Equity valuation: concepts and basic tools (Reading 52)

Exercise Problems:

1. An investor gathered the following data in order to estimate the value of the company's preferred stock:

The value of the company’s preferred stock is closest to:

A. $52.17

B. $74.53

C. $96.92

Ans: A;

The formula to calculate the intrinsic value of a non-callable, non-convertible preferred stock is:

Intrinsic Value= D_p/ k_p

where D_p refers to the fixed dividend and k_p refers to the required rate of return.

Therefore, intrinsic value = $100×0.060/0.115 = $52.17

2. A company’s $100 par perpetual preferred stock has a dividend rate of 7 percent and a required rate of return of 11 percent. The company’s earnings are expected to grow at a constant rate of 3 percent per year. If the market price per share for the preferred stock is $75, the preferred stock is most appropriately described as being:

A. overvalued by $11.36.

B. undervalued by $15.13.

C. undervalued by $36.36.

Ans: A;

Intrinsic Value of perpetual preferred stock

= D_p/ k_p

= $7/0.11

= $63.64

Therefore, the stock is overvalued by $75.00-64.64 = $11.36

3. A company’s series B, 8% preferred stock with a par value of $ 50 pays quarterly dividends. Its current market value is $35. The shares are retractable (at par) with the retraction date set for three years from today. Similarly rated preferred issues have an estimated nominal required rate of return of 12%. Analysts expect a sustainable growth rate of 4% for the company’s earnings. The intrinsic value estimate of a share of this preferred issue is closest to:

A. $33.33

B. $52.00

C. $45.02

Ans: C;

Quarterly dividend = ($50) (0.08) / 4 = $1 a share;

Quarterly required return = 12% / 4 = 3%;

V₀ = $1/1.03 +1/1.03² +1 / 1.03³ + …+1/1.03¹² + 50/1.03 ¹²

=$ 45.02

Using a financial calculator:

PMT = $1;

N=12;

FV = 50$;

I = 3%;

Compute PV = $ 45.02.

4. An investor evaluating a company's common stock for investment has gathered the following data:

Using the two-stage dividend discount model, the value per share of this common stock in 2012 is closest to:

A. $28.57

B. $31.57

C. $38.70

Ans: B ;

Dividend per share (2012) = $2.50 (0.6) = $1.50.

V₂₀₁₂

=1.50(1.25)/1.12+1.50(1.25)²/1.12²+1.50(1.25)² (1.05)/(0.12??0.05)×1/1.12²

= $1.67 + $1.87 + $28.03

= $31.57.

5. A company earned $3 a share last year and just paid a dividend of $2 a share. The company’s dividends are expected to grow by 8 percent annually for the next two years. An investor with an 11 percent required rate of return expects to sell the stock at $75 two years from now. The maximum amount the investor should be willing to pay for this company’s stock (in $) today is closest to:

A. 58.68.

B. 64.71.

C. 66.63.

Ans: B;

The value of the stock

= D₁/ (1 + k) + D₂/ (1 + k) ² + SP₂ / (1 + k) ²

= 2×1.08/1.11+2×1.08 ² /1.11 ² +75/1.11 ²

= $64.71

6. An analyst gathers the following information about a company:

The best estimate of the company’s value per share is closest to:

A. ??48.68.

B. ??50.68

C. ??85.93

Ans: A

7. An investor uses the data below and Gordon’s constant growth dividend discount model to evaluate a company’s common stock. To estimate growth, she uses the average value of the:

1) compounded annual growth rate over the period 2006–2011

2) sustainable growth rate for the year 2011.

If her required return is 15%, the stock’s intrinsic

value is closest to:

A. $23.71.

B. $25.31.

C. $30.14.

Ans: B ;

V0 = D1/(k – g)

To estimate growth, which is the average value of 1) and 2):

1) Dividend growth rate over the period 2006–2011

= 1.25(1 + g) ⁵ = 1.92;

Compounded annual growth rate g = 8.96% ≈ 9%.

2) sustainable growth rate for the year 2011 g

= b × ROE

=Earnings retention ratio × ROE

= (1- Dividend payout ratio) × ROE

=(1-1.92/3.20) × 12%

=4.8%

Therefore the average of the two approaches = (9+4.8)/2 = 6.9%

V0 = D1/(k – g)

= 1.92 ×1.069/(0.15 ??0.069)

= 2.05/0.081

= $25.31.

