Assume it is now January 1, 2012, and you are examining two unlevered firms that operate in the same industry that have identical assets worth $80 million that yield a net profit of 12.5% per year, and that have 10 million shares outstanding. During 2012 and all subsequent years, each firm has the opportunity to invest an amount equal to its net income in (slightly) positive-NPV investment projects. The Beta Company wants to finance its capital spending through retained earnings. The Gamma Company wants to pay out 100% of its annual earnings as cash dividends and to finance its investments with a new share offering each year. There are no taxes or transactions costs to issuing securities.
a. Calculate the overall and per-share market value of the Beta Company at the end of 2012 and each of the two following years (2013 and 2014). What return on investment will this firm’s shareholders earn?
b. Describe the specific steps that the Gamma Company must take today (1/1/2012) and at the end of each of the next three years (year-end 2012, 2013, and 2014) if it pays out all of its net income as dividends and still grows its assets at the same rate as that of the Beta Company.
c. Calculate the number and per-share price of shares that the Gamma Company must sell today, and at the end of 2012, 2013, and 2014, if it pays out all of its net income as dividends and still grow its assets at the same rate as that of the Beta Company.
d. Assuming that you currently own 100,000 shares (1%) of Gamma Company stock, compute the fraction of the company’s total outstanding equity that you will own three years from now if you do not participate in any of the share offerings the firm will make during this holding period.