Chapter 13 Self-Study

You find the following data on an Internet stock site: Firm XYZ Share price: $13.50 Common Shares outstanding (mil): 10,002 Sales (mil): $45,030 Net Income (mil): $12,542 Based on this data, the firm's market capitalization is __________ million and this number is the _____________. a. $135,027; market value of equity b. $135,027; book value of equity c. $607,905; price to sales d. $607,905; liquidation value

a. $135,027; market value of equity The market capitalization = $12.50 x 9,802 = $122,525 and this number is the market value of equity.

An analyst has the following estimates of cash flows for a firm (mill). Year After tax EBIT Depreciation CapEx Increase in NWC 1 $165 $56 $69 $10 2 $115 $21 $28 $30 3 $121 $28 $18 $10 4 $142 $22 $0 $28 The firm has an after tax cost of debt of 4% and a cost of equity of 16%. The firm uses 60% debt and 40% equity. From year 4 on the firm's FCFF will grow at a 7% rate per year. The market value of the firm's debt is $2,080 million. What is the market value of equity? a. $4,077 b. $6,157 c. $3,898 d. $4,032

a. $4,077 Free Cash Flow from a Firm or FCFF = After Tax EBIT + Depreciation - Capital Expenditures - Increases in Net Working Capital. In this case: Year FCFFt 1 $142 2 $78 3 $121 4 $136 From this point on FCFF is projected to grow at 5% per year so FCFF5 = $136(1.07) = $145.52. Firm value can now be estimated from: The WACC = a weighted average of the firm's funds costs = 0.6(4%) + 0.4(16%) = 8.8% The Terminal Value P4 = FCFF5 / (WACC - g) = $145.52 / ( 0.088 - 0.07) = $8,084.44 Firm Value= ($142/1.088)+($78/1.088^2)+($121/1.088^3)+($136/1.088^4)+($8084.44/1.088^4) =$6,156.87 The equity value = $6,156.87 - $2,080 = $4,076.87

A firm has earnings before interest and taxes of $61 million, has a corporate tax rate of 30%, depreciation expense of $13 million, increases in NWC of $3 million and capital expenditures of $6 million. What is the firm's free cash flow in millions? a. $46.70 b. $49.70 c. $68.50 d. $59.70

a. $46.70 Free Cash Flow from a Firm or FCFF = EBIT(1 - TC) + Depreciation - Capital Expenditures - Increases in Net Working Capital where TC = corporate tax rate. In this case FCFF = $61(1 - 0.30) + $13 - $6 - $3 = $46.70 million.

P/E and Value You are considering buying and holding a stock for 3 years. If k = 13% and you have the following estimates: Year Dividend Earnings P/E 1 0.89 2 1.06 3 1.26 3.10 22 4 4.40 What is the intrinsic value of the stock today? a. $69.58 b. $63.38 c. $67.79 d. $66.04

a. $69.58 ($0.89/1.13)+($1.06/1.13^2)+($1.26/1.13^3)+((22*$4.40)/1.13^3)=$69.58

A firm is expected to pay an annual dividend of $.90 next year. After next year the firm's dividends will grow at a steady state rate of 3% per year. You are trying to value the stock and Value Line lists a stock beta of 1.71 while Yahoo is reporting a beta of 1.68. The stock is currently priced at $11.30. If E(RM) - Rf = 8.0% and the risk free rate is 2.4% the stock is ____________________ if you use the Value Line beta and is ____________________ if you use the Yahoo beta. a. overpriced by $4.42; overpriced by $4.29 b. underpriced by $1.43; underpriced by $1.13 c. underpriced by $1.13; underpriced by $1.43 d. overpriced by $4.29; overpriced by $4.42

a. overpriced by $4.42; overpriced by $4.29 The required rate of return using the Value Line beta = rf + β[E(rM) - rf] = 2.4% + 1.71 (8.0%) = 16.08%. The intrinsic value V0 = (D1 + P1)/(1+k); P1 = D2/(k-g); thus P1 = $.90 (1.03)/.1608 - .03) = $7.0872. V0 = ($.90 + $7.0872)/1.1608 = $6.8807. Using the Value Line beta the stock is overpriced by $11.30-$6.88 = $4.42. The required rate of return using the Yahoo beta = rf + β[E(rM) - rf] = 2.4% + 1.68 (8.0%) = 15.840%. The intrinsic value V0 = (D1 + P1)/(1+k); P1 = D2/(k-g); thus P1 = $7.09 (1.03)/(.15840 - 7.09) = $7.21963. V0 = ($.90 + $7.08716)/1.15840 = $7.0093. Using the Yahoo beta the stock is overpriced by $11.30 - $7.0093 = $4.29.

