Question 7.5: Small Fry, Inc., has just invented a potato chip that looks ...
Small Fry, Inc., has just invented a potato chip that looks and tastes like a french fry. Given the phenomenal market response to this product, Small Fry is reinvesting all of its earnings to expand its operations. Earnings were $2 per share this past year and are expected to grow at a rate of 20% per year until the end of year 4. At that point, other companies are likely to bring out competing products. Analysts project that at the end of year 4, Small Fry will cut its investment and begin paying 60% of its earnings as dividends. Its growth will also slow to a long-run rate of 4%. If Small Fry’s equity cost of capital is 8%, what is the value of a share today?
Plan
We can use Small Fry’s projected earnings growth rate and payout rate to forecast its future earnings and dividends. After year 4, Small Fry’s dividends will grow at a constant 4%, so we can use the constant dividend growth model (Eq. 7.13) to value all dividends after that point. Finally, we can pull everything together with the dividend-discount model (Eq. 7.4).
P_{N}=\frac{Div_{N+1}}{r_{E}-g} (7.13)
P_{0}=\frac{Div_{1}}{1+r_{E}}+\frac{Div_{2}}{\left(1+r_{E}\right)^{2} } +…+\frac{Div_{N}}{\left(1+r_{E}\right)^{N} }+\frac{P_{N}}{\left(1+r_{E}\right)^{N} } (7.4)
Execute
The following spreadsheet projects Small Fry’s earnings and dividends:
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | |
| Earnings | ||||||||
| 1 EPS Growth Rate (versus prior year) | 20% | 20% | 20% | 20% | 4% | 4% | ||
| 2 EPS | $2.00 | $2.40 | $2.88 | $3.46 | $4.15 | $4.31 | $4.49 | |
| Dividends | ||||||||
| 3 Dividend Payout Rate | 0% | 0% | 0% | 60% | 60% | 60% | ||
| 4 Div | $__ | $__ | $__ | $2.49 | $2.59 | $2.69 | ||
Starting from $2.00 in year 0, EPS grows by 20% per year until year 4, after which growth slows to 4%.Small Fry’s dividend payout rate is zero until year 4, when competition reduces its investment opportunities and its payout rate rises to 60%. Multiplying EPS by the dividend payout ratio, we project Small Fry’s future dividends in line 4.
After year 4, Small Fry’s dividends will grow at the constant expected long-run rate of 4% per year. Thus, we can use the constant dividend growth model to project Small Fry’s share price at the end of year 3. Given its equity cost of capital of 8%,
P_{3}=\frac{Div_{4}}{r_{E}-g} =\frac{\$2.49}{0.08-0.04} =\$62.25We then apply the dividend-discount model (Eq. 7.4) with this terminal value:
P_{0}=\frac{Div_{1}}{1+r_{E}}+\frac{Div_{2}}{\left(1+r_{E}\right)^{2} } +\frac{Div_{3}}{\left(1+r_{E}\right)^{3} }+\frac{P_{3}}{\left(1+r_{E}\right)^{3} }=\frac{\$62.25}{\left(1.08\right)^{3} } =\$49.42Evaluate
The dividend-discount model is flexible enough to handle any forecasted pattern of dividends. Here, the dividends were zero for several years and then settled into a constant growth rate, allowing us to use the constant dividend growth model as a shortcut.