An analyst is valuing a company that reported earnings of $3.00 per share last year and pays out 30% of its earnings as dividends. The company reinvests the balance at an expected return on equity of 15%. The stock's required return is 13%, and the stock trades at $48 per share.
Which of the following statements is most accurate? Answer: The stock is overvalued; its forward P/E of approximately 14.5 exceeds the justified forward P/E of 12.0.
Justified P/E derived from the constant-growth dividend discount model. The sustainable growth rate is the return on equity times the retention ratio: g = 15% × (1 - 0.30) = 10.5%. The justified forward P/E is the payout ratio divided by the excess of the required return over growth: 0.30 / (0.13 - 0.105) = 12.0. Next year's earnings are E1 = $3.00 × 1.105 = $3.315, so the actual forward P/E is $48 / $3.315 = 14.5, above the justified multiple. The 28.0 justified P/E comes from putting the 70% retention ratio in the numerator instead of the 30% payout ratio. The 3.5 justified P/E comes from using 15% × 0.30 = 4.5%, ROE times the payout ratio, as the growth rate. The 13.3 figure is the justified trailing P/E, 0.30 × 1.105 / 0.025, compared with the forward P/E — a mismatch of bases that makes the overvaluation appear smaller than it is.
- A company is expected to earn $5.00 per share next year. The company pays out 40% of its earnings as dividends, its return on equity is 12%, and the required return on the stock is 10%. Using the constant-growth dividend discount model, the intrinsic value of the stock is closest to:
Answer: $71.43
The sustainable growth rate is return on equity multiplied by the retention ratio: g = 12% × (1 − 0.40) = 7.2%. Because the $5.00 figure is next year's earnings, the corresponding dividend is D1 = $5.00 × 0.40 = $2.00, with no further growth adjustment needed. Value = D1 ÷ (r − g) = $2.00 ÷ (0.10 − 0.072) = $2.00 ÷ 0.028 = $71.43. The $38.46 figure multiplies ROE by the payout ratio instead of the retention ratio (g = 4.8%), giving a denominator of 0.052. The $76.57 figure treats the next-year dividend as if it were the current dividend and grows it one more year ($2.00 × 1.072 = $2.144) before dividing by 0.028. The $107.14 figure computes the dividend using the retention ratio rather than the payout ratio, $5.00 × 0.60 = $3.00, before dividing by 0.028.
- A stock trades at $43.20 and just paid a dividend of $2.40 per share. The risk-free rate is 4%, the expected return on the market is 12%, and the stock's beta is 1.25. If the market price is exactly consistent with the constant-growth dividend discount model, the dividend growth rate the market is pricing in is closest to:
Answer: 8.0%
The capital asset pricing model gives the required return: r = 4% + 1.25 × (12% − 4%) = 14%. Setting the market price equal to the constant-growth value: $43.20 = $2.40(1 + g) ÷ (0.14 − g). Multiply through: $43.20 × 0.14 − $43.20g = $2.40 + $2.40g, so $3.648 = $45.60g and g = 8.0%. As a check, $2.40 × 1.08 = $2.592, and $2.592 ÷ 0.06 = $43.20. The 8.4% figure comes from solving the model with the current dividend in the numerator, $43.20 = $2.40 ÷ (0.14 − g), without growing the dividend to next year. The 5.6% figure is the current dividend yield ($2.40 ÷ $43.20) mistaken for the implied growth rate. The 14.0% figure is the CAPM required return mistaken for the growth rate the market is pricing in.
An analyst is valuing a company with an enterprise value of $600 million, EBITDA of $75 million, net income of $30 million, cash and equivalents of $50 million, and total debt of $100 million. The company has 10 million shares outstanding.
