Final answer:
The calculation for the present value of the firm's growth opportunities (PVGO) requires subtracting the present value of dividends from the stock's actual market price. However, the final PVGO cannot be determined without the actual market price of the stock.
Step-by-step explanation:
The present value of the firm's growth opportunities (PVGO) can be calculated by first determining the present value of dividends and then subtracting this value from the stock's price. Given that the expected earnings per share (EPS) next year is $7.42 and the dividend payout ratio is 0.8, the amount reinvested in the firm is 20% of the EPS (which equates to $1.484). This reinvested amount is expected to earn a return of 10%, leading to a growth rate in dividends of 0.2 x 10% = 2%. Given the stock's required rate of return of 13.7%, the value of the dividends can be represented as a perpetuity with growth as Dividend / (r - g), which would be ($7.42 x 0.8) / (0.137 - 0.02). This calculation provides the market price per share without growth opportunities. To calculate PVGO, we thus subtract the present value of dividends from the actual market price of the stock, which can be found using the same perpetuity formula with the required rate of return but without growth. However, the actual market price is not provided in this question, so we cannot complete the final step of the calculation without this data.