Question

Voila is an all‐equity firm with pre‐tax earnings expected to be $800,000 in perpetuity. The firm has 100,000 shares outstanding. The cost of capital is 20% and the firm faces a 40% tax on all corporate earnings.

Voila is considering a major expansion of its facilities, which will require an initial outlay of $750,000 and is expected to produce additional annual pre‐tax earnings of $250,000 per year in perpetuity. Management considers the expansion to have the same risk as the firm’s existing assets.

(a) What is the value of the firm’s assets prior to announcing or undertaking the proposed expansion? What is the value of the firm’s equity? What is the price per share?

(b) Assume that Voila has announced the expansion and markets have responded reasonably to the announcement. Suppose Voila plans to finance the expansion by issuing common stock. How many shares of stock must be issued? What is the value of the firm’s equity after the new stock issue? What is the price per share of the firm’s stock?

Answer 1

Value of the firm assets, shall be the earnings on asset divide by the cost of the asset, as the earnings are going to be earned in perpetuity.

Value of the Firm = Net Earnings / Cost of equity = 800000 (1-0.4)/ 20% = 2,400,000

Number og shares = 100000

Value per share = 2,400,000 / 100,000 = 24 per share'

b) Assuming all the financing of 750,000 will be done from raising of new equity.

Number of equity shares to be raised = 750,000 / 24 = 31,250

Total number of shares = 131,250 shares

Total Earnings after expansion = (800,000 + 250,000)(1-0.4) = 630,000

Value of the Firm = Net Earnings / Cost of equity = 630,000/ 20% = 3,150,000

Price per share = 3,150,000 / 131,250 = 24

We observe that the price of the share does not change, this is becausethe required return of existing assets is 20%, and return on expansion project is (250000(1-0.4)/ 750,000) = 20%, which is the same. As the required return and return on expansion is the same, there is no change in the price of the share.