Final answer:
The present value of growth opportunities (PVGO) is calculated by subtracting the no-growth price of a stock from its total price. The formulas needed involve the earnings per share, payout ratio, return on equity, and the required rate of return on equity. However, the stock price must be known or calculated to find the PVGO, which is not directly provided in the question.
Step-by-step explanation:
The question asks to calculate the present value of growth opportunities for a firm given its earnings per share (EPS), payout ratio, return on equity (ROE), and the required rate of return on equity. To find the present value of growth opportunities (PVGO), we use the formula derived from the Gordon Growth Model:
PVGO = P - (EPS × (1 - Payout Ratio)) / Required Return
Where:
- P is the price of the stock,
- EPS is the earnings per share,
- Payout Ratio is the percentage of earnings paid to shareholders in dividends,
- Required Return is the investor's required rate of return on equity.
First, we calculate the stock price (P) using the dividend discount model (assuming all earnings are paid out as dividends), and the growth in dividends comes from the retained earnings which are reinvested at the ROE:
P = (EPS × Payout Ratio) / (Required Return - (ROE × (1 - Payout Ratio)))
The next step involves the calculation of the no-growth price which represents the value of the firm if there are no growth opportunities:
No-growth price = EPS × (1 - Payout Ratio) / Required Return
Last, subtract the no-growth price from the previously calculated stock price to obtain the PVGO.
The student's initial question cannot be directly calculated without the stock price, which is not provided. But, with the given formula and inputs, one can find the present value of growth opportunities following the steps of calculating the stock price, the no-growth price, and then finding the difference.