Reading 42: Market-Based Valuation: Price and Enterprise Val 2010, interpret, center, common, style

土豆妮

Session 12: Equity Investments: Valuation Models
Reading 42: Market-Based Valuation: Price and Enterprise Value Multiples

LOS j: Calculate and interpret the justified price-to-earnings ratio (P/E), price-to-book ratio, and price-to-sales ratio for a common stock, based on forecasted fundamentals.

 

 

 

A firm’s return on equity (ROE) is 15%, its required rate of return is 12%, and its expected growth rate is 7%. What is the firm’s justified price to book value (P/B) based on these fundamentals?

A) 1.71.

B) 0.63.

C) 1.60.

---

 

P₀/B₀ = (ROE – g) / (r – g) = (0.15 – 0.07) / (0.12 – 0.07) = 1.60

土豆妮

What is the appropriate price-to-sales (P/S) multiple of a stock that has a retention ratio of 45%, a return on equity (ROE) of 14%, an earnings per share (EPS) of $5.25, sales per share of $245.54, an expected growth rate in dividends and earnings of 6.5%, and shareholders require a return of 11% on their investment?

A) 0.158.

B) 0.278.

C) 0.227.

---

Recall that profit margin is measured as E₀ / S₀. In this example, the profit margin is (5.25 / 245.54) = 0.0214. Thus:

P₀ / S₀ = [(E₀ / S₀)(1 ? b)(1 + g)] / (r ? g) = [0.0214(0.55)(1.065)] / (0.11 ? 0.065) = 0.278

土豆妮

A firm’s return on equity (ROE) is 14%, its required rate of return is 10%, and its expected growth rate is 8%. What is the firm’s justified price-to-book value (P/B) based on these fundamentals?

A) 2.00.

B) 2.75.

C) 3.00.

---

P₀/E₀ = (ROE – g) / (r – g) = (0.14 – 0.08) / (0.10 – 0.08) = 3.00

土豆妮

What is the appropriate leading price-to-earnings (P/E) multiple of a stock that has a projected payout ratio of 40% if shareholders require a return of 15% on their investment and the expected growth rate in dividends is 5%?

A) 6.30.

B) 13.20.

C) 4.00.

---

P₀/E₀ = 0.40 / (0.15 – 0.05) = 4.00

Note that the leading P/E omits (1 + g) in the numerator, which is present in the formula for the trailing P/E.

土豆妮

What is the appropriate justified trailing price-to-earnings (P/E) multiple of a stock that has a payout ratio of 40% if shareholders require a return of 15% on their investment and the expected growth rate in dividends is 5%?

A) 6.30.

B) 3.80.

C) 4.20.

---

P₀/E₀ = (0.40 × 1.05) / (0.15 – 0.05) = 4.20

土豆妮

The Farmer Co. has a payout ratio of 70% and a return on equity (ROE) of 14%. What will be the appropriate price-to-book value (PBV) based on fundamentals if the expected growth rate in dividends is 4.2% and the required rate of return is 11%?

A) 0.64.

B) 1.44.

C) 1.50.

---

Based on fundamentals:
P/BV = (0.14 ? 0.042) / (0.11 ? 0.042) = 1.44.

土豆妮

What is the justified leading price-to-earnings (P/E) multiple of a stock that has a retention ratio of 60% if the shareholders require a return of 16% on their investment and the expected growth rate in dividends is 6%?

A) 6.36.

B) 4.24.

C) 4.00.

---

P₀/E₁ = 0.40 / (0.16 – 0.06) = 4.00

土豆妮

What is the justified trailing price-to-earnings (P/E) multiple of a stock that has a payout ratio of 65% if the shareholders require a return of 10% on their investment and the expected growth rate in dividends is 6%?

A) 9.28.

B) 16.25.

C) 17.23.

---

P₀/E₀ = (0.65 × 1.06) / (0.10 – 0.06) = 17.225

土豆妮

A firm has a payout ratio of 40%, a profit margin of 7%, an estimated growth rate of 10%, and its shareholders require a return of 14% on their investment. Based on these fundamentals, a reasonable estimate of the appropriate price-to-sales ratio for the firm (based on trailing sales) is:

A) 0.77.

B) 0.70.

C) 0.56.

---

土豆妮

The Lewis Corp. had revenue per share of $300 in 2001, earnings per share of $4.50, and paid out 60% of its earnings as dividends. If the return on equity (ROE) and required rate of return of Lewis are 20% and 13% respectively, what is the appropriate price/sales (P/S) multiple for Lewis?

A) 0.12.

B) 0.19.

C) 0.18.

---

Profit Margin = EPS / Sales per share = 4.50 / 300 = 0.015 or 1.5%.

Expected growth in dividends and earnings = ROE × (1 ? payout ratio) = 0.20 × 0.40 = 0.08 or 8%.

P₀/S₀ = [profit margin × payout ratio × (1 + g)] / (r ? g) = [0.015 × 0.60 × (1.08)] / (0.13 ? 0.08) = 0.1944.