MT217 Unit 7 Stock Valuation Exercise Example

Four Ways to Price a Propane Distributor's Shares: A Unit 7 Stock Valuation Exercise

[Student Name]

Purdue University Global

MT217: Finance

Unit 7 Stock Valuation Exercise

[Instructor Name]

[Date]

Hearthside Propane and every figure are composite and illustrative; the sources cited are real.

The Company

Hearthside Propane is a composite distributor that delivers propane to about [140,000] homes and farms across the upper Midwest. Its business is steady, since customers heat with propane every winter, but growth is slow because rural populations are flat. Weather moves results from year to year: a mild winter can cut gallons delivered by a tenth, while a cold one lifts them, so the company keeps its dividend increases modest to protect the payout in warm years. That record of small, regular increases is what makes a dividend model sensible here. It has preferred shares and common shares outstanding. Investors require a 7.5 percent return on the preferred and 9.0 percent on the common.

Problem 1: The Preferred Stock

Each preferred share pays a fixed [$4.50] dividend every year with no maturity date. A payment that continues forever is a perpetuity, and its value is the payment divided by the required return. At 7.5 percent, 4.50 divided by 0.075 gives [$60.00] a share.

What it means: if required returns on similar preferred shares rose to 9 percent, the value would fall to [$50.00], a drop of about 17 percent, because the dividend never changes. Preferred stock behaves much like a very long bond. Preferred holders are paid before common holders but have no claim on growth, so the share's value depends almost entirely on what investors require.

Problem 2: Constant Growth

Hearthside paid a common dividend of [$1.84] last year and has raised it about 3.5 percent a year, in line with modest price increases and steady customer counts. Under the constant growth model associated with Gordon (1959), Hearthside's share is worth the coming year's dividend over the spread between 9.0 and 3.5 percent. Next year's dividend is 1.84 times 1.035, or [$1.9044], and dividing by 0.09 minus 0.035, or 0.055, gives [$34.63].

What it means: the model treats the dividend stream as rising forever at the same rate, which suits a mature company like Hearthside. The result is very sensitive to the gap between the two rates; if growth were 4.0 percent instead of 3.5, the value would rise to about [$38.27].

Problem 3: A Faster Growth Period

Suppose Hearthside buys two smaller distributors, lifting dividends 10 percent a year for three years before growth settles back to 3.5 percent. The dividends become [$2.0240] in year one, [$2.2264] in year two and [$2.4490] in year three. From year four on, ordinary growth resumes, so the year-three price comes from the year-four dividend, 2.4490 times 1.035, spread over the same 0.055, which gives [$46.09].

Discounting each year's dividend and the year-three price back at 9 percent gives a present value of about [$1.857], [$1.874] and [$1.891] for the three dividends, and [$35.59] for the year-three price, a total of [$41.21].

What it means: three years of faster growth add about [$6.58] a share, nearly 19 percent above the constant growth value. Most of that comes from the higher base the faster growth leaves for every year after it, not from the three dividends themselves.

Problem 4: The Return the Market Implies

Hearthside's common stock trades at [$36.50]. Turning the model around shows what buyers at that price expect to earn: the dividend yield on the coming payment plus 3.5 points of growth. The dividend yield is 1.9044 divided by 36.50, about 5.22 percent, and adding 3.5 percent growth gives about 8.72 percent.

What it means: at [$36.50] the market expects about 8.7 percent, below the 9.0 percent required return used above. Either investors see Hearthside as slightly less risky than the 9.0 percent assumes, or they expect a little more growth than 3.5 percent, perhaps from the acquisitions in Problem 3. Analysts covering Hearthside would test this by asking management how much of the acquisition plan is already agreed. The price sits between the constant growth value of [$34.63] and the faster growth value of [$41.21], which suggests the market gives some weight to the acquisition plan.

The market price is a vote on which growth story investors believe, and it lands between the two.

Limits of the Models

Brigham and Houston (2019) caution that dividend discount models work best for stable companies that pay regular dividends, and poorly for firms that pay little or none. Hearthside fits the first group well. Even so, the results depend heavily on two inputs that cannot be observed directly: the required return and the long-run growth rate. A sensible check is to compare the model's value with how the market prices similar propane and heating oil distributors, using their price to earnings or dividend yields. Fama and French (2004) showed that the most common way of estimating required returns, the capital asset pricing model, has weak empirical support, so Hearthside's 9.0 percent hurdle is a judgment an analyst could reasonably set a point higher or lower.

References

Brigham, E. F., & Houston, J. F. (2019). Fundamentals of financial management (15th ed.). Cengage.

Fama, E. F., & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25-46. https://doi.org/10.1257/0895330042162430

Gordon, M. J. (1959). Dividends, earnings, and stock prices. The Review of Economics and Statistics, 41(2), 99-105. https://doi.org/10.2307/1927792