Corporate finance chapter 9 questions

Change, Inc., is expected to maintain a constant 4.9 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 5.2 percent, what is the required return on the company's stock?

R = Dividend yield + Capital gains yield R = .049 + .052 R = .1010, or 10.10%

Stoneworks, Inc. has an odd dividend policy. The company ha just paid a dividend of $15 per share and has announced that it will increase the dividend by $3 per share for reach of the next five years, and then never pay another dividend. If you require a return of 11 percent on the company's stock, how much will you pay for a share today?

P0 = $18/1.11 + $21/1.112 + $24/1.113 + $27/1.114 + $30/1.115 P0 = $86.40

The Nearside Co. just paid a dividend of $2.07 per share on its stock. The dividends are expected to grow at a constant rate of 4.3 percent per year, indefinitely. If investors require a return of 11 percent on the stock, what is the current price? What will the price be in 3 years, in 15 years?

Pt = Dt × (1 + g)/(R - g) P0 = $32.22 P3 = P0(1 + g)3 P3 = $32.22(1 + .043)3 P3 = $36.56

The next dividend payment by Skippy, Inc., will be $2.95 per share. The dividends are anticipated to maintain a growth rate of 4.8 percent, forever. If the stock currently sells for $53.10 per share, what is the required return?

R = (D1/P0) + g R = ($2.95/$53.10) + .048 R = .1036, or 10.36%

Filth National Bank just issued some new preferred stock. The issue will pay an annual dividend of $4 in perpetuity, beginning five years from now. If the market requires a return of 4.3 percent on this investment, how much does a share of preferred stock cost today?

The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 5, so we can find the price of the stock in Year 4, one year before the first dividend payment. Doing so, we get: P4 = $4.00/.043 P4 = $93.02 The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = $93.02/(1.043)4 P0 = $78.61

Cardinal Corporation stock currently sells for $74.32 per share. The market requires a return 10.5 percent on the firms stock. If the company maintains a constant 4 percent growth rate in dividends, what was the most recent dividend per share paid on the stock?

We are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. Using the constant dividend growth model, we get: P0 = $74.32 = D0(1 + g)/(R - g) Solving this equation for the dividend gives us: D0 = $74.32(.105 - .04)/(1.04) D0 = $4.65

Fuji Co. is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. If the required return is 11 percent and the company just paid a dividend of $3.24, what is the current share price?

With differential dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the differential growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 3, one year before the constant dividend growth begins as: P3 = D3(1 + g)/(R - g) = D0(1 + g1)3(1 + g2)/(R - g2) P3 = $3.24(1.20)3(1.05)/(.11 - .05) P3 = $97.98 The price of the stock today is the PV of the first three dividends, plus the PV of the Year 3 stock price. The price of the stock today will be: P0 = $3.24(1.20)/1.11 + $3.24(1.20)2/1.112 + $3.24(1.20)3/1.113 + $97.98/1.113 P0 = $83.02

Suppose you know that a company's stock currently sells for $74 per share and the required return on the stock is 9.9 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. If its the company's policy to maintain a constant growth rate in its dividends, what is the current dividend per share? Don't have to do

Dividend yield = 1/2(.099) = .0495 = Capital gains yield D1 = .0495($74) = $3.66 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D1 = D0(1 + g) We can solve for the dividend that was just paid: $3.66 = D0(1 + .0495) D0 = $3.66/1.0495 D0 = $3.49

For the company in the previous problem, what is the dividend yield? What os the ex[ected ca[ota; gams use;d

Dividend yield = D1/P0 Dividend yield = $2.95/$53.10 Dividend yield = .0556, or 5.56% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 4.8%

Four years ago, Bling Diamond, Inc. paid a dividend of $1.65 per share. The company paid a dividend of $2.10 per share yesterday. Dividends will grow over the next five years at the same rate they grew over the last four years. Thereafter, dividends will grow at 5 percent per year. What will the company's dividend be in seven year?

