Question

Prokter and Gramble​ (PKGR) has historically maintained a​ debt-equity ratio of approximately 0.18. Its current stock price is $51 per​ share, with 2.6 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 4.6​%, just 20 basis points over the​ risk-free rate of 4.4​%. The expected return of the market is 9.5​%, and​ PKGR's tax rate is 30​%.

a. This​ year, PKGR is expected to have free cash flows of $6.1 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 4.9​%. 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

a). Using the constant growth, dividend discount model, we have

Firm value (V0) = FCF1/(WACC-g) where FCF1 = free cash flow next year; g = growth rate;

WACC = (weight of debt*cost of debt*(1-Tax rate)) + (weight of equity*cost of equity)

D/E = 0.18, so E/(D+E) = E/V = 1/(1+0.18) = 0.847

D/V = 1-(E/V) = 1-0.847 = 0.153

Cost of debt = 4.6%

Cost of equity (using CAPM) = risk-free rate + beta*(market return - risk-free rate) = 4.4% + 0.45*(9.5%-4.4%) = 6.70%

WACC = (0.153*4.6%*(1-30%)) + (0.847*6.70%) = 6.16%

Equity value (E0) = share price*number of shares = 51*2.6 = 132.6 bn; FCF1 = 6.1 bn

Debt value (D0) = (D/E)*E0 = 0.18*132.6 = 23.87 bn

V0 = D0 + E0 = 23.87 + 132.6 = 156.47 bn

g = WACC - (FCF1/V0) = 6.16% - (6.1/156.47) = 2.27%

b). Unlevered cost of equity (rsU) = (weight of debt*cost of debt) + (weight of equity*cost of equity)

= (0.153*4.6%) + (0.847*6.70%) = 6.38%

New D/E ratio = 0.45

Levered cost of equity (rsL) = rsU + (rsU -rd)*D/E where rd = cost of debt = 4.9%; D/E = 0.45

rsL = 6.38% + (6.38%-4.9%)*0.45 = 7.04%

E/V = 1/(1+0.45) = 0.69; D/V = 1-0.69 = 0.31

WACC = (0.69*7.04%) +(0.31*4.9%*(1-30%)) = 5.92%

New firm value (V1) = FCF1/(WACC-g) = 6.1/(5.92%-2.27%) = 166.99 bn

Gain = 166.99 - 156.47 = 10.52 bn

Per share increase = 10.52/number of shares = 10.52/2.6 = $4.05

New share price = old share price - decrease per share = 51 + 4.05 = $55.05