The company's price-to-earnings ratio is closest to which of the following? Answer: 18.3
Enterprise value to equity value conversion. Enterprise value equals equity value plus debt minus cash, so equity value is 600 - 100 + 50 = 550 (in millions). Per share, equity value is 550 / 10 = $55.00. Net income per share is 30 / 10 = $3.00, giving a P/E of 55 / 3 = 18.3. The 16.7 figure subtracts the debt but fails to add back the cash, using $500 million as equity value. The 20.0 figure uses the $600 million enterprise value directly as market capitalization, ignoring both the debt and the cash adjustment. The 21.7 figure adds the cash to enterprise value without subtracting the debt, using $650 million as equity value.
- Which of the following statements regarding common stock valuation methods is true?
Answer: A stock with a dividend yield of 3% and expected dividend growth of 5% has an expected total return of 8% under the constant-growth dividend discount model.
Constant-growth dividend discount model (Gordon growth model): expected total return = dividend yield + dividend growth rate, so 3% + 5% = 8%; this identity comes from rearranging current price = next year's dividend ÷ (required return - growth rate) to solve for r. The dividend-yield statement defines the payout ratio, not the yield: dividend yield is annual dividends per share divided by market price per share. The price-to-book statement is wrong because internally developed intangible assets generally are not recorded on the balance sheet, so book value understates intangible-heavy companies; price-to-book is most useful when tangible assets are substantial. The zero-earnings statement is wrong because the P/E ratio is price per share divided by earnings per share, so zero earnings make the ratio undefined; dividing earnings per share by market price gives the earnings yield, not the P/E ratio.
A cyclical manufacturing company earned $4.00 per share last year, a cyclical peak, and the stock trades at $24 per share. The company's earnings at the trough of the cycle were $1.50 per share, and its average earnings over a full business cycle are estimated at $2.00 per share.
Which of the following statements about the stock is most accurate? Answer: The stock is not as cheap as its trailing P/E suggests; normalized earnings of $2.00 give a P/E of 12.0, twice the trailing figure.
Normalized (mid-cycle) earnings in valuing cyclical companies. The trailing P/E of $24 / $4.00 = 6.0 is mechanically low because $4.00 is peak earnings; declaring the stock undervalued on that basis ignores the cyclical distortion. Normalized earnings of $2.00 produce a P/E of $24 / $2.00 = 12.0, twice the trailing multiple, so the stock is not as inexpensive as its trailing P/E suggests. Trough earnings of $1.50 would produce a P/E of $24 / $1.50 = 16.0, but a high multiple at trough earnings is equally distorted and is not evidence of overvaluation. The P/E ratio remains usable for cyclical companies when earnings are normalized, so the claim that no comparison can be drawn is too broad.
- An IAR is evaluating a stock for a client. The stock has a forward P/E of 22 and analysts expect earnings to grow at 11% per year. The average forward P/E for the industry is 20, and the industry's expected earnings growth rate is 10%. Based on PEG analysis, which statement is most accurate?
Answer: The stock is priced in line with the industry on a growth-adjusted basis because its PEG of 2.0 matches the industry's PEG of 2.0.
The PEG ratio divides a P/E multiple by the expected earnings growth rate: PEG = P/E ÷ growth. The stock's PEG is 22 ÷ 11 = 2.0; the industry's PEG is 20 ÷ 10 = 2.0. Because the two ratios match, the stock is neither cheaper nor more expensive than the industry on a growth-adjusted basis. The 2.2 PEG figure comes from dividing the stock's P/E by the industry's growth rate (22 ÷ 10), and the overvalued conclusion rests on that miscomputed ratio. The claim that the stock is undervalued because its 10% P/E premium is no greater than its 10% growth premium mistakes an equal growth adjustment for a bargain, since equal PEGs indicate consistent relative pricing. The statement that any PEG above 1.0 signals overvaluation misapplies a rough rule of thumb; PEG norms vary by industry, and the relevant comparison here shows the stock matching the industry at 2.0.
