Question

An all-equity firm has 250,000 shares outstanding. The firm’s assets will generate an expected EBIT of $2,000,000 per year (beginning one year from today) in perpetuity. The firm will make no new capital or working capital investments and all assets are fully depreciated. The assets have a beta of 1.5, therisk-free rate is 5%, and the market risk premium is 5%. The financial analysts at the firm have estimated the optimal capital structure to be wd= 40%; we= 60% (or, D/E = 0.67). The investment bank hired by the firm estimates that theycan issue bonds at par paying an annual coupon at a 7% annual rate. The corporate tax rate is 40%.

a)What is the value of the firm with no debt?

b)What isthe WACC at the new capital structure?

c)What is the value of firm’s operationsif it issues debt to shift to the new capital structure?

d)How much debt does the firm have to issue in order to operate at the new capital structure?

e)Assuming that the shares can be repurchased at the price that existed prior to the recapitalization, what would the price be following the recapitalization?

Answer 1

a.

Cost of Equity = Risk free rate + beta (market risk premium)

Cost of Equity = 5% + 1.5 (5%)

Cost of Equity = 5% + 7.5%

Cost of Equity = 12.5%

Since there is no debt, WACC is equal to Cost of Equity

WACC = 12.5%

EBIT = $2,000,000 per year

Perpetual free cash flow to firm = EBIT * (1-tax rate)

Perpetual free cash flow to firm = 2000000 * (1-40%)

Perpetual free cash flow to firm = 2000000 * 60%

Perpetual free cash flow to firm = 1200000

Value of the firm = Perpetual free cash flow to firm / WACC

Value of the firm = 1200000 / 12.5%

Value of the firm = 9600000

b.

WACC = [Weight of equity * cost of equity] + [weight of debt * Cost of debt * (1-tax rate)]

WACC = [60% * 12.5%] + [40% * 7% * (1-40%)]

WACC = 7.5% + [40% * 4.2%]

WACC = 7.5% + 1.68% = 9.18%

c.

Value of the firm = Perpetual free cash flow to firm / WACC

Value of the firm = 1200000 / 9.18%

Value of the firm = 13071895.42 (rounded off to 2 decimal places)

d.

Amount of debt the firm has to issue in order to operate at the new capital structure = 13071895.42 * 40%

= 5228758.16

e.

Number of Shares = 250000

Value per share = 9600000 / 250000 = 38.4

Because there is no additional requirement of capital or working capital investments, the shares equal to the value of debt issued will be repurchased.

Shares repurchased = 5228758.16 / 38.4 = 136165.58 or 136166 (because shares in fraction cannot be repurchased)

Remaining shares = 250000 - 136166 = 113834

Value of Equity = 13071895.42 - (136166 * 38.4)

Value of Equity = 13071895.42 - 5228774.4

Value of Equity = 7843121.02

Price per share =  7843121.02 / 113834 = 68.90

Price following recapitalization = 68.90