Question

Prokter and Gramble​ (PKGR) have historically maintained a​ debt-equity ratio of approximately 0.15. Its current stock price is $ 54 per​ share, with 2.8 billion shares outstanding. The firm enjoys very stable demand for its​ products, and consequently, it has a low equity beta of 0.375 and can borrow at 4.0%, just 20 basis points over the​ risk-free rate of 3.8%. The expected return of the market is 10.5%  and​ PKGR's tax rate is 32%.

a. This​ year, PKGR is expected to have free cash flows of ​$6.5 billion. What constant expected a 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 0.375, it believes its borrowing costs will rise only slightly to 4.3%. If PKGR announces that it will raise its​ debt-equity ratio to 0.375 through a leveraged​ recap, determine the increase or decrease in the stock price that would result from the anticipated tax savings.

(round to two decimal places.)

Answer 1

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+0.15) = 0.870

D/V = 1-(E/V) = 1-0.870 = 0.130

Cost of debt = 4.0%

Cost of equity (using CAPM) = risk-free rate + beta*(market return - risk-free rate) = 3.80% + 0.375*(10.5%-3.8%) = 6.31%

WACC = (0.130*4.0%*(1-32%)) + (0.870*6.31%) = 5.84%

Equity value (E0) = share price*number of shares = 54*2.8 = 151.2 bn; FCF1 = 6.5 bn

Debt value (D0) = (D/E)*E0 = 0.15*132.6 = 22.68 bn

V0 = D0 + E0 = 22.68 + 151.2 = 173.88 bn

g = WACC - (FCF1/V0) = 5.84% - (6.5/173.88) = 2.34%

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

= (0.130*4.0%) + (0.870*6.31%) = 6.01%

New D/E ratio = 0.375

Levered cost of equity (rsL) = rsU + (rsU -rd)*D/E where rd = cost of debt = 4.3%; D/E = 0.375

rsL = 6.01% + (6.01%-4.3%)*0.375 = 6.65%

E/V = 1/(1+0.375) = 0.727; D/V = 1-0.727 = 0.273

WACC = (0.727*6.65%) +(0.273*4.3%*(1-32%)) = 5.64%

New firm value (V1) = FCF1/(WACC-g) = 6.1/(5.64%-2.34%) = 184.86 bn

Gain = 184.86 - 173.88 = 10.98 bn

Per share increase = Total gain/number of shares = 10.98/2.8 = $3.92

New share price = old share price - decrease per share = 54 + 3.92 = $57.92