Corporate Finance - CH7 Study Guide

One Period Example Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year. You believe you can sell the stock for $14 at that time. You require a return of 20% on investments of this risk. What is the maximum you would be willing to pay now?

D1 = $2 dividend expected in one year R = 20% P1 = $14 CF1 = $2 + $14 = $16 Compute the PV of the expected cash flows P0 = (2+14)/1.20 = $13.33

Nonconstant Growth. 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 then pay a dividend of $19 per share 10 years from today and will increase the dividend by 5 percent per year thereafter. If the required return on this stock is 13 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 the 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 present value of an annuity and the present value of a perpetuity: The equation gives you the present value one period before the first payment. So, the price of the stock in Year 9 will be: P9 = D10 / (R - g) P9 = $19.00 / (.13 - .05) P9 = $237.50 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 = $237.50 / (1.13)^9 P0 = $79.06

Stock Valuation. Wesen Corp. will pay a dividend of $3.14 next year. The company has stated that it will maintain a constant growth rate of 4.5 percent a year forever. If you want a return of 12 percent, how much will you pay for the stock? What if you want a return of 8 percent? What does this tell you about the relationship between the required return and the stock price?

If you want a 12% return: P0 = D1 / (R-g) P0 = 3.14 / (.12-.045) P0 = $41.87 If you want an 8% return: P0 = 3.14 / (.08-.045) P0 = $89.71

Stock Valuation. Burkhardt Corp. pays a constant $13.50 dividend on its stock. The company will maintain this dividend for the next 9 years and will then cease paying dividends forever. If the required return on this stock is 9.2 percent, what is the current share price?

P0 = D1/(1+g) + D2/(1+g)^2 + D3/(1+g)^3 + ... + D9/(1+g)^9 P0 = $80.28

Stock Values. The next dividend payment by Dizzle, Inc., will be $2.48 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. If the stock currently sells for $39.85 per share, what is the required return?

R = (D1/P1) = g R = (2.48 / 39.85) + .045 R = 10.72%

Valuing Preferred Stock. Smiling Elephant, Inc., has an issue of preferred stock outstanding that pays a $3.45 dividend every year, in perpetuity. If this issue currently sells for $77.32 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. This is a special case of the dividend growth model where the growth rate is zero, or the level perpetuity equation. Using this equation, we find the price per share of the preferred stock is: R = D / P0 R = $3.45/$77.32 R = .04461, or 4.46%

Stock Valuation. Mitchell, Inc., is expected to maintain a constant 4.6 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 5.8 percent, what is the required return on the company's stock?

The required return of a stock is made up of two parts: The dividend yield and the capital gains yield. So, the required return of this stock is: R = Dividend yield + Capital gains yield R = 5.8 + 4.6 R = 10.4%

Stock Values. Take Time Corporation will pay a dividend of $3.65 per share next year. The company pledges to increase its dividend by 5.1 percent per year, indefinitely. If you require a return of 11 percent on your investment, how much will you pay for the company's stock today?

Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R - g) P0 = $3.65 / (.11 - .051) P0 = $61.86

Nonconstant Dividends. Apocalyptica Corporation is expected to pay the following dividends over the next four years: $6, $12, $17, and $3.25. Afterward, the company pledges to maintain a constant 5 percent growth rate in dividends, forever. If the required return on the stock is 11 percent, 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 present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as: P4 = D4 (1 + g) / (R - g) P4 = $3.25(1.05) / (.11 - .05) P4 = $56.875 The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be: P0 = ($6 / 1.11) + ($12 / 1.11)^2 + ($17 / 1.11)^3 + ($3.25 / 1.11)^4 + ($56.875 / 1.11)^4 P0 = $67.18

Stock Values. For the company in the previous problem, what is the dividend yield? What is the expected capital gains yield?

R = [ D0(1 + g)/P0 ] + g Dividend Yield = (D1/P0) Dividend Yield = (2.48/39.85) = 6.22% Capital Gains Yield = g [this was given]

Nonconstant Dividends. Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of $3 per share and has announced that it will increase the dividend by $5 per share for each of the next four years, and then never pay another dividend. If you require a return of 10.4 percent on the company's stock, how much will you pay for a share today?

The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends discounted at the required return. So, the price of the stock is: P0 = ($8/ 1.104) + ($13 / 1.12)^2 + ($18 / 1.104)^3 + ($23 / 1.104)^4 P0 = $46.77

Stock Valuation. Suppose you know that a company's stock currently sells for $67 per share and the required return on the stock is 11.5 percent. You also know that the total return on the stock is evenly divided between capital gains yield and 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 11.5 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.115) Dividend yield = .0575 Therefor, capital gains yield = .0575 Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D1 = .0575($67) D1 = $3.85 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: D0 = $3.85 / 1.0575 D0 = $3.64