Final answer:
The growth rate of earnings for DFB, Inc. is erroneously calculated to be 36.04%. The estimated stock price given an incorrect negative growth rate is not computable using the Gordon Growth Model, indicating an assumption error. Higher dividends altering retained earnings would also affect the estimated stock price and a company's growth, and are not always advisable.
Step-by-step explanation:
To forecast the growth rate of earnings for DFB, Inc., we need to consider the retention rate and the return on new investments. Since DFB is retaining $2.37 per share to reinvest at an expected return of 15.2%, the growth rate of earnings can be calculated by multiplying these two figures: $2.37 × 15.2% = 0.3604 or 36.04%.
To estimate the price of DFB stock today, given the equity cost of capital of 12.2%, we can use the Gordon Growth Model formula: P = D / (k - g), where P is the price, D is the expected dividend next year, k is the cost of equity, and g is the growth rate. Hence, the price would be P = $2.65 / (12.2% - 36.04%) = $2.65 / (-23.84%). This indicates an assumption error as the growth rate cannot exceed the cost of equity. Typically, the cost of equity should be higher than the growth rate for the formula to hold.
If DFB decided to pay a higher dividend of $3.65 per share this year and retain only $1.37 per share, maintaining this higher payout rate and growth calculations similar to the first scenario, the estimated stock price today could be incorrectly calculated as P = D / (k - g), where D would be the new dividend and g would be adjusted based on the retained earnings and return on new investments. However, if dividends are not sustainable or affect the company's growth negatively, raising the dividend may not be advisable.
Real stock price calculations must be more nuanced, considering multiple factors and stable growth assumptions. The prices per share given in the prompt are unrealistic and do not reflect practical stock market prices or valuation methods.