invic

Margin and Sales Trade-off for CVR, Inc. and Home, Inc., for Next Year
Firm	Strategy	Retention Rate	Profit Margin	Sales/Book Value of Equity
CVR, Inc.	High Margin / Low Volume	20%	8%	1.25
CVR, Inc.	Low Margin / High Volume	20%	2%	4.00
Home, Inc.	High Margin / Low Volume	40%	9%	2.00
Home, Inc.	Low Margin / High Volume	40%	1%	20.0

(Note: CVR, Inc., has a book value of equity of $80 and a required rate of return of 10%. Home, Inc., has a book value of equity of $100 and a required rate of return of 11%.)
If CVR, Inc., has a required return for shareholders of 10%, what is its appropriate leading price-to-sales (P/S) multiple if the firm undertakes the high margin/low volume strategy?

A) 1.46.

B) 0.80.

C) 0.20.

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g = Retention Rate × Profit Margin × Sales/book value of equity = 0.20 × 0.08 × 1.25 = 0.02.
If profit margin is based on the expected earnings next period,
Leading P/S = (profit margin × payout ratio) / (r − g) = (0.08 × 0.80) / (0.10 − 0.02) = 0.80.

invic

Margin and Sales Trade-off for CVR, Inc. and Home, Inc., for Next Year
Firm	Strategy	Retention Rate	Profit Margin	Sales/Book Value of Equity
CVR, Inc.	High Margin / Low Volume	20%	8%	1.25
CVR, Inc.	Low Margin / High Volume	20%	2%	4.00
Home, Inc.	High Margin / Low Volume	40%	9%	2.00
Home, Inc.	Low Margin / High Volume	40%	1%	20.0

(Note: CVR, Inc., has a book value of equity of $80 and a required rate of return of 10%. Home, Inc., has a book value of equity of $100 and a required rate of return of 11%.)
If CVR, Inc., has a required return for shareholders of 10%, what is its appropriate leading price-to-sales (P/S) multiple if the firm undertakes the high margin/low volume strategy?

A) 1.46.

B) 0.80.

C) 0.20.

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n

g = Retention Rate × Profit Margin × Sales/book value of equity = 0.20 × 0.08 × 1.25 = 0.02.
If profit margin is based on the expected earnings next period,
Leading P/S = (profit margin × payout ratio) / (r − g) = (0.08 × 0.80) / (0.10 − 0.02) = 0.80.

invic

An analyst has gathered the following data about Jackson, Inc.:

• Payout ratio = 60%.
• Expected growth rate in dividends = 6.7%.
• Required rate of return = 12.5%.

What will be the appropriate price-to-book value (PBV) ratio for Jackson, based on fundamentals?

A) 0.58.

B) 1.73.

C) 1.38.

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Return on equity (ROE) = g / (1 − payout ratio) = 0.067 / 0.40 = 0.1675 or 16.75%.
Based on fundamentals:
PBV = (0.1675 − 0.067) / (0.125 − 0.067) = 1.73.

invic

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) 4.00.

B) 6.30.

C) 13.20.

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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.

invic

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) 4.20.

C) 3.80.

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

invic

An analyst has gathered the following fundamental data:

	Firm A	Firm A	Firm B	Firm B
Strategy	High Margin Low Volume	Low Margin High Volume	High Margin Low Volume	Low Margin High Volume
Payout Ratio	40%	40%	40%	40%
Required Rate of Return	11%	11%	11%	11%
Growth Rate in Dividends	9%	5%	5%	7%
Sales/Book Value of Equity	1.5	4.5	1.0	3
Profit Margin	10%	2%	9%	4%
Book Value	$150	$150	$125	$125

What is the price-to-sales (P/S) multiple for Firm A in the high-margin, low-volume strategy?

A) 2.18.

B) 2.00.

C) 0.13.

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The P/S multiple = [Profit Margin × Payout Ratio × (1 + g)] / (r − g) = (0.10 × 0.4 × 1.09) / (0.11 − 0.09) = 2.18.

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What is the P/S multiple for Firm B in the low-margin, high-volume strategy?

A) 0.60.

B) 0.43.

C) 2.00.

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The P/S multiple = [Profit Margin × Payout Ratio × (1 + g)] / (r − g) = (0.04 × 0.4 × 1.07) / (0.11 − 0.07) = 0.428 or 0.43.

invic

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) 0.18.

C) 0.19.

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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.

invic

A firm has a payout ratio of 35%, a return on equity (ROE) of 18%, an estimated growth rate of 13%, and its shareholders require a return of 17% on their investment. Based on these fundamentals, a reasonable estimate of the appropriate price-to-book value ratio for the firm is:

A) 2.42.

B) 1.25.

C) 1.58.

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invic

What is the justified trailing price-to-earnings (P/E) multiple of a stock that has a payout ratio of 40% if the shareholders require a return of 16% on their investment and the expected growth rate in dividends is 6%?

A) 4.24.

B) 4.00.

C) 6.36.

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P0/E0 = (0.40 × 1.06) / (0.16 – 0.06) = 4.24

JonnyKay

The Farmer Co. has a payout ratio of 65% and a return on equity (ROE) of 16% (assume that this is expected ROE for the upcoming year). What will be the appropriate price-to-book value (PBV) based on return differential if the expected growth rate in dividends is 5.6% and the required rate of return is 13%?

A) 1.41.

B) 1.48.

C) 0.71.

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Based on return differential:
P0 / BV0 = (ROE1 − g) / (r − g) = (0.16 − 0.056) / (0.13 − 0.056) = 1.41.