How to Value Stocks
15 Feb 2025
The basic assumption behind valuation by comparables is that similar companies should have similar financial characteristics. One very crude analysis is to consider the P/E ratios of similar companies and use that to estimate the stock price of the company in question. For example, suppose that we want to estimate the stock price of the Bank of America, and that the P/E ratios of similar banks are:
The average P/E ratio of these banks is 15.58. The latest quarterly report (Sep 2024) of Bank of America indicates an EPS of $0.82 over the last 3 months. Therefore, the estimated stock price of Bank of America is:
15.58 × 0.82 × 4 = $51.10
As of writing, the actual stock price of Bank of America is $47.01, or 8% lower than the estimated price, which we admit is not too bad for a crude analysis. A more sophisticated analysis would consider other financial ratios, such as the P/B ratio, or would put more weight on the P/E ratios of banks that better match the size and business model of Bank of America.
An alternative to valuation by comparables is to discount all future dividends of the company in question:
Stock price = Σn=1→∞ (Dividend / (1 + r)n)
where r is the discount rate and n is the number of years in the future. r is the cost of equity, i.e. the return that investors expect from similar investments. This formula is called the dividend discount model, and it is independent of the stock price of the company. The reason capital gains are ignored is because, in the long run, they are expected to be negligible compared to total dividend payouts. An alternative formula that takes into account capital gains is:
Stock price = Σn=1→H (Dividend / (1 + r)n) + (PH / (1 + r)H)
where PH is the expected stock price at year H.
The dividend discount model is more appropriate for income stocks, because dividend payouts are regular and predictable. We can model stocks that pay dividends that grow at a constant rate as a constant growth perpetuity:
Stock price = Div1 / (r - g)
where Div1 is the dividend at year 1, r is the discount rate, and g is the growth rate of the dividend. g is typically obtained from analysts' estimates or from the historical growth rate of the dividend. One estimate is to take the product of the retention ratio and the return on equity:
g = ROE × (1 - Dividend payout ratio)
Sometimes it is helpful to model stocks using multi-stage growth models, where the growth rate of earnings and dividends occurs in stages. For instance, a company may have a high growth rate in the first 5 years, before maturing to a lower growth rate in subsequent years.
Investors buy income stocks with the intent of receiving regular dividend payouts. Therefore, the dividend discount model is more appropriate for income stocks. Growth stocks, on the other hand, are bought with the intent of receiving capital gains. The price of growth stocks is often assumed to have a second component that represents the present value of growth opportunities (PVGO). PVGO is the net present value of all future investments that the company will make to grow its business (i.e. earnings capacity). We can estimate PVGO using the company's EPS, retention ratio and the return on equity.
For instance, the net present value of growth opportunities of a company at year 1 is:
Initial cash outlay for investment = -1 × EPS × retention ratio
Extra earnings in year 1 = Initial cash outlay × ROE
NPV1 = Initial cash outlay + (Extra earnings in year 1 / (1 + r))
If we assume that the company grows at a constant rate g, then we can model the PVGO component as a growing perpetuity:
PVGO = NPV1 / (r - g)
The stock price of the company is then:
P0 = Div1 / (r - g) + PVGO
The first component of the stock price represents the present value of the company with no-growth in its earning capacity. The second component represents the present value of all future investments having a positive NPV.
An alternative to evaluating stocks based on dividends is to use free cash flow. Free cash flow is the cash that a company generates from its operations after accounting for capital expenditures (i.e. spending on projects that will generate future cash flows). Free cash flow is useful when the company does not pay dividends, or pays dividends irregularly.