Equity valuation foundations

What an equity valuation is trying to estimate

A share price is the market's current transaction price. An intrinsic value estimate is an analyst's model-based view of the present value of expected benefits from owning the share. The two can differ because investors use different forecasts, required returns, information, and assumptions. A valuation is therefore conditional: it answers what the share is worth if the inputs and model make sense.

For CFA Level I, the central work is matching a model to the cash flows or comparison being described, using the right timing, and interpreting the result. A calculation is only useful after the candidate understands what is being valued. Dividends paid to equity holders, for example, are different from cash flows available to all capital providers.

Start with the constant-growth dividend model

The Gordon growth model is a constant-growth dividend discount model. It assumes dividends grow at a constant rate indefinitely, with the required return greater than that growth rate. Its formula is: value today = next period's expected dividend divided by required return minus expected growth.

Written as symbols, P0 = D1 / (r - g). P0 is the estimated value today, D1 is the dividend expected in the next period, r is the required return on equity, and g is the constant dividend growth rate. The denominator is a spread between two rates, not the required return alone.

Worked example: stable dividend growth

Suppose a company just paid a dividend of $1.80 per share. Dividends are expected to grow at 4% annually, and the required return is 10%. First find the next dividend: D1 = $1.80 x 1.04 = $1.872. Then calculate P0 = $1.872 / (0.10 - 0.04) = $1.872 / 0.06 = $31.20.

The result is an estimate, not a target guaranteed by the model. It says that under the stated perpetual growth and required return assumptions, the present value of the expected dividend stream is $31.20. If the stock trades for $28, the model suggests it is below that estimate; whether that is a good investment depends on whether the assumptions are credible and whether other risks have been considered.

The first dividend timing is a frequent error. The prompt says the company just paid $1.80, which is D0. The model uses D1, so grow it once. If the question instead states the dividend expected next year is $1.80, that amount is already D1 and should not be grown again.

The required return and growth spread drives value

In the example, the spread r - g is 6%. The denominator compresses when the expected growth rate rises or the required return falls. That raises estimated value. The reverse lowers value. This direction is intuitive: stronger expected dividends increase value, while a higher return demanded for risk reduces the present value of those dividends.

Hold the dividend and growth estimate constant, but raise the required return from 10% to 12%. The denominator becomes 12% - 4% = 8%, so estimated value becomes $1.872 / 0.08 = $23.40. A two-percentage-point change in the required return cuts the estimate from $31.20 to $23.40. The change is large because a perpetual stream is sensitive to its discount rate.

If instead the required return were 8% and growth stayed at 4%, the value would be $1.872 / 0.04 = $46.80. As the required return approaches the growth rate, the denominator becomes very small and the estimated value rises sharply. At or above growth, the constant-growth formula no longer produces a finite, meaningful value under its assumptions. Do not use a growth rate that equals or exceeds the required return.

Relate dividend yield, growth, and required return

Rearrange the Gordon equation by dividing both sides through by price: r = D1 / P0 + g. The required return is the expected dividend yield plus the expected growth rate under the model's assumptions. In the worked example, D1 / P0 = $1.872 / $31.20 = 6%, and growth is 4%, so the required return is 10%.

This relationship helps check a valuation. If an analyst claims a 4% dividend yield, 3% growth, and 12% required return for a stable growing company, those assumptions do not reconcile under the constant-growth model. Either the price, dividend, growth, or required return must differ. The relation is a model consistency check, not a promise that realized returns will equal 10%.

Worked example: a two-stage dividend forecast

A company may grow quickly for a few years before settling into a more sustainable rate. A two-stage dividend model handles that pattern by forecasting early dividends individually, calculating a terminal value when stable growth begins, and discounting each amount to today.

Assume the company just paid D0 = $2.00. Dividends grow 10% annually for three years, then 4% perpetually. The required return is 9%. The forecast dividends are D1 = $2.20, D2 = $2.42, and D3 = $2.662. Stable growth starts after Year 3, so calculate D4 = $2.662 x 1.04 = $2.76848.

At the end of Year 3, the terminal value is D4 / (r - g) = $2.76848 / (0.09 - 0.04) = about $55.37. That is a value at Year 3, not today. Discount the three dividends and terminal value to the present: $2.20/1.09 + $2.42/(1.09)^2 + ($2.662 + $55.37)/(1.09)^3. The estimated value is about $48.87 per share.

Two checks prevent common timing mistakes. Use D4 in the terminal value because it is the first dividend in the stable-growth stage, and discount the terminal value three years because it is measured at the end of Year 3. Using D3 in the numerator or treating the terminal value as a current value shifts the result.