8. The Gordon growth model is most appropriate for valuing the common stock of a dividend-paying company that is:

A. young and just entering the growth phase.

B. experiencing a higher than the sustainable growth rate.

C. mature and relatively insensitive to the economic fluctuations.

Ans: C ;

The Gordon growth model is most appropriate for valuing common stock of a dividend-paying company that is mature and relatively insensitive to the business cycle or economic fluctuations.

9. An analyst gathered the following data about a company in order to estimate its P/E ratio.

The P/E ratio is closest to:

A. 6.7x

B. 13.3x

C. 20.0x

Ans: B

Growth rate = g = Retention ratio × ROE =(1-0.40) × 15 = 9%

P/E = D₁/E₁ /(k - g) = 0.40 /(0.12 - 0.09) = 13.33

10. Ming Xi, an analyst, collects the following data for two companies, Walnert and Almand. Using a required return of 12.4% for both companies, she computes the justified forward P/E ratios, which are also given below.

If Company M increases its dividend payout ratio to 40% and Company N decreases its dividend payout ratio to 30%, which of the following will most likely occur? The justified P/E ratio of:

A. both companies would increase.

B. both companies would decrease.

C. Walnert would increase but Almand would decrease

Ans: A;

Dividend growth rate = (1 – Payout ratio) × ROE;

Justified forward P/E: P₀/E₁ = p/(k – g).

Using the new payout ratios, the justified forward P/Es, calculated below, of both firms would increase.

Company Walnert:

New dividend growth rate = (1 – 0.4) x 12% = 7.2%;

New Justified forward P/E = 0.4/(0.124 – 0.072) = 7.7x.

Company Almand:

New dividend growth rate = (1 – 0.3) x 14% = 9.8%;

New Justified forward P/E = 0.3/(0.124 – 0.098) = 11.5x.

11. An investor gathers the following data of a stock:

To estimate the stock's justified forward P/E, the investor prefers to use the compounded annual earnings growth and the average of the payout ratios over the relevant period (2008–2011). If the investor uses 11.5% as her required rate of return, the stock's justified forward P/E ratio is closest to:

A. 10

B. 12

C. 21

Ans: C ;

Justified forward P/E = ===

Dividend Payout Ratio (ex 2011)=1.92/3.20=0.60

Average Payout Ratio=(0.60+0.50+0.70+0.64)/4=0.61

Earning growth rate (g) over the period of 2008 to 2011 : 2.50 (1+g) ³ =3.20; g=8.6%

Required rate of return = 11.5% , which is given.

Therefore, justified forward P/E =0.61/(0.115-0.086)=21.0

12. A stock selling at $50 has a P/E multiple of 20 on the basis of the current year’s earnings. An analyst estimates that next’s earnings per share will be 10% higher and that the stock should be valued on a forward looking basis at the industry average P/E of 18. Based on the analyst’s assessment, it is most likely that the stock is currently:

A. undervalued.

B. fairly valued.

C. overvalued.

Ans: C ;

If company P/E > industry P/E, overvalued;

If company P/E = industry P/E, fairly valued;

If company P/E < industry P/E, undervalued;

Next year’s EPS = ($50 / 20) × 1.10 = $2.75;

?? Company forward P/E = $50/2.75 = 18.18

Since company forward P/E (18.18) is greater than the industry forward P/E (18), the stock is overvalued.

13. An analyst has gathered the following data for a company whose common stock is currently priced at $40 per share:

If markets are in equilibrium, which of the following statements best describes the company’s price-to-earnings (P/E) ratio? The company’s P/E ratio based on the infinite period dividend discount model ( DDM) is :

A. greater than the company’s trailing P/E ratio

B. the same as the company’s trailing P/E ratio

C. less than the company’s trailing P/E ratio

Ans: C;

Trailing P/E ratio

=Current stock price / Current or Trailing 12-month EPS

DDM P/E ratio

=Current stock price / Expected 12-month EPS

For trailing P/E, since markets are in equilibrium, current stock price (P) reflects the value determined by the constant growth dividend, which equals to ($2.40) (1+8%) / (15.0%-8%) = $37.03. Therefore, The trailing P/E = $37.03 / $6 = 6.17

For DDM P/E, since expected 12-month earnings = ($6.00) (1+8%) = $6.48, the DDM P/E = $37.03 / $6.48 = 5.71

6.17 > 5.71

DDM P/E is less than trailing P/E.