FV = PV(1 + R)t $2.10 = $1.65(1 + R)4 R = ($2.10/$1.65)1/4 - 1 R = .0621, or 6.21% We know the dividend will grow at this rate for five years before slowing to a constant rate indefinitely. So, the dividend amount in seven years will be: D7 = D0(1 + g1)5(1 + g2)2 D7 = $2.10(1 + .0621)5(1 + .05)2 D7 = $3.13

Gruber Corp. pays a constant $8.50 dividend on its stock. The company will maintain this dividend for the next 11 years and will then cease paying dividends forever. If the required return on this stock is 9.6 percent, what is the current share price?

P0 = $8.50(PVIFA9.5%,11) P0 = $56.50

Bretton, Inc., just paid a dividend of $3.15 on its stock. The growth rate in dividends is expected to be a constant 4 percent per year, indefinitely. Investors require a 15 percent return on the stock for the first three years, a 13 percent return for the next three years, and then an 11 percent return thereafter. What is the current share price for the stock?

P6 = D6(1 + g)/(R - g) = D0(1 + g)7/(R - g) P6 = $3.15(1.04)7/(.11 - .04) P6 = $59.22 Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is: P3 = $3.15(1.04)41.13 + $3.15(1.04)5/1.132 + $3.15(1.04)6/1.133 + $59.22/1.133 P3 = $50.07 Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is: P0 = $3.15(1.04)/1.15 + $3.15(1.04)2/(1.15)2 + $3.15(1.04)3/(1.15)3 + $50.07/(1.15)3 P0 = $40.67

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 9 years because the firm needs to plow back its earnings to fuel growth. The company will pay a dividend of $15.75 per share in 10 years and will increase the dividend by 4.8 percent per year thereafter. If the required return on this stock is 12 percent, what is the current share price?

Here we have a stock that pays no dividends for 9 years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember that the general form of the constant dividend growth formula is: Pt = [Dt × (1 + g)]/(R - g) This means that since we will use the dividend in Year 10, we will be finding the stock price in Year 9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation gives you the PV one period before the first payment. So, the price of the stock in Year 9 will be: P9 = D10/(R - g) P9 = $15.75/(.12 - .048) P9 = $218.75 The price of the stock today is the PV of the stock price in the future. We discount the future stock price at the required return. The price of the stock today will be: P0 = $218.75/1.129 P0 = $78.88

Synovcc Corp, is experiencing rapid growth. Dividends are expected to grow at 25 percent per year during the next three years, 17 percent over the following year, and then 5 percent per year, indefinitely. The required reurn on this stock is 11 percent and the stock currently sells for $65 per share. What is the projected dividend for the coming year?

Here we need to find the dividend next year for a stock experiencing differential growth. We know the stock price, the dividend growth rates, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the current dividend times the FVIF. The dividend in Year 3 will be: D3 = D0(1.25)3 And the dividend in Year 4 will be the dividend in Year 3 times one plus the growth rate, or: D4 = D0(1.25)3(1.17) The stock begins constant growth after the 4th dividend is paid, so we can find the price of the stock in Year 4 as the dividend in Year 5, divided by the required return minus the growth rate. The equation for the price of the stock in Year 4 is: P4 = D4(1 + g)/(R - g) Now we can substitute the previous dividend in Year 4 into this equation as follows: P4 = D0(1 + g1)3(1 + g2)(1 + g3)/(R - g3) P4 = D0(1.25)3(1.17)(1.05)/(.11 - .05) P4 = 39.99D0 When we solve this equation, we find that the stock price in Year 4 is 39.99 times as large as the dividend today. Now we need to find the equation for the stock price today. The stock price today is the PV of the dividends in Years 1, 2, 3, and 4, plus the PV of the Year 4 price. So: P0 = D0(1.25)/1.11 + D0(1.25)2/1.112 + D0(1.25)3/1.113+ D0(1.25)3(1.17)/1.114 + 39.99D0/1.114 We can factor out D0 in the equation, and combine the last two terms. Doing so, we get: P0 = $65.00 = D0{1.25/1.11 + 1.252/1.112 + 1.253/1.113 + [(1.25)3(1.17) + 39.99]/1.114} Reducing the equation even further by solving all of the terms in the braces, we get: $65 = $31.67D0 D0 = $65/$31.67 D0 = $2.05 This is the dividend today, so the projected dividend for the next year will be: D1 = $2.05(1.25) D1 = $2.57

Newkirk, Inc, is expected to pay equal dividends at the end of each of the next two years. Thereafter, the dividend will grow at a constant annual rate of 3.5 percent, forever. The current stock price is $59. What is next year's dividend payiment if the required rate of return is 11 percent?

