Company ABC expects to pay a dividend per share of $10 next year, which represents 100% of its earning. The expected return from investors is 10%. The company's return on equity is 12%.

a) Calculate the price of a share assuming that the company pays out 100% of its earning in dividend.

b) Calculate the price of a share if the company decides to plowback 80% of its earning into the firm's operations and investments.

c) Assuming a plowback ratio of 80%, calculate the firm's present value of growth opportunities (PVGO).

d) Explain why it may be optimal for a firm to lower its plowback ratio as it matures.