Understanding valuations. Bank of Pacific Northwest (BPN) has current earnings per share of $10. The appropriate discount rate for the BPN stock is 20%. Suppose BPN distributes all of its earnings as dividends and that BPN's assets will remain equally productive so that it will generate the same earnings in every period.

a) What is the intrinsic value of the BPN stock?

The BPN management discovers some new investment opportunities that can offer a return on equity (ROE) of 25%. To finance these investments, they announce that they increase the firm's plowback ratio to 0.4 permanently.

b) What is the intrinsic value of BPN according to its management?

c) YC the pessimist believes that the BPN management has overestimated the ROE. She estimates the ROE to be 12.5%. Without doing any calculation, could you predict whether the intrinsic value of BPN according to YC the pessimist is this higher or lower than the firm's value before the announcement (when BPN distributes all its earnings)? Explain. Now calculate the valuation under YC's ROE estimate.

Suppose half of the investor population shares the beliefs of the BPN management about the ROE, while the other half of the population shares the beliefs of YC the pessimist.

d) What is the intrinsic value of the BPN stock according to the "average" investor? Suppose the current price of the stock equals this average. Construct a trading strategy for YC that earns abnormal high returns (over a long horizon) according to her beliefs.

Suppose the government temporarily banned short-selling due to concerns about financial stability.

e) What is the price of the BC stock after the announcement by the firm's management and the implementation of the short selling ban by the government? Is this higher or lower than the average intrinsic value calculated in part d)? Explain.