A firm projects that dividends will grow at a rate of 12% per year for four years and then will grow at a rate of 7% per year forever. The stock's required return is 14% and the last annual dividend paid was $1.90. The most an investor should be willing to pay for this stock today is ______. (Watch your rounding, carry out dividends to four or more decimal places.) a. $32.39 b. $34.33 c. $39.00 d. $37.67

b. $34.33 here Do = $1.90; T = 4; g1 = 12%; g2 = 7%; k=14% D0 = $1.90; D1 = $1.90(1.12) = $2.13; D2 = $2.13(1.12) = $2.3834; D3 = $2.3834(1.12) = $2.6694; D4 = $2.6694(1.12) = $2.9897

JJ Industries retains 30% of its income. Last year's EPS was $2.45 and ROE is 10%. Investors require a 8% return on this stock. What is the intrinsic value of the stock? a. $30.26 b. $35.33 c. $32.71 d. $31.05

b. $35.33 g = ROE x b = 0.10(0.30) = 3%. The P/E = (1 - b) / (k - g) = 0.70 / (0.08 - 0.03) = 14. With E0 = $2.45 we can find V0 = P/E x E1 or P/E x E0(1+g) = 14($2.45)(1.03) = $35.33

A firm has projected earnings of $7 per share for next year and has a 60% dividend payout ratio. The firm's required return is 13%. The firm's ROE is 14%. What is the intrinsic value of the stock? a. $49.06 b. $56.76 c. $51.28 d. $54.84

b. $56.76 b = the plowback ratio or 1 - the dividend payout ratio = 1 - 60% = 40%. g = ROE x b, thus g = 14% x 40% = 5.60%; D1 = $7(0.60) = $4.20. V0 = $4.20 / (0.13 - 0.056) = $56.76.

A firm has projected annual earnings per share of $4.60 and a dividend payout ratio of 55%. The firm's required return is 13% and dividends and earnings are expected to grow at 5% per year indefinitely. For this firm the present value of its growth opportunities is ________. a. $7.52 b. $67.01 c. $70.30 d. $59.49

b. $67.01 PVGO = [D1/(k-g)] - E1/k = 0.55($4.60) / (0.13 - 0.05) - ($4.60 / 0.13) = $67.01

A firm has positive ROE but zero growth in earnings. The stock is priced at $36.40 and has earnings of $3.40 per share. What is the firm's required return and optimal retention ratio? a. 9.34%; 1 b. 9.34% ; 0 c. 10.71%; 0 d. 10.71%; 1

b. 9.34% ; 0 1 / required return is equal to the P/E ratio in the no growth case thus k = $3.40 / $36.40 = 9.34%. g = ROE x b and with a positive ROE and zero growth b must equal 0.

At the beginning of 2010 stock of Boatright Stores is projecting the following dividends Year Dividend 2010 1.35 2011 1.51 2012 1.67 After this dividend growth will be steady. Value Line forecasts a retention rate of 10% and a long term ROE of 6%. The required return for Boatright is 14%. The intrinsic value of Boatright is ________. a. $-3.09 b. $-0.85 c. $11.94 d. $10.79

c. $11.94 g2 = ROE x b = 6%(0.1) = 0.6%

This year a firm has FCFF of $11.75 million. The firm has interest expense of $3 million and is in a 34% tax bracket and debt increased by $4 million. The firm's free cash flow to equity is ____________ million. a. $11.75 b. $9.77 c. $13.77 d. $4.75

c. $13.77 Free Cash Flow to Equity FCFE = FCFF - Interest Expense(1 - TC) + Increase in Net Debt = $11.75 - $3(1 - 0.34) + $4 = $13.77.

A stock just paid a dividend of $0.90 per share. Dividends are expected to grow at a constant rate of 7% per year forever. Investors expect and require a 11% return on this investment. The intrinsic value of this stock is __________. a. $23.83 b. $23.52 c. $24.08 d. $23.63

c. $24.08 V0 = D1 / (k - g) = (0.90(1.07)) / (0.11 - 0.07) = $24.08

Downloads for Cheap, Inc. has a new business that allows customers to download music and movies directly onto their IPhones or MP3 players in grocery stores. The downloaded items can be played on their TVs or computers at home. The firm is in the high growth phase and does not currently pay dividends. Managers are estimating that the firm will begin paying an annual dividend per share of $1.80 in four years and that dividends will then grow at 8% per year thereafter. What is the most you should be willing to pay for the stock today if the required return on the stock is 10%? a. $68.28 b. $2.00 c. $67.62 d. $66.76

c. $67.62 V0 = D4 /[(k-g)(1+k)3]= $1.80 /[(0.10 - 0.08)(1.103)] = $67.62

A firm has a book value of assets of $410 million, book value of liabilities of $370 million, replacement cost of the assets of $433 million and replacement cost of the liabilities of $390 million. The stock's current market value at today's stock price is $52 million. The Tobin's Q ratio for this firm is equal to ______. a. 1.110 b. 1.300 c. 1.2090 d. 1.514

c. 1.2090 The Tobin's Q ratio = Market Value/Replacement Cost. This ratio = $52m/($433m − $390m) = 1.2090