Here we need to find the dividend next year for a stock with irregular growth in dividends. We know the stock price, the dividend growth rate, and the required return, but not the dividend. First, we need to realize that the dividend in Year 3 is the constant dividend times the FVIF. The dividend in Year 3 will be: D3 = D(1.035) The equation for the stock price will be the present value of the constant dividends, plus the present value of the future stock price, or: P0 = D/1.11 + D/1.112 + D[(1.035)/(.11 - .035)]/1.112 $59 = D/1.11 + D/1.112 + D[(1.035)/(.11 - .035)]/1.112 We can factor out D0 in the equation. Doing so, we get: $59 = D{1/1.11 + 1/1.112 + [(1.035)/(.11 - .035)]/1.112} Reducing the equation even further by solving all of the terms in the braces, we get: $59 = D(12.9129) D = $59/12.9129 D = $4.57

The Rose Co. has earnings of $3.41 per share. The benchmark PE for the company is 18. What stock price would you consider appropriate? What if the benchmark PE were 21?

P = Benchmark PE ratio × EPS So, with a PE ratio of 18, we find: P = 18($3.41) P = $61.38 And with a PE ratio of 21, we find: P = 21($3.41) P = $71.61

Saine Corporation will pay a $3.25 per share dividend next year. The company pledges to increase its dividends by 5 percent per year, indefinitely. If you require a return of 10.5 percent on your investment, how much will you pay for the company's stock today?

P0 = D1/(R - g) P0 = $3.25/(.105 - .05) P0 = $59.09

Pasqually Mineral Water, Inc,. will pay a quarterly dividend per share of $.85 at the end of each of the next 12 quarters. Thereafter, the dividend will grow at a quarterly rate of 1 percent, forever. The appropriate rate of return on the stock is 10 percent, compounded quarterly. What is the current stock price?

PVA = C(PVIFAR,t) PVA = $.85(PVIFA2.5%,12) PVA = $8.72 Now we can find the present value of the dividends beyond the constant dividend phase. Using the present value of a growing annuity equation, we find: P12 = D13/(R - g) P12 = $.85(1 + .01)/(.025 - .01) P12 = $57.23 This is the price of the stock immediately after it has paid the last constant dividend. So, the present value of the future price is: PV = $57.23/(1 + .025)12 PV = $42.56 The price today is the sum of the present value of the two cash flows, so: P0 = $8.72 + 42.56 P0 = $51.28

Meteora, Inc., has an issue on preferred stock outstanding that pays a $3.75 dividend every year, in perpetuity. If this issue currently sells for $81 per share, what is the required return?

R = D/P0 R = $3.75/$81 R = .0463, or 4.63%

Antiques R Us is amateur manufacturing firm. The company just paid a dividend of $12, but management expects to reduce the payout by 4 percent per year, indefinitely. If you require a return of 9 percent on this stock, what will you pay for a share today?

The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0 (1 + g)/(R - g) P0 = $12(1 - .04)/[.09 - (-.04)] P0 = $88.62

Jupiter Satellite Corporation earned $29 million for the fiscal year ending yesterday. The firm also paid out 30 percent of its earnings as dividends yesterday. The firm will continue to pay out 30 percent of its earnings as annual, end-of-year dividends. The remaining 70 percent of earnings is retained by the company for use in projects. The company has 2.6 million shares of common stock outstanding. The current stock price is $105. The historical return on equity (rOE) of 11 percent is expected to continue in the future. What is the required rate of return on the stock?