An analyst is comparing two companies in the same industry. Stock A trades at $60 per share and has forward earnings per share of $3.00, with earnings expected to grow at 20% per year. Stock B trades at $40 per share and has forward earnings per share of $2.50, with earnings expected to grow at 10% per year.
On the basis of PEG ratios alone, which of the following statements is most accurate? Answer: Stock A is more attractive on a PEG basis; its PEG ratio of 1.0 is lower than Stock B's PEG ratio of 1.6, even though Stock A trades at a higher P/E.
PEG ratio, or P/E divided by expected earnings growth. Stock A's forward P/E is $60 / $3.00 = 20.0, so its PEG is 20 / 20 = 1.0. Stock B's forward P/E is $40 / $2.50 = 16.0, so its PEG is 16 / 10 = 1.6. On a PEG basis the lower ratio makes Stock A more attractive despite its higher P/E. The earnings-yield comparison ($3.00 / $60 = 5.0% versus $2.50 / $40 = 6.25%) is a legitimate metric but does not answer the stated PEG question. The claim that Stock B's lower P/E must produce the lower PEG skips the growth adjustment entirely. The growth-rate-only conclusion treats rapid growth as attractive without relating it to the price paid, which is the purpose of the PEG ratio.
A stock just paid an annual dividend of $2.00 per share. Dividends are expected to grow at 7% per year indefinitely. The stock's beta is 1.1, the risk-free rate is 3%, and the expected return on the market is 9%.
Using the capital asset pricing model and the constant-growth dividend discount model, the intrinsic value of the stock is closest to which of the following? Answer: $82.31
Constant-growth dividend discount model (Gordon growth model). The required return comes from the CAPM: r = 3% + 1.1 × (9% - 3%) = 9.6%. Because the $2.00 dividend was just paid, the next dividend is D1 = $2.00 × 1.07 = $2.14, and intrinsic value is V = $2.14 / (0.096 - 0.07) = $82.31. The $76.92 figure uses the current dividend of $2.00 in the numerator without growing it to next year's dividend. The $107.00 figure substitutes the 9% expected market return for the stock's CAPM required return, ignoring beta and the risk-free rate. The $36.27 figure applies the CAPM incorrectly as 3% + 1.1 × 9% = 12.9%, multiplying beta by the full market return instead of by the market risk premium of 6%.
An analyst is valuing a privately held manufacturer using the comparable companies approach. The target company is expected to earn $4.5 million next year and has 1.5 million shares outstanding. The analyst selects a publicly traded comparable whose earnings are expected to grow 12% annually and that trades at 18 times next year's earnings. The target company's earnings are expected to grow 15% annually.
Using the comparable company's PEG ratio as the valuation benchmark, which of the following is closest to the estimated value per share of the target company? Answer: $67.50
Relative valuation using the PEG ratio: the comparable's PEG = (P/E)/growth = 18/12 = 1.5. Applying that PEG to the target's 15% expected growth gives a justified P/E of 1.5 × 15 = 22.5. The target's forward EPS is $4.5 million/1.5 million shares = $3.00, so the estimated value per share is 22.5 × $3.00 = $67.50. The $54.00 figure applies the comparable's raw P/E of 18 to the target's EPS, ignoring that the target's growth is higher. The $22.50 figure is the justified P/E itself, omitting the final step of multiplying by EPS. The $45.00 figure uses the target's 15% growth rate as if it were the P/E multiple (15 × $3.00).
