Nick contends that a share repurchase will increase the company’s ROA, ROE, and P/E ratio. Do you agree? How will a share repurchase affect the value of the firm?

A share repurchase, also known as a stock buyback, is when a company uses its own cash or borrowing to repurchase its own shares from its shareholders. Let's break down the effects of a share repurchase on financial ratios and the value of a firm:

1. Return on Assets (ROA): ROA is calculated by dividing net income by total assets. A share repurchase reduces the number of outstanding shares, which in turn reduces the equity portion of the balance sheet without affecting net income. As a result, the company's total assets become larger in proportion to the reduced equity, leading to an increase in ROA.

2. Return on Equity (ROE): ROE is calculated by dividing net income by shareholders' equity. Similar to ROA, a share repurchase reduces the equity portion of the balance sheet while keeping net income unchanged. Therefore, the decrease in equity will cause the ROE to increase, as the net income is divided by a smaller equity base.

3. Price-Earnings Ratio (P/E ratio): The P/E ratio is a measure of a company's valuation, comparing its stock price to its earnings per share. When a company repurchases shares, the number of outstanding shares decreases, which in turn reduces the denominator (earnings per share) in the P/E ratio calculation. As a result, the P/E ratio tends to increase, making the stock appear more attractively priced to investors.

Regarding the effect of a share repurchase on the value of the firm, it can be a bit more nuanced. In the short term, a share repurchase may increase the value of the firm by boosting the stock price and signaling confidence from management. However, in the long run, the value of a firm is based on its ability to generate cash flows and create value for shareholders. A share repurchase does not directly impact a company's operations, so its impact on the firm's intrinsic value might be limited.

It's important to note that the impact of a share repurchase on financial ratios and firm value can vary depending on the specific circumstances and factors at play, such as the company's financial position, market conditions, and management's intentions. Therefore, it's essential to thoroughly analyze the company's financials and overall strategy before assessing the effects of a share repurchase.