The required return of a stock consists of two components, the capital gains yield and the dividend yield. In the constant dividend growth model (growing perpetuity equation), the capital gains yield is the same as the dividend growth rate, or algebraically: R = D1/P0 + g We can find the dividend growth rate by the growth rate equation, or: g = ROE × b g = .11 × .70 g = .0770, or 7.70% This is also the growth rate in dividends. To find the current dividend, we can use the information provided about the net income, shares outstanding, and payout ratio. The total dividends paid is the net income times the payout ratio. To find the dividend per share, we can divide the total dividends paid by the number of shares outstanding. So: Dividend per share = (Net income × Payout ratio)/Shares outstanding Dividend per share = ($29,000,000 × .30)/2,600,000 Dividend per share = $3.35 Now we can use the initial equation for the required return. We must remember that the equation uses the dividend in one year, so: R = D1/P0 + g R = $3.35(1 + .0770)/$105 + .0770 R = .1113, or 11.13%

Full Boat Manufacturing has project sales of $115 million next year. Costs are expected to be $67 million and net investment is expected to be $12 million. Each of these values is expected to grow at 14 percent the following year. With the growth rate declining by 2 percent per year until the growth rate reaches 6 percent, where it is expected to remain indefinitely. There are 5.5 million shares of stock outstanding and investors require a return of 13 percent on the company's stock. The corporate tax rate is 21 percent. a)What is your estimate of the current stock price? b) Suppose instead that you estimate the terminal value of the company using a PE multiple. The industry PE multiple is 11. What is your new estimate of your company's stock price?

To value the stock today, we first need to calculate the cash flows for the next 6 years. The sales, costs, and net investment all grow by the same rate, namely 14 percent, 12 percent, 10 percent, and 8 percent, respectively, for the following 4 years, then 6 percent indefinitely. So, the cash flows for each year will be: Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Sales $115,000,000 $131,100,000 $146,832,000 $161,515,200 $174,436,416 $184,902,601 Costs 67,000,000 76,380,000 85,545,600 94,100,160 101,628,173 107,725,863 EBT $48,000,000 $54,720,000 $61,286,400 $67,415,040 $72,808,243 $77,176,738 Taxes 10,080,000 11,491,200 12,870,144 14,157,158 15,289,731 16,207,115 Net income $37,920,000 $43,228,800 $48,416,256 $53,257,882 $57,518,512 $60,969,623 Investment 12,000,000 13,680,000 15,321,600 16,853,760 18,202,061 19,294,184 Cash flow $25,920,000 $29,548,800 $33,094,656 $36,404,122 $39,316,451 $41,675,438 To find the terminal value of the company in Year 6, we can discount the Year 7 cash flows as a growing perpetuity, which will be: Terminal value = $41,675,438(1 + .06)/(.13 - .06) Terminal value = $631,085,210 So, the value of the company today is: Company value today = $25,920,000/1.13 + $29,548,800/1.132 + $33,094,656/1.133 + $36,404,122/1.134 + $39,316,451/1.135 + ($41,675,438 + 631,085,210)/1.136 Company value today = $435,821,483 Dividing the company value by the shares outstanding to get the share price, we get: Share price = $435,821,483/5,500,000 Share price = $79.24 b. In this case, we are going to use the PE multiple to find the terminal value. All of the cash flows from part a will remain the same. So, the terminal value in Year 6 is: Terminal value = 11($60,969,623) Terminal value = $670,665,851 Under this assumption for the terminal value, the value of the company today is: Company value today = $25,920,000/1.13 + $29,548,800/1.132 + $33,094,656/1.133 + $36,404,122/1.134 + $39,316,451/1.135 + ($41,675,438 + 670,665,851)/1.136 Company value today = $454,832,798 Dividing the company value by the shares outstanding to get the share price, we get: Share price = $454,832,798/5,500,000 Share price = $82.70

Consider Pacific Energy Company and Atlantic Energy, Inc., both of which reported earnings of $720,000 in perpetuity. Assume that all earnings are paid as dividends and that both firms require a retune of 11 percent. a)what is the current PE ratio for each company? b)Pacifc Energy Company has a new project that will generate additional earnings for $150,000 each year in perpetuity. Calculate the new PE ratio of the company c)Atlantic Energy has a new project that will increase earnings by $300,000 in perpetuity. Calculate the new PE ratio of the firm.