- An analyst is valuing a company that just paid an annual dividend of $2.00 per share. The analyst expects the dividend to grow at 20% per year for the next two years and then grow at 4% per year indefinitely. Assuming a required return of 12%, the stock's intrinsic value per share is closest to:
Answer: $34.29
The dividend discount model values a share as the present value of expected future dividends. Project the dividends: D1 = $2.00 × 1.20 = $2.40; D2 = $2.40 × 1.20 = $2.88; D3 = $2.88 × 1.04 = $2.9952. The constant-growth (Gordon) value at the end of year 2 is D3 ÷ (r − g) = $2.9952 ÷ 0.08 = $37.44. Discount D1 and the year-2 total (dividend plus terminal value): $2.40 ÷ 1.12 + ($2.88 + $37.44) ÷ 1.12² = $2.1429 + $32.1429 = $34.29. The $38.14 figure discounts the year-2 dividend and the terminal value for only one year instead of two. The $33.14 figure starts the constant-growth stage with the year-2 dividend itself ($2.88 ÷ 0.08 = $36.00) instead of first growing it to D3. The $26.00 figure ignores the 20% growth stage entirely and applies the single-stage model to the current dividend, $2.00 × 1.04 ÷ (0.12 − 0.04).
An analyst uses the Gordon growth model to value the common stock of a mature manufacturing company. The company just paid an annual dividend of $2.00 per share. The company's return on equity is 12%, and it pays out 40% of its earnings as dividends. The stock's required rate of return is 10%.
Which of the following is closest to the intrinsic value per share of the company's stock? Answer: $76.57
Gordon growth model (the constant-growth dividend discount model): intrinsic value today = next year's dividend ÷ (required return - growth rate). The sustainable growth rate is g = ROE × (1 - payout ratio) = 12% × 60% = 7.2%. Because the $2.00 dividend was just paid, the numerator is next year's dividend: $2.00 × 1.072 = $2.144. Intrinsic value = $2.144/(0.10 − 0.072) = $76.57. The $71.43 figure uses the just-paid $2.00 dividend in the numerator instead of next year's $2.144. The $21.44 figure grows the dividend to $2.144 but divides by the full 10% required return, omitting the subtraction of the 7.2% growth rate in the denominator. The $191.43 figure substitutes expected earnings per share ($5.00 × 1.072 = $5.36) for the dividend in the numerator; the model prices expected dividends, not earnings.
An analyst is valuing a company using the asset-based approach. The most recent balance sheet shows total assets of $50 million and total liabilities of $20 million. A parcel of land carried at $8 million has an appraised fair value of $14 million. Inventory carried at $6 million is estimated to have a net realizable value of $4 million. The company has 2 million shares outstanding, and the stock trades at $40 per share.
Based on the analyst's adjusted book value per share, the stock's price-to-book ratio is closest to which of the following? Answer: 2.35
Asset-based valuation marks balance-sheet items to fair value. Reported equity is $50M − $20M = $30M. The land write-up adds $6M and the inventory write-down subtracts $2M, so adjusted equity is $34M, or $17 per share. The price-to-book ratio is $40/$17 = 2.35. The 2.67 ratio uses the unadjusted book value per share of $15, ignoring both fair-value adjustments. The 2.22 ratio reflects only the land write-up (book value per share of $18) and omits the inventory write-down. The 2.86 ratio reflects only the inventory write-down (book value per share of $14) and omits the land write-up.
- An IAR is valuing a mature utility company for a client. The stock just paid a dividend of $3.00 per share. The risk-free rate is 2%, the expected return on the market is 9%, and the stock's beta is 1.2. Assuming dividends will grow at 4% indefinitely, the stock's intrinsic value is closest to:
Answer: $48.75
The required return comes from the capital asset pricing model: r = 2% + 1.2 × (9% − 2%) = 10.4%. The next dividend is D1 = $3.00 × 1.04 = $3.12. Under the constant-growth dividend discount model, P = D1 ÷ (r − g) = $3.12 ÷ 0.064 = $48.75. The $62.40 figure uses the expected market return (9%) as the stock's required return: $3.12 ÷ (0.09 − 0.04). The $35.45 figure applies beta to the full market return instead of the market risk premium, producing r = 2% + 1.2 × 9% = 12.8%, then divides $3.12 by 0.088. The $46.88 figure uses the just-paid dividend without growing it to next year: $3.00 ÷ 0.064.