Use a price-to-earnings multiple as a relative check

The price-to-earnings ratio compares a company's share price with earnings per share. A forward P/E uses expected future earnings per share; a trailing P/E uses earnings already reported for a past period. The denominator's timing must be clear before comparing ratios.

Suppose a company is expected to earn $4.25 per share next year. A reasonably comparable group of firms trades at a forward P/E of 15. A simple relative estimate is $4.25 x 15 = $63.75 per share. If the company trades at $55, the multiple comparison indicates a discount to that peer-implied figure.

The calculation does not prove that $63.75 is intrinsic value. The company may deserve a lower multiple because its earnings are riskier, its growth is slower, or its capital needs are higher. It may deserve a higher multiple if its prospects differ favorably, but that requires evidence. The peer multiple is a reference point, not an automatic answer.

A negative or very small earnings denominator makes P/E difficult to interpret. Cyclical earnings can also make a low multiple look attractive near a peak and expensive near a trough. Check what earnings represent and whether the comparison group uses similar accounting and business economics.

Why valuation methods can disagree

A dividend model values a forecast stream of distributions. A P/E comparison prices earnings relative to market expectations for a peer group. They can produce different estimates without either calculation being arithmetically wrong. One model may use a conservative long-run growth rate while the peer multiple embeds optimistic expectations.

When estimates disagree, inspect the inputs before averaging them. Are dividends expected to grow at the stated pace? Are peer earnings comparable? Does one method include a temporary earnings spike? Is the required return consistent with the company's risk? A blended number can disguise bad assumptions rather than resolve them.

Common calculation and interpretation errors

• Using D0 instead of D1 in the Gordon model, or growing D1 a second time.
• Subtracting growth from the dividend rather than from the required return.
• Entering 10 for a 10% rate in a formula that expects 0.10.
• Using a high perpetual growth rate that is not supportable or that approaches the required return.
• Discounting a terminal value from the wrong year.
• Treating a peer multiple as proof of fair value without checking the businesses and earnings measures.
• Calling a model estimate a certain future share price or realized return.

When to be cautious with dividend models

A dividend discount model is less useful when a company does not pay dividends, its payout policy is changing sharply, or near-term distributions are not representative of long-run capacity. A company can create value while reinvesting cash rather than distributing it. In those cases, an analyst may examine cash flows available to equity holders or a relative valuation approach, while still scrutinizing the assumptions.

A high-growth company also may not grow at one rate forever. That is why a multistage model separates a forecast period from a stable-growth period. The choice of when growth stabilizes is itself a judgment. Extending the high-growth period raises value; shortening it lowers value. The math can be exact while the forecast remains uncertain.

When a cash flow model uses equity cash flow

Dividends are one way a shareholder receives cash, but a company may retain cash or repurchase shares instead. A cash-flow-to-equity model focuses on cash available to equity holders after operating needs, investment, and debt cash flows. In a simple constant-growth illustration, if next year's cash flow available to equity is $9 million, the required return is 9%, and sustainable growth is 3%, estimated equity value is $9 million / (0.09 - 0.03) = $150 million. With 3 million equivalent shares, that is $50 per share.

The arithmetic resembles the dividend model, but the numerator is different. Do not insert total firm cash flow before debt payments into an equity model and then discount it at the required return on equity. A firm-wide cash flow requires a firm valuation framework and a discount rate that reflects all capital providers. The value must then be reconciled to equity.

A cash-flow estimate also depends on how capital expenditure, working capital, and borrowing are forecast. A small error in a forecast can persist through the explicit period and affect terminal value. Check what the cash-flow measure includes before interpreting the output as a share value.

Add a sensitivity table before treating a model output as precise

A valuation range communicates assumption risk better than a single number. Return to the stable dividend example: with D1 of $1.872, growth of 4%, and required return of 10%, value is $31.20. If required return is 9% while growth remains 4%, value is $37.44. If next year's dividend stays at $1.872 but long-run growth is 3%, value is about $26.74. Each change modifies one assumption, making its influence visible.

This is not a probability forecast. The cases simply show the model's sensitivity. An analyst should choose assumptions from evidence about the company, industry, and risk, then explain which factors could make the assumptions wrong. The purpose of sensitivity analysis is to reveal dependence, not to make a chosen value look more certain.

A reasonable valuation process therefore has three parts: select a method suited to the business, check the arithmetic and timing, and challenge assumptions with alternatives. The conclusion can be that a share appears inexpensive under one set of assumptions and fairly priced under another. That disagreement is information about uncertainty, not a reason to hide the range.

Valuation is most useful as a structured comparison between price and explicit assumptions. It makes the analyst say what must happen for a price to make sense. It does not remove uncertainty, guarantee a trading result, or replace analysis of the business and its risks.