Question

Prokter and Gramble​ (PKGR) has historically maintained a​ debt-equity ratio of approximately

0.18. Its current stock price is $45 per​ share, with 2.3 billion shares outstanding. The firm enjoys very stable demand for its​ products, and consequently it has a low equity beta of 0.45 and can borrow at 4.3​%, just 20 basis points over the​ risk-free rate of 4.1​%. The expected return of the market is 10.4​%, and​ PKGR's tax rate is 35​%.

a. This​ year, PKGR is expected to have free cash flows of ​$5.4 billion. What constant expected growth rate of free cash flow is consistent with its current stock​ price?

b. PKGR believes it can increase debt without any serious risk of distress or other costs. With a higher​ debt-equity ratio of 0.45​, it believes its borrowing costs will rise only slightly to 4.6​%. If PKGR announces that it will raise its​ debt-equity ratio to 0.45 through a leveraged​ recap, determine the increase or decrease in the stock price that would result from the anticipated tax savings

Answer 1

Equity value (E) = price per share*number of shares = 45*2.3 = 103.50 B

Debt value (D) = D/E ratio*E = 0.18*103.50 = 18.63 B

Value of levered firm (VL) = D+E = 18.63+103.50 = 122.13 B

WACC calculation:

WACC = Debt ratio*cost of debt*(1-Tax rate) + Equity ratio*cost of equity

Debt ratio = D/VL = 18.63/122.13 = 0.1525

Equity ratio = E/VL = 103.50/122.13 =0.8475

Cost of debt = 4.3%; Tax rate = 35%

Cost of equity (using CAPM) = risk-free rate + equity beta*(market return - risk-free rate)

= 4.1%+0.45*(10.4%-4.1%) = 6.94%

WACC = 0.1525*4.3%*(1-35%) + 0.8475*6.94% = 6.30%

Now, VL = expected FCF/(WACC -g) where g = constant growth rate of the FCF (free cash flow)

122.13 = 5.4/(6.30%-g)

g = 6.30% - (5.4/122.13) = 1.88% (Answer)

b). Cost of unlevered equity (Eu) = Debt ratio*cost of debt + Equity ratio*cost of equity

= 0.1525*4.3% + 0.8475*6.94% = 6.53%

New cost of equity = Eu + equity beta*(Eu - new cost of debt)

= 6.53% + 0.45*(6.53%-4.60%) = 7.40%

New WACC (with 0.45 D/E ratio):

Equity ratio = 1/(1+D/E) = 1/(1+0.45) = 0.6897

Debt ratio = 1- equity ratio = 1-0.6897 = 0.3103

New WACC = (0.3103*4.60%*(1-35%)) + (0.6897*7.40%) = 6.03%

New value of levered firm (VL) = expected FCF/(WACC -g)

= 5.4/(6.03%-1.88%) = 130.08 B

Increase in value of the firm = 130.08 - 122.13 = 7.95 B

Increase in share price = increase in firm value/number of shares

= 7.95/2.3 = 3.45 per share

New share price = 45 + 3.45 = 48.45