Question

Suppose Levered Bank is funded with 1.6 % equity and 98.4 % debt. Its current market capitalization is ​$9.72 ​billion, and its​ market-to-book ratio is 1.1. Levered Bank earns a 4.23 % expected return on its assets​ (the loans it​ makes), and pays 3.6 % on its debt. New capital requirements will necessitate that Levered Bank increase its equity to 3.2 % of its capital structure. It will issue new equity and use the funds to retire existing debt. The interest rate on its debt is expected to remain at 3.6 %. a. What is Levered​ Bank's expected ROE with 1.6 % ​equity? b. Assuming perfect capital​ markets, what will Levered​ Bank's expected ROE be after it increases its equity to 3.2 %​? c. Consider the difference between Levered​ Bank's ROE and its cost of debt. How does this​ "premium" compare before and after the​ Bank's increase in​ leverage? d. Suppose the return on Levered​ Bank's assets has a volatility of 0.26 %. What is the volatility of Levered​ Bank's ROE before and after the increase in​ equity? e. Does the reduction in Levered​ Bank's ROE after the increase in equity reduce its attractiveness to​ shareholders? Explain.

Answer 1

Market-to-book ratio = Market Capitalization / Total Book Value

or, 1.1 = $9.72 billion / Total Book Value

or, Total Book Value = $9.72 billion / 1.1

or, Total Book Value = $8.836 billion

So, Total Assets = $8.836 billion

Return on Assets (ROA) = Net profit margin x Asset Turnover Ratio

= (Net Profit / Sales) x (Sales / Assets)

= Net Profit / Assets

So, ROA = Net Profit / Assets

or, 4.23 / 100 = Net Profit / $8.836 billion

So, Net Profit = (4.23 x $8.836 billion) / 100 = $0.374 billion

a. In order to calculate Levered Bank's expected ROE, we need the value of shareholders' equity because,

ROE = ROA x (Assets / Shareholders' Equity)

Now, Shareholders' Equity = Assets - Total Liabilities

or, Equity Capital + Net Profit = $8.836 billion - Total Liabilities

or, Equity Capital + Total Liabilities = $8.836 billion - $0.374 billion

or, Equity Capital + Total Liabilities = $8.462 billion

Therefore, Equity Capital = 1.6% of $8.462 billion = $0.135 billion

Debt Capital = 98.4% of $8.462 billion = $8.327 billion

So, Shareholders' Equity = $0.135 billion + $0.374 billion = $0.509 billion

ROE = ROA x (Assets / Shareholders' Equity)

= (Net Profit / Assets) x (Assets / Shareholders' Equity)

= Net Profit / Shareholders' Equity

= $0.374 billion / $0.509 billion

= 0.7348, expressed as a percentage, that is, 73.48%.

b. If the equity is increased to 3.2%, Equity Capital = 3.2% of $8.462 billion = $0.271 billion

Debt Capital = 96.8% of $8.462 billion = $8.191 billion

Therefore, shareholders' Equity = $0.271 billion + $0.374 billion = $0.645 billion

So, expected ROE after equity is increased to 3.2% is:

Net Profit / Shareholders' Equity = $0.374 billion / $0.645 billion = 0.5798, expressed as a percentage, that is, 57.98%.

c. Due to the reduction of debt because of new issue of equity, the amount of interest on debt has decreased. It will increase the amount of profit. At the same time, number of equity shares increased. Therefore, both these incidents taken together, has a significant impact on earnings per share.

d. The volatility of ROA is 0.26%. We assume that ROA increases by 0.26%. After the increase in equity by 26.71%, the ROE will decrease. If ROA decreases by 0.26%, the increase in equity remaining the same, ROE will decrease more.

[increase in equity = ($0.645 billion - $0.509 billion) / $0.509 billion = 26.71%]

e. ROE is used to measure the financial performance of a company. Here, the ROE reduced after increase in equity. This shows the capital invested by the shareholders has not been utilized effectively. So the decreased ROE might reduce the attractiveness to shareholders to invest in the bank.