HW 8

The Perfect Rose Co. has earnings of $3.18 per share. The benchmark PE for the company is 18. a.What stock price would you consider appropriate? b.What if the benchmark PE were 21?

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 18, we find: P = 18($3.18) P = $57.24 And with a PE ratio of 21, we find: P = 21($3.18) P = $66.78

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 30 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 11 percent, and the company just paid a dividend of $2.45, what is the current share price?

With supernormal 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 supernormal 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) P3 = D0(1 + g1)^3(1 + g2)/(R − g) P3 = $2.45(1.30)^3(1.04)/(.11 - .04) P3 = $79.97 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 = $2.45(1.30)/1.11 + $2.45(1.30)^2/1.11^2 + $2.45(1.30)^3/1.11^3 + $79.97/1.11^3 P0 = $68.64 We could also use the two-stage dividend growth model for this problem, which is: P0 = [D0(1 + g1)/(R − g1)]{1 − [(1 + g1)/(1 + R)]^t} + [(1 + g1)/(1 + R)]^t[D0(1 + g2)/(R − g2)] P0 = [$2.45(1.30)/(.11 - .30)][1 - (1.30/1.11)^3] + [(1 + .30)/(1 + .11)]^3[$2.45(1.04)/(.11 - .04)] P0 = $68.64

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years because the firm needs to plow back its earnings to fuel growth. The company will pay a dividend of $17 per share 10 years from today and will increase the dividend by 3.9 percent per year thereafter. If the required return on this stock is 12.5 percent, what is the current share price?

Here we have a stock that pays no dividends for 10 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 general 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 = $17/(.125 - .039) P9 = $197.67 The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P0 = $197.67/1.1259 P0 = $68.48

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $2.15 per share on its stock. The dividends are expected to grow at a constant rate of 4 percent per year indefinitely. Investors require a return of 10.5 percent on the company's stock. a.What is the current stock price? b.What will the stock price be in 3 years? c.What will the stock price be in 15 years?

The constant dividend growth model is: Pt = Dt × (1 + g)/(R − g) So the price of the stock today is: P0 = D0(1 + g)/(R − g) P0 = $2.15(1.04)/(.105 - .04) P0 = $34.40 The dividend at Year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so: P3 = D3(1 + g)/(R − g) P3 = D0(1 + g)^4/(R − g) P3 = $2.15(1.04)^4/(.105 - .04) P3 = $38.70 We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: P15 = D15(1 + g)/(R − g) P15 = D0(1 + g)^16/(R − g) P15 = $2.15(1.04)^16/(.105 - .04) P15 = $61.95 There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be: P3 = P0(1 + g)^3 P3 = $34.40(1 + .04)^3 P3 = $38.70 And the stock price in 15 years will be: P15 = P0(1 + g)^15 P15 = $34.40(1 + .04)^15 P15 = $61.95

The next dividend payment by Savitz, Inc., will be $2.34 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. The stock currently sells for $37 per share. a.What is the dividend yield? b.What is the expected capital gains yield?

The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1/P0 Dividend yield = $2.34/$37 Dividend yield = .0632, or 6.32% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 4.5%

Bedekar, Inc., has an issue of preferred stock outstanding that pays a $3.40 dividend every year in perpetuity. If this issue currently sells for $91 per share, what is the required return?

The price of a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is: R = D/P0 R = $3.40/$91 R = .0374, or 3.74%

Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $3.65 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company's stock is 8 percent, 11 percent, and 14 percent, respectively. What is the stock price for each company?

We can use the constant dividend growth model, which is: Pt = Dt × (1 + g)/(R - g) So the price of each company's stock today is: Red stock price = $3.65/(.08 - .04) = $91.25 Yellow stock price = $3.65/(.11 - .04) = $52.14 Blue stock price = $3.65/(.14 - .04) = $36.50 As the required return increases, the stock price decreases. This is a function of the time value of money: A higher discount rate decreases the present value of cash flows. It is also important to note that relatively small changes in the required return can have a dramatic impact on the stock price.

After successfully completing your corporate finance class, you feel the next challenge ahead is to serve on the board of directors of Schenkel Enterprises. Unfortunately, you will be the only person voting for you. If the company has 650,000 shares outstanding, and the stock currently sells for $43, how much will it cost you to buy a seat if the company uses straight voting?

If the company uses straight voting, you will need to own one-half of the shares, plus one share, in order to guarantee enough votes to win the election. So, the number of shares needed to guarantee election under straight voting will be: Shares needed = (650,000 shares/2) + 1 Shares needed = 325,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 325,001 × $43 Total cost = $13,975,043

A7X Corp. just paid a dividend of $1.55 per share. The dividends are expected to grow at 21 percent for the next eight years and then level off to a growth rate of 3.5 percent indefinitely. If the required return is 12 percent, what is the price of the stock today?

We can use the two-stage dividend growth model for this problem, which is: P0 = [D0(1 + g1)/(R − g1)]{1 − [(1 + g1)/(1 + R)]^t} + [(1 + g1)/(1 + R)]^t[D0(1 + g2)/(R − g2)] P0 = [$1.55(1.21)/(.12 - .21)][1 - (1.21/1.12)^8] + [(1.21)/(1.12)]^8[$1.55(1.035)/(.12 - .035)] P0 = $52.86

Suppose you know that a company's stock currently sells for $74 per share and the required return on the stock is 10.6 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share?

We know the stock has a required return of 10.6 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.106) = .053 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D1 = .053($74) D1 = $3.92 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: $3.92 = D0(1 + .053) D0 = $3.92/1.053 D0 = $3.72

Domergue Corp. currently has an EPS of $3.76, and the benchmark PE for the company is 21. Earnings are expected to grow at 5.1 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?

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 21, we find: P = 21($3.76) P = $78.96 b. First, we need to find the earnings per share next year, which will be: EPS1 = EPS0(1 + g) EPS1 = $3.76(1 + .051) EPS1 = $3.95 Using the equation to calculate the price of a share of stock with the PE ratio: P1 = Benchmark PE ratio × EPS1 P1 = 21($3.95) P1 = $82.99 c. To find the implied return over the next year, we calculate the return as: R = (P1 − P0)/P0 R = ($82.99 - 78.96)/$78.96 R = .051, or 5.1%

After successfully completing your corporate finance class, you feel the next challenge ahead is to serve on the board of directors of Schenkel Enterprises. Unfortunately, you will be the only person voting for you. Schenkel has 650,000 shares outstanding, and the stock currently sells for $43. Assume the company uses cumulative voting and there are four seats in the current election. How much will it cost you to buy a seat?

f the company uses cumulative voting, you will need 1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats up for election. So, the percentage of the company's stock you need will be: Percent of stock needed = 1/(N + 1) Percent of stock needed = 1/(4 + 1) Percent of stock needed = .20, or 20% So, the number of shares you need to purchase is: Number of shares to purchase = (650,000 × .20) + 1 Number of shares to purchase = 130,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 130,001 × $43 Total cost = $5,590,043