Question

Prokter and Gramble​ (PKGR) has historically maintained a​ debt-equity ratio of approximately 0.15 . Its current stock price is $48 per​ share, with 2.7 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 4.1​%, just 20 basis points over the​ risk-free rate of ​3.9%. The expected return of the market is 10.3​%, and​ PKGR's tax rate is 25​%.

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 0.375 ​, it believes its borrowing costs will rise only slightly to ​4.4%. If PKGR announces that it will raise its​ debt-equity ratio 0.375 to through a leveraged​ recap, determine the increase or decrease in the stock price that would result from the anticipated tax savings.

Answer 1

Current Stock Price = $48 per share

No. of Shares O/S = 2.7 Billion

Market Value of Equity = Current Stock Price * No. of Shares O/S = 48 * 2.7 = $129.6 Billion.

Debt - Equity Ratio = 0.15

Market Value of Debt = Debt - Equity Ratio * Market Value of Equity = 0.15 * 129.6 = $19.44 Billion

Total Value of Firm = Market Value of Debt + Market Value of Equity = 129.6 + 19.44 = $149.04 Billion

Cost of Debt = 4.1% (Pre - Tax)

Tax Rate = 25%

Cost of Debt (After Tax) = Cost of Debt (Pre - Tax) * (1 - Tax Rate) = 4.1% * (1 - 25%) = 3.08%

Risk Free Rate = 3.9%

Expected Return on Market = 10.3%

Equity Beta = 0.375

Cost of Equity = Risk Free Rate + Beta * (Expected Return on Market - Risk Free Rate)

Cost of Equity = 3.9% + 0.375 * (10.3% - 3.9%) = 6.3%

WACC = Cost of Equity * Proportion of Equity + Cost of Debt (After Tax) * Proportion of Debt

WACC = 6.3% * (129.6 / 149.04) + 3.08% * (19.44 / 149.04) = 5.88%

(A) Implied Growth Rate Calculation:

Value of Firm = Expected Free Cash Flow to Firm / (WACC - Growth Rate)

149.04 = 6.1 / (5.88% - Growth Rate)

Growth Rate = 5.88% - (6.1 / 149.04) = 1.79%

Implied growth rate is 1.79% given that firm value is correctly priced.

(b)

New Debt to be Issued = 149.04 * (0.375 / 1 + 0.375) - 19.44 = $21.21 Billion

Tax Rate = 25%

Additional expected Tax Savings = New debt issued * Tax Rate = 21.21 * 25% = $5.30 Billion

Increase in Share Price = 5.30 / 2.7 = $1.96 per Share

Stock Price would rise by $1.96 only because of tax savings benefits.