Problems for week 10

1. This a simple exercise to get you used to taxes in DDM calculation. A firm is expected to pay its next dividend of $2 one year from now. This dividend will grow at a constant rate of 5%. The cost of equity for the firm is 10%.
a) If all investors pay (and are expected to continue paying) income taxes on all income at 30%, what is the price of the stock?
b) Now, if one investor pays no tax (due to special circumstances) but all other (large number) investors pay taxes at 30% how will your response change?

Solution 1:
a) The DDM now changes to P = 2*(1-30%)/(10% - 5%) = $28
b) The response would not change. The tax rate is the rate for the marginal investor. Since there are a large number of investors that pay 30%, vs. only one at a different rate, the 30% rate investor will always be the marginal investor. However, things are different when it is not this overwhelming. In those situations, you cannot get an exact answer.

2. A firm is going to repurchase stock. Its (market value) balance sheet as of now looks as follows:
Cash = $150,000
Debt = 0
Other assets = $850,000
Equity = $1 million
Value of firm = $1 million
Value of firm = $1 million
Number of shares = 100,000. Price per share = $10
Suppose the management are aware of information that there are growth opportunities with NPVGO = $50,000. The market is NOT aware of this. With this in mind, the management is going to repurchase shares worth $100,000.
a) What is the true value per share before the repurchase (true value