# Stock share price valuation

## Stock valuation

Stock valuation is a fundamental tenet of finance that holds that the value of a security is determined by the present value of its future cash flows. As a result, common stock valuation tries at the difficult task of forecasting the future. Consider that the average dividend yield on large-cap stocks is around 2%. This implies that the present value of dividends payable over the next ten years accounts for only a small portion of the stock price. As a result, the majority of the value of a typical stock is derived from dividends that will be paid more than ten years from now.

### Absolute Valuation

Absolute stock valuation models seek to determine an investment’s intrinsic or “true” value-based solely on fundamentals. Looking at fundamentals simply means focusing solely on a single company’s dividends, cash flow, and growth rate—without regard for any other companies. This category includes valuation models such as the dividend discount model, discounted cash flow model, residual income model, and asset-based model.

### Relative Stock Valuation

Relative valuation models, on the other hand, work by comparing the company under consideration to other similar companies. These methods involve calculating multiples and ratios, such as the price-to-earnings (P/E) ratio, and comparing them to similar companies’ multiples. For example, if a company’s P/E ratio is lower than that of a comparable company, the original company may be considered undervalued. The relative valuation model is typically much easier and faster to calculate than the absolute valuation model, which is why many investors and analysts start their analysis with this model.

We will, however, concentrate on the various absolute valuation models, such as “The Dividend Discount Model,” “Constant Dividend Growth RateModel,” “Constant Perpetual Growth,” and “Two-stageDividend Growth Model.”

### The Dividend Discount Model

A fundamental financial principle states that the economic value of a security is properly measured by the sum of its future cash flows, where the cash flows are adjusted for risk and the time value of money. Assume, for example, that risky security will pay \$100 or \$200 with equal probability one year from now. The expected future payoff is \$150 = (\$100 + \$200) / 2, and the security’s the current value is the \$150 discounted for a one-year waiting period. If the appropriate discount rate is, say, 5%, the present value of the expected future cash flow is \$150 / 1.05 = \$142.86. If the appropriate discount rate is 15%, the present value is \$150 / 1.15 = \$130.43. As this example shows, the selection of a discount rate can have a significant impact on an assessment of security value.

Assume the company pays a dividend at the end of each year. Let D(t) represent a dividend payable t years from now, and V (0) represent the present value of the future dividend stream. Let k also represent the appropriate risk-adjusted discount rate. The present value of a share of this company’s stock is calculated using the dividend discount model as the sum of discounted future dividends:

V (0) = \$100 / (1.15) + \$100 /(1.15) 2 + \$100 /(1.15) = \$228.32

### Constant Dividend Growth Rate Model

The dividend discount model is greatly simplified for many applications by assuming that dividends will grow at a constant rate. This is referred to as a constant growth rate model. If g represents a constant growth rate, then successive annual dividends are written as D(t+1) = D(t)(1+g).

Assume that the next dividend is D (1) = \$100 and the dividend growth rate is g = 10%. This rate of growth results in a second annual dividend of D (2) = \$100 1.10 = \$110 and a third annual dividend of D (3) = \$100 1.10 1.10 = \$100 (1.10)2 = \$121. If the discount rate is k = 12%, the present value of these three consecutive dividend payments is equal to the sum of their individual present values:

V (0) = \$100 / (1.12) + \$110 /(1.12) 2 + \$121 / (1.12) 3 = \$263.10

Constant Perpetual Growth

A particularly simple form of the dividend discount model occurs when a company pays dividends that grow at a constant rate g in perpetuity. This is known as the constant perpetual growth model. The following formula is used to calculate present values in the constant perpetual growth model:

It is important to note that the constant perpetual growth model requires that the growth rate be strictly less than the discount rate, i.e., g k. If this were not true, the share value appears to be negative. In this case, the formula is simply not valid. The reason for this is that a perpetual dividend growth rate greater than a discount rate implies an infinite value because the dividends’ present value grows and grows. Because no security can have infinite value, requiring that g k simply makes good economic sense. Assume the growth rate is g = 4%, the discount rate is k = 9%, and the current dividend is D (0) = \$10 to illustrate the constant perpetual growth model. In this case, a straightforward calculation yield,

V (0) = \$10 (1.04) / .09 – .04 = \$208

### Sustainable Growth Rate

When using the constant perpetual growth model, an estimate of g, the dividend growth rate, is required. We discussed two approaches in previous examples: (1) using the company’s historical average growth rate, or (2) using the industry median or average growth rate. We now describe a third method, known as the sustainable growth rate, which involves estimating g using a company’s earnings.

Sustainable growth rate = ROE × Retention ratio = ROE × (1 – Payout ratio)

Return on equity is a common accounting-based performance measure that is calculated by dividing a company’s net income by its stockholders’ equity:

Return on equity (ROE) = Net income / Equity

A two-stage Dividend Growth Model

For example, consider the term “valuing.” ABC is a Dow Jones Industrial Average stock that trades on the New York Stock Exchange. ABC’s previous 5-year growth rate was 19.6 percent in mid-2020, and analysts predicted a 13.2 percent long-term growth rate. Assume ABC grows at a 19.6 percent annual rate for the next 5 years, then at a 13.2 percent annual rate after that. What is the value of ABC if we assume a 14.5 percent discount rate? ABC’s dividend for 2020 was \$0.92.

When all of the relevant numbers are entered into a two-stage present value calculation, the following results are obtained:

This present value estimate is slightly higher than ABC’s midyear 2020 stock price of \$80, implying that ABC is undervalued or that these growth rate estimates are overly optimistic.

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