14. An analyst gathers the following information about a company:

The analyst expects the information above to accurately reflect the future. If the company wants to achieve a growth rate of 15% without changing its capital structure or issuing new equity, the company’s maximum dividend payout ratio ( in %) is closest to:

A. 25.

B. 40.

C. 60.

Ans: B;

ROE = ROA × Financial Leverage

= (10.0%) (2.5)

= 25%;

Retention ratio = growth rate / ROE

= 0.15/0.25

= 0.60;

Payout ratio = 1 – Retention ratio

= 1 – 0.60

=40%

15. A analyst gathers the following data on two companies:

Based on the information provided, the most accurate conclusion is that Company X’s stock is more attractive relative to that of Company Y’s because of its:

A. greater financial leverage

B. smaller P/E ratio

C. higher dividend growth rate

Ans: B ;

From the above table, we could conclude that

1). Company X has a lower financial leverage,;

2). Company X has a smaller P/E ratio;

3). Company X and Y share the same dividend growth.

Therefore, Company X’s stock is more attractive because of its smaller P/E ratio.

16. Most of the differences among companies with respect to quality of earnings are addressed when companies are compared using:

A. price to earnings ratio.

B. price to cash flow ratio.

C. both price to earnings ratio and price to cash flow ratios

Ans: B ;

The price to cash flow ratio is less subject to manipulation by management than earnings, generally more stable than earnings, and it addresses the issue of differences in accounting conservatism between companies.

17. The issue of differences in accounting conservatism between companies is best addressed when companies are compared using which of the following ratios?

A. Price-to-earnings

B. Price-to-cash flow

C. Price-to-book value

Ans: B;

Using price-to-cash flow rather than price-to-earnings addresses the issue of differences in accounting conservatism between companies (differences in quality of earnings).

18. Among a company’s price to earnings (P/E), price to sales (P/S), and price to cash flow (P/CF) ratios, it is most accurate to state that P/E ratios are generally more stable period to period than:

A. P/S ratios but not P/CF ratios.

B. P/CF ratios but not P/S ratios.

C. neither P/S ratios nor P/CF ratios.

Ans: C;

Both sales and cash flow tend to be more stable than earnings, making the multiples based on sales and cash flow more stable than those based on EPS.

19. Which of the following is the least accurate rationale to justify the use of price-to-book value (P/B) ratio as a measure of relative valuation of companies?

A. P/B is a useful measure of value for firms that are not expected to continue as a going concern.

B. Compared to P/E, the P/B ratio is not influenced by such accounting effects as expensing a capital investment as opposed to capitalizing it.

C. P/B is particularly appropriate to value companies primarily composed of liquid assets, for example, those in the financial services industry.

Ans: B;

Choice B is a drawback rather than a rationale for using P/B as a measure of relative valuation. P/B does not correctly reflect a company’s value due to the historical cost basis of assets in P/B ratio.

Choice A and C are both rationale for using P/B ratio as a measure of relative valuation.

20. In calculating free cash flow to equity, adjustment is needed for payments made to which of the following capital providers?

Ans: B;

Free cash flow to equity is after subtracting payments to both debt holders and preferred stockholders.

21. Which of the following is the most appropriate reason for using a free-cash-flow-to-equity (FCFE) model to value equity of a company?

A. FCFE models provide more accurate valuations than the dividend discount models.

B. A firm’s borrowing activities could influence dividend decisions but they would not impact FCFE.

C. FCFE is a measure of the firm’s dividend-paying capacity.

Ans: C ;

FCFE is a measure of the firm’s dividend paying capacity.

22. The measures of free cash flow and discount rate to use when estimating the total value of a firm, respectively, are:

A. Operating cash flow before interest payments on debt; cost of equity

B. Operating cash flow before interest payments on debt but after deducting base capital expenditures; cost of equity

C. Operating cash flow before interest payments on debt but after deducting base capital expenditures; cost of equity; weighted average cost of capital.

