Q: Alphabet (GOOGL) has yet to pay a dividend, but in 2018 it announced it would repurchase $8.6 billion in shares over the next year. If Alphabet’s equity cost of capital is 8% and it has 700 million shares outstanding, what stock price does this correspond to?

$$\frac{8.6 \text{ billion}}{0.08} \div 700 \text{ million} = 153.57$$

Q: Suppose Sora’s revenue and free cash flow are expected to grow at a 5% rate beyond year 4. If Sora’s weighted average cost of capital is 10%, what is the value of Sora’s stock at the end of year 4 if its free cash flow in year 4 is $66 million?

$$\frac{66 \times 1.05}{0.10 - 0.05} = 1,386$$

Question 1

Evco, Inc. has a current stock price of $$50 and will pay a 2 $$dividend in one year. If its equity cost of capital is 15%, what price do you expect the stock to sell for right after paying the dividend in one year?

Accepted Answer

$$50 	imes 1.15 - 2 = 55.5$$

Question 2

Axe Corporation has a current price of $$20, is expected to pay a dividend of 1 in $$one year, and its expected price after paying that dividend is $22. What is Axe’s expected capital gain rate?

Accepted Answer

$$\frac{22 - 20}{20} = 10\%$$

Question 3

Suppose Acap Corporation will pay a dividend of $$2.80 per share at the end of this year and 3 $$per share next year. You expect Acap’s stock price to be $52 at year two. If Acap’s equity cost of capital is 10%, what is the current price of Acap stock?

Accepted Answer

$$\frac{2.80}{1.10} + \frac{3 + 52}{1.10^2$} = 2.545 + 45.45 = 47.995$$

Question 4

NetGrow Corporation currently pays a dividend of $2 per year, and it will continue to pay this dividend forever. If its equity cost of capital is 8%, what is the price per share?

Accepted Answer

$$\frac{2}{0.08} = 25$$

Question 5

Summit Systems will pay a dividend of $1.50 this year. If you expect Summit’s dividend to grow by 6% per year, what is its price per share if its equity cost of capital is 15%?

Accepted Answer

$$\frac{1.50}{0.15 - 0.06} = 16.67$$

Question 6

Dergo Corporation is a dividend growth stock. Its dividend yield is 1.5%, its equity cost of capital is 8.5%, and its dividends are expected to grow at a constant rate. What is the expected growth rate of Dergo’s dividend?

Accepted Answer

$$8.5\% - 1.5\% = 7\%$$

Question 7

Suppose General Electric (GE) paid annual dividends of $$0.97 in 2007 and 1.02 in 2008. If $$the price of GE stock at the end of 2008 was $16.67, what was the total return for a shareholder who bought at the end of 2007 and sold at the end of 2008?

Accepted Answer

Question 8

DFB, Inc. expects earnings of $$8 per share at the end of this year and plans to pay a 3 $$dividend. If its equity cost of capital is 15% and it plans to reinvest the rest of its earnings in new projects with a return equal to its cost of capital, what is the expected price of DFB’s stock at the end of this year?

Accepted Answer

Question 9

Cooperative Mining just raised its dividend from $$4.50 to 5.40 $$per share and expects to pay $5.40 per share next year. If the equity cost of capital is 10%, what is the price of Cooperative Mining’s stock?

Accepted Answer

$$\frac{5.40}{0.10} = 54$$

Question 10

If a firm’s initial dividend $$D_1$$ grows for $$n$$ years at rate $$g$$ and then at rate $$r$$ forever, with equity cost of capital $$k$$, what is the value of the firm?

Accepted Answer

$$P_0$$ = \sum_{t=1}^{n} \frac{$$D_1$$ $$(1+g)^{t-1}$$}{(1+k)^t} + \frac{D_{n+1}}{k - r} \cdot \frac{1}{(1+k)^n}$$

Question 11

Halliford Corporation expects to earn $3 per share for the next two years, retaining all earnings. For the subsequent ten years, it will pay out 50% of earnings as dividends, with earnings growing at 12% per year. If the equity cost of capital is 10%, what is the present value of Halliford’s stock at the start of year 0?

Accepted Answer

The present value is the sum of the present value of dividends in years 3-12 and the present value of the terminal value at year 12, discounted to year 0.

Question 12

Alphabet (GOOGL) has yet to pay a dividend, but in 2018 it announced it would repurchase $8.6 billion in shares over the next year. If Alphabet’s equity cost of capital is 8% and it has 700 million shares outstanding, what stock price does this correspond to?

Accepted Answer

$$\frac{8.6 	ext{ billion}}{0.08} \div 700 	ext{ million} = 153.57$$

Question 13

Maynard Steel plans to pay a dividend of $3 this year. The company has an expected earnings growth rate of 5% per year and an equity cost of capital of 10%. What is Maynard’s expected price per share?

Accepted Answer

$$\frac{3}{0.10 - 0.05} = 60$$

Question 14

Benchmark Metrics, Inc. (BMI) is expected to pay a dividend of $$1.50 per share, and its stock price is expected to be 40 at $$the end of the year. If BMI’s equity cost of capital is 8%, what is the expected total return for a shareholder?

Accepted Answer

$$\frac{1.50 + 40 - 38}{38} = 9.21\%$$

Question 15

Heavy Metal Corporation is expected to generate the following free cash flows over the next five years: $$53, 68$$, $$78, 75$$, and $82 million. If the weighted average cost of capital is 9%, what is the present value of these cash flows?

Accepted Answer

$$\sum_{t=1}^{5} \frac{FCF_t}{(1+0.09)^t}$$

Question 16

IDX Technologies is expected to have excess cash of $$110 million, debt of 80 $$million, and 50 million shares outstanding. If the enterprise value is $1,510 million, what is the equity value per share?

Accepted Answer

$$\frac{1,510 + 110 - 80}{50} = 31.8$$

Question 17

Suppose Sora’s revenue and free cash flow are expected to grow at a 5% rate beyond year 4. If Sora’s weighted average cost of capital is 10%, what is the value of Sora’s stock at the end of year 4 if its free cash flow in year 4 is $66 million?

Accepted Answer

$$\frac{66 	imes 1.05}{0.10 - 0.05} = 1,386$$

Chapter 9: Valuing Stocks: Concepts, Formulas, and Applications

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