For part D, the problem deliberately does not provide enough information to determine book equity.
I believe the whole point is to demonstrate that if we use market equity instead of book equity, then we will always compute zero growth opportunities. This is Jacob's error.
In addition to the given information, if we were given any one of (Book Equity per share) or (Cap Rate) or (Dividend Growth Rate) or (PVGO) then we could compute the other three quantities.
Example:
Suppose a stock is currently $300 per share with a 10% dividend yield, and suppose next year's earnings will be $50. In addition, suppose the book equity is $2.5 billion with 10 million shares outstanding.
Next year's dividend is 10% of $300 = $30.
The payout ratio is $30/$50 = 60%, so the plowback ratio is 40%.
The book equity per share is $2.5 billion / 10 million = $250.
The ROE is $50 / $250 = 20%, using book equity and not market equity.
The dividend growth rate is 20% of 40% = 8%.
The cap rate is $30/$300 + 8% = 18%.
If all earnings were paid out as dividends, then the stock price would be $50/18% = $277.78, so the PVGO is $300 - $277.78 = $22.22.
Alternatively, suppose book equity is $5 billion with 10 million shares outstanding.
In this case:
The book equity per share is $5 billion / 10 million = $500. This exceeds the stock price!
The ROE is $50 / $500 = 10%, using book equity and not market equity.
The dividend growth rate is 10% of 40% = 4%.
The cap rate is $30/$300 + 4% = 14%.
If all earnings were paid out as dividends, then the stock price would be $50/14% = $357.14, so the PVGO is $300 - $357.14 = $-57.14 which is negative because the market price is less than the book equity.