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

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

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

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

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

An analyst has gathered the following fundamental data:

	Firm A	Firm B	Firm C	Firm D
Payout Ratio	75%
Required Rate of Return	12%	12%	12%	12%
Return on Equity (ROE)	20%	15%	30%	14%
Price/Book Value (PBV) Ratio		3.00	0.70	3.50

What is the PBV ratio for Firm A?

A) 1.25.

B) 2.14.

C) 0.71.

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The growth rate in dividends (g) = ROE(1 − payout ratio) = 0.20 × (1 − 0.75) = 0.05 or 5%. The PBV ratio = (ROE − g) / (r − g) = (0.20 − 0.05) / (0.12 − 0.05) = 2.14

invic

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) 0.70.

B) 0.56.

C) 0.77.

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invic

Margin and Sales Trade-off for CVR, Inc. and Home, Inc., for Next Year
Firm	Strategy	Retention Rate	Profit Margin	Sales/Book Value (SBV) 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 Home, Inc., has a required return for shareholders of 11%, what is its appropriate leading price-to-sales (Po / S1) multiple if the firm undertakes the low margin/high volume strategy?

A) 1.00.

B) 0.20.

C) 0.80.

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g = Retention Rate × Profit Margin × SBV of equity = 0.40 × 0.01 × 20.0 = 0.08.
If profit margin is based on the expected earnings next period,
P/S = (profit margin × payout ratio) / (r − g) = (0.01 × 0.60) / (0.11 − 0.08) = 0.20.

invic

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) 17.23.

B) 9.28.

C) 16.25.

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

invic

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) 3.00.

B) 2.00.

C) 2.75.

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The firm’s justified price-to-book value = (ROE – g) / (r – g) = (0.14 – 0.08) / (0.10 – 0.08) = 3.00