Nutrition, Inc, a vitamin supplement manufacturer, is financed entirel

Nutrition, Inc, a vitamin supplement manufacturer, is financed entirely with equity that is currently privately owned by its managers. The firm is expected to generate earnings of $5 mn.

per year into perpetuity, and all earnings are paid out in dividends. The owner-managers receive no additional compensation. For all of the owner-managers, their shares of the firm’s equity accounts for the bulk of their personal wealth. As a result, in determining their personal valuation of the firm they apply a high discount rate of 33 percent to their future expected dividends, and therefore they value the firm at $15.15mn. (=$5mn./0.33). The firm’s management team has recently consulted with an investment-banking firm about selling all of the firm’s equity publicly; that is, about going public with the firm’s shares. Assuming that the current management will continue to operate the firm, the investment-banking firm estimates that the market will value the firm’s equity applying a 25% discount rate to expected future dividends. However, expected dividends to public shareholders will be only $4 mn., because managers will now be paid a total of $1 mn. per year in salaries. (Ignore taxes and transaction costs.) The total market value of the firm’s public shares is (i). Accounting for both the present value of management’s salaries (discounted into perpetuity at 33%) and the proceeds from the public sale of shares, management’s wealth gain from going public is (ii).
(i) (ii)
a. $12 mn. $2.22 mn.
b. $12 mn. $3.88 mn.
c. $16 mn. $2.22 mn.
d. $16 mn. $3.88 mn.

ANSWER

D