FIN 3010 Module 3 Stock Valuation Problems Example

Valuing a Water Utility's Common Stock: Required Return, Dividend Growth, P/E and Market Efficiency

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Bachelor of Science in Business Administration, Thomas Edison State University

FIN-3010: Principles of Finance

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Month Day, Year

Valuing a Water Utility's Common Stock: Required Return, Dividend Growth, P/E and Market Efficiency

The problems below value the common stock of Delaware and Raritan Water Company, a composite investor-owned water utility serving central New Jersey, whose regulated business produces steady earnings and dividends. The company paid a dividend of $2.40 per share last year, earns $3.10 per share and has a beta of 0.65. The risk-free rate is 4.2% and the expected market risk premium is 5.5%. Each problem shows the formula and the work (Mayo & Lavelle, 2024).

Problem 1: Required Return From the CAPM

The capital asset pricing model sets the return investors should require given the stock's systematic risk.

A beta below one means the stock tends to move less than the market, so investors accept a return below the market's expected 9.7%.

Problem 2: Constant Growth Dividend Model

Analysts expect dividends to grow 3.5% a year indefinitely, roughly in line with allowed rate increases and customer growth.

The model is sensitive to its inputs. Raising the assumed market risk premium by one point, to 6.5%, the required return would be 8.43% and the value would fall to about $50.44, a 13% drop from a one-point change in one assumption.

Problem 3: Price-to-Earnings Cross-Check

Similar water utilities trade at about 19 times earnings.

The holding period return can be split into its two parts: a dividend yield of $2.40 / $52.00, or 4.6%, and a capital gain of $4.75 / $52.00, or 9.1%. For a utility, the dividend usually supplies a large share of the return, so a year with a 9% price gain is unusually strong.

The relative valuation is close to the dividend model's $58.11, which adds confidence that a value near $58 to $59 is reasonable.

Problem 4: Holding Period Return

An investor bought shares a year ago at $52.00, received the $2.40 dividend and now sees a price of $56.75.

Problem 5: Growth Implied by the Market Price

If the stock trades at $61.00, what constant growth rate is the market assuming, given the 7.78% required return?

At $61 the market is pricing in slightly faster growth than the analysts' 3.5%. Whether that is optimistic depends on future rate cases, which regulators decide.

Models, Markets and Their Limits

Two strands of research qualify these calculations. Fama (1970) reviewed tests of whether stock prices fully reflect available information and concluded that the evidence was broadly consistent with efficient markets in their weak and semi-strong forms, meaning that past prices and public information are already reflected in prices. If so, the gap between a model value of $58.11 and a market price of $61.00 more likely reflects differences in assumptions than a bargain or an overpricing that an investor can exploit. Later work challenged the CAPM used in Problem 1. Fama and French (1992) found that, for U.S. stocks over several decades, beta did little to explain differences in average returns once firm size and book-to-market ratios were considered. The CAPM remains a standard teaching and practice tool, but its required return should be treated as an estimate, and valuations should be checked with more than one method, as Problem 3 does.

References

Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417. https://doi.org/10.2307/2325486

Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. The Journal of Finance, 47(2), 427-465. https://doi.org/10.1111/j.1540-6261.1992.tb04398.x

Mayo, H. B., & Lavelle, M. (2024). Basic finance: An introduction to financial institutions, investments, and management (13th ed.). Cengage Learning.