the ratio of the bank's total assets to the total capital of the bank. It is given that the leverage ratio is 5. When the total assets of the bank decline by a given percentage, it will have the leverage ratio to impact the value of the capital of the bank multiple times. That is, the value of the capital of the bank declines by the percentage decline multiplied with the leverage ratio.

It is given that the decline in the value of the bank's assets is by 10 percent and the leverage ratio of the bank is 5. It is also given that the bank has a capital of $200. Thus, the decline in the capital of the bank can be calculated by multiplying the leverage ratio with the percentage decline as follows:

Decline in the total capital=Leverage ratio×percentage decline in asset=5×10=50

Thus, there will be 50 percent decline in the total capital of the bank, which is equal to $100

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