We can find the price of all the outstanding company stock by using the dividends the same way we would value an individual share. Since earnings are equal to dividends, and there is no growth, the value of the company's stock today is the present value of a perpetuity, so: P = D/R P = $720,000/.11 P = $6,545,454.55 The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings ratio of each company with no growth is: PE = Price/Earnings PE = $6,545,454.55/$720,000 PE = 9.09 times b. Since the earnings have increased, the price of the stock will increase. The new price of the outstanding company stock is: P = D/R P = ($720,000 + 150,000)/.11 P = $7,909,090.91 The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings with the increased earnings is: PE = Price/Earnings PE = $7,909,090.91/$720,000 PE = 10.98 times c. Since the earnings have increased, the price of the stock will increase. The new price of the outstanding company stock is: P = D/R P = ($720,000 + 300,000)/.11 P = $9,272,727.27 The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings ratio with the increased earnings is: PE = Price/Earnings PE = $9,272,727.27/$720,000 PE = 12.88 times

FFDP Corp, has yearly sales of $48 million and costs $15 million. The company's balance sheet shows debt of $64 million and cash of $23 million. There are 1.95 million shares outstanding and the industry EV/EBITDA multiple is 6.4. What is the company's enterprise value? What is the stock price per share?

We need to find the enterprise value of the company. We can calculate EBITDA as sales minus costs, so: EBITDA = Sales - Costs EBITDA = $48,000,000 - 15,000,000 EBITDA = $33,000,000 Solving the EV/EBITDA multiple for enterprise value, we find: Enterprise value = $33,000,000(6.4) Enterprise value = $211,200,000 The total value of equity is the enterprise value minus any outstanding debt, plus cash, so: Equity value = Enterprise value - Debt + Cash Equity value = $211,200,000 - 64,000,000 + 23,000,000 Equity value = $170,200,000 So, the price per share is: Stock price = $170,200,000/1,950,000 Stock price = $87.28

Upton Corporation is expected to pay the following dividends over the next four years: 9$, 7$, $5.75, and 2.55. Afterwards, the company pledges to maintain a constant 4.5 percent growth rate in dividends forever. If the required return on the stock is 10 percent, what is the current share price?

With differential dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the differential growth period. The stock begins constant growth in Year 5, so we can find the price of the stock in Year 4, one year before the constant dividend growth begins, as: P4 = D4(1 + g)/(R - g) = $2.55(1.045)/(.10 - .045) P4 = $48.45 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 4 stock price. So, the price of the stock today will be: P0 = $9/1.10 + $7/1.102 + $5.75/1.103 + ($2.55 + 48.45)/1.104 P0 = $53.12

Rise Above This Corp. currently has an EPS of $3.47 and the benchmark PE for the company is 19. Earnings are expected to grow at 6 percent per year. a)what is your estimate of the current stock price? b)What is the target stock price in one year? c)Assuming the company pays no dividends, what is the implied return on the company's stock over the next year? What does this tell you about the implicit stock return using PE valuation?

a. Using the equation to calculate the price of a share of stock with the PE ratio: P = Benchmark PE ratio × EPS So, with a PE ratio of 19, we find: P = 19($3.47) P = $65.93 b. First, we need to find the earnings per share next year, which will be: EPS1 = EPS0(1 + g) EPS1 = $3.47(1 + .06) EPS1 = $3.68 Using the equation to calculate the price of a share of stock with the PE ratio: P1 = Benchmark PE ratio × EPS1 P1 = 19($3.68) P1 = $69.89 c. To find the implied return over the next year, we calculate the return as: R = (P1 - P0)/P0 R = ($69.89 - 65.93)/$65.93 R = .06, or 6% Notice that the return is the same as the growth rate in earnings. Assuming a stock pays no dividends and the ratio is constant, this will always be true when using price ratios to evaluate the price of a share of stock.

The newspaper reported last week that Bennington Enterprises earned $17.5 million this year. The report also stated that the firm's return on equity is 13 percent. The firm retains 80 percent of its earnings. What is the firm's earnings growth rate? What will next ear's earnings be?

g = ROE × b g = .13(.80) g = .1040, or 10.40% Next year's earnings = Current earnings(1 + g) Next year's earnings = $17,500,000(1 + .1040) Next year's earnings = $19,320,000