Question

Recapitalization An unlevered firm has a perpetual cash flow depending on the state of the economy as follows:

Economy	Cash Flow	Probability
Strong	1500	55%
Weak	900	45%

The firm has

Ru = 15%

N0 = 1000.00 shares outstanding.

The company plans to recapitalize its capital structure by issuing a perpetual debt (a debt that pays a perpetual interest) to buy back shares to achieve D/E ratio of

D/E = 1.50

Suppose the riskless rate is

Rf = 10%

Can the firm issue risk-free debt?

At what price will the firm have to pay for its shares and how many shares will be repurchased? Draw the market value balance sheet for the transaction

What is the cost of equity capital after the transaction?

What is the firm's expected equity cash flow per share after the recap? How does it change from before the recap?

Answer 1

Expected cash flows = 1500*0.55 + 900*0.45 = 1230

Equity value = Firm value = Perpetual cashflows/Interest rate = 1230/0.15 = 8200

No of shares = 1000

Share price = Equity/no of shares = 8200/1000 = $ 8.2

Expected D/E = 1.5

D = 1.5E

D+E =1 -> 1.5E+E = 1

E = 40%

D = 60%

To raise 60% debt to increase the D/E ratio, they need to buyback 60% equity i.e. 60 shares at $8.2

Remaining equity = 40% = 400 shares

EPS will increase by 1/0.4 = 2.5 times i.e. 150%

Since share price will remain the same, cost of equity will also increase by 150% i.e. 37.5%

Equity cash flow per share after the recap = 1230/400 = 3.075

Equity cash flow per share before the recap = 1230/1000 = 1.23

Chnage in EPS = (3.075-1.23)/1.23 = 150%

Since after the issue of debt firm is increasing the risk, to they cannot issue the risk free sebt.

Balance sheet:

Equity = 8.2*400 = 3280

Debt = 8200-3280 = 4920