Daisy Pixie Stix pays out 60% of its earnings as dividends. The firm has been earnings $0.14 cents per dollar of equity invested in the firm and investors require a 8.25% return. The last annual earnings were $5.00 per share. What is the P/E ratio of the stock? a. 31.31 b. 53.30 c. 22.64 d. 44.96

c. 22.64 g = ROE x b = 0.14(1 - 0.60) = 5.6%. The P/E = (1 - b) / (k - g) = 0.60 / (0.0825 - 0.056) = 22.64

A firm has a constant dividend payout ratio. Last year the firm had net income of $50 million and paid out dividends of $20 million. The firm's return on equity is expected to be 12% for the foreseeable future. This stock's growth rate in dividends (g) should be ______. a. 5.85% b. 4.80% c. 7.20% d. 8.25%

c. 7.20% g = ROE x b, where b = the plowback ratio or 1 - the dividend payout ratio. The firm's dividend payout ratio = $20m / $50m = 40%, so b = 1 - 40% = 60%. Thus g = 12% x 60% = 7.20%

You plan on holding a stock for two years. The annual dividend per share is $0.15 and you believe you will be able to sell the stock in two years for $39.00. You believe this stock should pay a 10% rate of return per year. If the stock is currently priced at $36.00 the stock is __________________. a. undervalued by more than 5% b. undervalued by less than 5% c. overvalued by more than 5% d. overvalued by less than 5%

c. overvalued by more than 5% For a two year holding period the stock's intrinsic value today = ($0.15 / 1.10) + (($0.15 + $39.00) / 1.102) = $32.49. The actual price is $36.00 so the stock is more than 5% overvalued by ($32.49 - $36.00) / $32.49 = 9.75%, which is more than 5%.

Harley Davidson stock has a beta of 1.82. The market risk premium is 8% and the risk free rate is 3%. What is Harley's required rate of return? a. 11.70% b. 14.56% c. 13.95% d. 17.56%

d. 17.56% The required return is calculated from the Capital Asset Pricing Model (CAPM) = rf + β[E(rM) - rf]. The [E(rM) - rf] term is often called the market risk premium. Thus the required return = 3% + 1.82(8%) = 17.56%

A stock is expected to pay a dividend per share of $0.84 next year and you believe the stock will sell for $26.50 in one year. You bought the stock for $20.10. Your expected return on the stock is ______. a. 33.35% b. 34.03% c. 32.59% d. 36.02%

d. 36.02% The expected return = [$0.84 + $26.50 - $20.10] / $20.10 = 36.02%.

Firm A has an ROE of 9% and Firm B has an ROE of 12%. Both stocks have a required return of 9%. Ignoring risk and taxes the optimal dividend payout for Firm A is ______ and the optimal dividend payout for Firm B is ______. a. irrelevant; irrelevant b. < 100%; < 100% c. 100%; 100% d. irrelevant; < 100%

d. irrelevant; < 100% irrelevant since the required return for Firm A = ROEA; < 100% since ROEB > required return for B.

A stock has an expected dividend yield of 4% a price today of $31 and an expected sale price in one year of $32. The stock has a beta of 1.3 and the expected return on the market is 9% while the risk free rate is 6%. This stock is _____________ by ________ basis points. a. undervalued; 78 b. overvalued; 78 c. undervalued; 267 d. overvalued; 267

d. overvalued; 267 The stock's expected return = 4% dividend yield + capital gain yield of ($32-$31)/$31 = 7.23%. The stock's required return from the CAPM = rf + β[E(rM) - rf]. Thus the required return = 4% + 1.3(9%-6%) = 9.90%. The stock's expected return is < the required return so the stock is overvalued by 9.90% - 7.23% = 267 basis points.

A perpetual preferred stock pays an annual dividend of $2.80 per share and investors require an 8% return. The intrinsic value of a share of this stock is _______. a. $35.00 b. $ 22.40 c. $30.24 d. $31.43

a. $35.00 V0 = $2.80 / 0.08 = $35.00

A stock has a required return of 14%, a dividend of $.50 per share and an expected sale price in one year of $33.00. The intrinsic value of this stock is _______. a. $49.35 b. $29.39 c. $50.14 d. $47.33

b. $29.39 The intrinsic value (V0) = [(E(D1) + E(P1)] / (1+k) = ($0.50 + $33.00) / 1.14 = $29.39

A firm's balance sheet indicates current assets of $79 million and fixed assets of $161 million. The balance sheet also indicates current liabilities of $62 million and long term debt of $70 million. If the current assets were liquidated they would bring in $79 million and if the fixed assets could be sold for $136 million. The market value of current liabilities is $60 million and the market value of the long term debt is $80 million. The firm's book value of equity is equal to ______ million and the firm's market value of equity is equal to ______ million. a. $8; $79 b. $79; $8 c. $75; $108 d. $108; $75

d. $108; $75 The book value of equity is equal to the balance sheet value of assets minus the balance sheet value of liabilities or ($79m + $161m) − ($62m + $70m) = $108m. The market value or liquidation value is the market value of the assets minus the market value of the liabilities or ($79m + $136m) − ($60m + $80m) = $75m.