Ans: C;

In estimating the value of total firm, we should use the free cash flow available to both stockholders and bondholders. Therefore, operating cash flow before debt related costs and after subtracting the required capital expenditure is the appropriate measure of free cash flow.

As the value of the total firm includes the value of equity and the value of debt, the weighted average cost of capital is the relevant discount rate.

23. Which of the following multiples is most helpful when comparing with significant differences in capital structure?

A. EV/EBITDA.

B. Price-to-book ratio.

C. Price-to cash flow ratio

Ans: A ;

EBITDA is computed prior to payment to any of the company’s financial stakeholders and is not impacted by the amount of debt leverage and therefore most useful when comparing companies with significant differences in capital structure.

24. An analyst using the enterprise value approach to valuation gathers the following data:

The value per share of the company’s stock is closest to:

A. $13.43

B. $22.35

C. $22.90

Ans: C;

Step 1: compute the enterprise value (EV) from EBITDA × EV/EBITDA multiple;

Step 2: determine market capitalization (value of equity) using EV

= Market capitalization + MV of preferred stock + MV of debt –Cash and investments

Step3: compute the value per share

=Market capitalization/No. of common stock outstanding

25. Rebecca Lee, CFA, gathers the following information about a company.

Balance Sheet:

Using asset-based valuation approach, the estimated value per share is closest to:

A. $ 9.57.

B. $10.29.

C. $11.00.

Ans: A;

Asset-based Model: Equity value is the market value of assets minus the market value of liabilities.

26. An investor wants to determine the intrinsic value of the common stock for a company with the following characteristics:

?? The firm maintains a constant dividend payout ratio

?? Goodwill and patents account for 40% of the firm’s assets

?? The firm’s revenues and earnings are highly correlated with the business cycle

?? Further, the investor focuses on the firm’s capacity to pay dividends rather than expected dividends.

Considering the above, the investor will most likely use which of the following valuation models?

A. Asset-based valuation model.

B. Free-cash-flow-to-equity model.

C. Gordon dividend growth model.

Ans: B ;

Choice B is correct. Free-cash-flow-to-equity (FCFE) is a measure of the firm’s dividend-paying capacity which should be reflected in the cash flow estimates rather than expected dividends.

Choice C is not correct. Analysts must make projections of financials to forecast future FCFE and thus the constant growth assumption as in the Gordon growth model is not an issue.

Choice A is not correct. An asset-based valuation model is not appropriate considering the high proportion of intangibles (goodwill and patents) in the firm’s assets.

27. The latest annual report of Giolias, Inc. presents the following data:

The company’s ending inventories based on LIFO are valued at $5,000,000 and a footnote to financial statements reports inventories valued using FIFO basis would be $ 6,000,000. The company’s tax rate is 30%. The un-adjusted and adjusted price-to-book values of Giolias, respectively, are closest to:

Ans: B;

28. An analyst gathers the following information about a company:

The analyst expects sales in 2012 to grow at the historical compound annual growth rate from the year 2004 to 2011. For the year 2012, the net profit margin and the number of shares outstanding are expected to remain unchanged from the year 2011. The company's earnings per share (EPS) for the year 2012 is closest to:

A. $2.77.

B. $2.83.

C. $3.96.

Ans: A;

To compute the compounded Annual Sales Growth g:

128.4 × (1+g) ⁷=220.0

g=8%

EPS 2009

= Sales 2008× (1+g) × NPM / # of shares

= 220 (1.08) (0.07) / 6

=$2.77

29. An analyst gathers the following information about a company:

Using the dividend discount model and the other data given, the company’s stock is best described as a:

A. speculative stock.

B. cyclical stock.

C. growth stock.

Ans: B;

A speculative stock is

1) Substantially overvalued.

2) Its P/E is much higher than the industry average P/E.

Intrinsic value of the stock = ??2.00 / (15%-10%) = ??44.00

where the implied dividend growth rate

= ROE × Retention Rate

= 20%×0.5

=10%.

1) current stock price (50) > intrinsic value (44) : substantially overvalued;

2) Company P/E (30x) > Industry average P/E (20x)

?? The company’s stock is best described as a speculative stock.