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When it comes to evaluating a company's stock price, one popular method is the Dividend Discount Model (DDM). This model is based on the premise that a stock is worth the sum of all its future dividend payments, discounted back to their present value. Essentially, it provides a way to value a company's stock based on the theory that its stock is worth the dividends it will generate in the future.

In its simplest form, the DDM requires two key inputs: the expected dividends per share and the required rate of return (or discount rate). The formula looks like this: \[ Market\text{ }Price\text{ }per\text{ }Share = \frac{Dividends\text{ }per\text{ }Share}{Required\text{ }Rate\text{ }of\text{ }Return} \]
When dividends are expected to grow at a constant rate into perpetuity, the model is often referred to as the Gordon Growth Model. For companies like Pacific Energy and U.S. Bluechips in the exercise, where earnings and thus dividends are expected to be constant, the DDM simplifies the valuation process significantly. This involves calculating the market price by dividing the annual dividends by the required rate of return, which the solution has depicted.

As a content improvement, it’s important to note that in real-world scenarios, dividend payments are not always constant and can grow over time. To adjust for growth, the DDM incorporates a growth variable, making it a bit more complex but more reflective of long-term investment horizons. However, for the purpose of the exercise, we've assumed a perpetuity formula, which is a simplified version suitable for educational illustration.

Earnings Per Share (EPS) is a key financial metric used by investors to measure a company's profitability relative to the number of shares outstanding. It's calculated by taking the company's total earnings and dividing it by the total number of shares. Here's the formula: \[ EPS = \frac{Total\text{ }Earnings}{Total\text{ }Number\text{ }of\text{ }Shares} \]
In the context of the PE ratio, EPS serves as the denominator. The higher the EPS, the more earnings there are available to be paid out as dividends or reinvested in the company. It's a quick way to check how much money a company makes for each share of its stock, and it's often used to compare the financial performance of companies within the same industry or sector.

It’s instrumental in calculating the Price-Earnings ratio, where a higher EPS indicates a more profitable company, and thus, potentially a more valuable investment, depending on the market’s perception. When Pacific Energy and U.S. Bluechips consider new projects that increase their earnings, it, in turn, could influence the EPS if the number of shares outstanding remains the same, which may or may not affect the PE ratio significantly, as seen in the provided exercise solution.

Rate of Return (RoR) is a comprehensive term that refers to the gain or loss on an investment over a specified period, expressed as a percentage of the investment's initial cost. It's an essential concept in finance because it allows investors to compare the efficiencies of different investments. The required rate of return, specifically, is the minimum annual percentage earned by an investment that will induce individuals or companies to put money into a particular security or project.

The RoR plays a crucial role in the Dividend Discount Model; it acts as the discount rate that brings the future dividend payments to present value terms. In our example, both Pacific Energy Company and U.S. Bluechips require a 14 percent rate of return on their investments. This means that investors expect a 14 percent return on their investment each year.

Understanding how to compute and interpret the RoR helps investors make informed decisions about the relative attractiveness of different securities. It’s essential for the textbook exercise, as it forms the basis for assessing company value through the DDM, as well as understanding the implications of changes in earnings and dividends on the PE ratio.