Your bank account pays an interest rate of 8 percent. You are considering buying a share of stock in XYZ Corporation for $$ 110 .\( After \)1,2,\( and 3 years, it will pay a dividend of \)85 .\( You expect to sell the stock after 3 years for $$ 120 .\) Is XYZ a good investment? Support your answer with calculations.

Investment analysis is a technique that helps an investor determine whether an investment is worth taking considering the current costs and future revenues. It involves evaluating various financial factors, such as the rate of return, risk level, and the time horizon of the investment. In our example, to analyze the merits of purchasing XYZ Corporation's stock, we must consider not only the upfront cost but also the present value of future cash flows the stock will provide. This includes dividends and the potential sale price of the stock. If the total present value of the future cash flows is greater than the cost to buy the stock, it indicates a potentially profitable investment.

For a comprehensive investment analysis, other factors like market conditions, the company's financial health, and investors' own financial goals should also be considered. However, our focus here is on the quantitative aspect of valuation through present value calculations.

The time value of money is a financial concept that underlines the idea that a dollar today is worth more than a dollar in the future. This is due to the potential earning capacity the money could have if invested. Therefore, future cash flows must be discounted to reflect their value in today's terms. This allows for a fair comparison between the money spent today and the money received in the future.

When calculating present value, as demonstrated in the XYZ Corporation stock evaluation, the dividends and future sale value are discounted back to the present using a discount rate, which is typically the interest rate. In our example, the 8% interest rate is used to discount future dividends and sale price, allowing us to understand what those future cash flows would be worth at present, considering the opportunity cost of the investment.

Dividend discounting is a method of valuing a company's stock based on the premise that its value is equal to the present value of all future dividends it is expected to provide. Investors anticipate these dividends as a return on their investment for holding the company's stock.

In our example, XYZ Corporation is expected to pay a dividend of $85 at the end of each year for three years. To value these payments correctly, each expected dividend is discounted back to its present value using the formula: \[\begin{equation}\text{PV} = \frac{D}{(1+r)^t}\end{equation}\]where \(D\) is the dividend payment, \(r\) is the discount rate (interest rate), and \(t\) is the time in years until the dividend is received. By discounting each dividend, we calculate their worth in current dollars, which enables us to understand the part of the stock's value that comes from future dividends.

Discounted cash flows (DCF) is a valuation method used to estimate the value of an investment based on its expected future cash flows. The principle behind DCF is to calculate the present value of each cash flow that the investment is anticipated to generate, which could be dividends, interest payments, or even the final sale value of an asset.

In the step-by-step solution for XYZ Corporation, the DCF method is applied by first discounting each annual dividend and then the anticipated sale price of the stock after three years. By summing these discounted values, we attain the total present value of the investment's cash flows. An investment is typically seen as attractive if the total present value of the cash flows exceeds the initial investment cost. This approach is fundamental in various financial decisions, from choosing stocks to making capital budgeting decisions for large projects.