STOCKS AND THEIR VALUATION EXERCISE

(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)

Note that there is some overlap between the T/F and the multiple choice questions, as some T/F statements are used in the MC questions. See the preface for information on the AACSB letter indicators (F, M, etc.) on the subject lines.

Multiple Choice: True/False

(10-1) Proxy F G Answer: a EASY1. A proxy is a document giving one party the authority to act for another

party, including the power to vote shares of common stock. Proxies can be important tools relating to control of firms.

a. Trueb. False

(10-1) Preemptive right F G Answer: a EASY2. The preemptive right gives current stockholders the right to purchase,

on a pro rata basis, any new shares issued by the firm. This right helps protect current stockholders against both dilution of control and dilution of value.

a. Trueb. False

(10-1) Preemptive right F G Answer: b EASY3. If a firm's stockholders are given the preemptive right, this means that

stockholders have the right to call for a meeting to vote to replace the management. Without the preemptive right, dissident stockholders would have to seek a change in management through a proxy fight.

a. Trueb. False

(10-2) Classified stock F G Answer: a EASY4. Classified stock differentiates various classes of common stock, and

using it is one way companies can meet special needs such as when owners of a start-up firm need additional equity capital but don't want to relinquish voting control.

a. True

1. (10-1) Proxy F G Answer: a EASY

2. (10-1) Preemptive right F G Answer: a EASY

3. (10-1) Preemptive right F G Answer: b EASY

4. (10-2) Classified stock F G Answer: a EASY

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CHAPTER 10STOCKS AND THEIR VALUATION

b. False

(10-2) Founders' shares F G Answer: a EASY5. Founders' shares are a type of classified stock where the shares are

owned by the firm's founders, and they generally have more votes per share than the other classes of common stock.

a. Trueb. False

(10-4) Total stock returns F G Answer: b EASY6. The total return on a share of stock refers to the dividend yield less

any commissions paid when the stock is purchased and sold.

a. Trueb. False

(10-4) Common stock cash flows F G Answer: a EASY7. The cash flows associated with common stock are more difficult to

estimate than those related to bonds because stock has a residual claim against the company versus a contractual obligation for a bond.

a. Trueb. False

(10-4) Stock valuation F G Answer: b EASY8. According to the basic DCF stock valuation model, the value an investor

should assign to a share of stock is dependent on the length of time he or she plans to hold the stock.

a. Trueb. False

(10-4) Marginal investor and price F G Answer: a EASY9. When a new issue of stock is brought to market, it is the marginal

investor who determines the price at which the stock will trade.

a. Trueb. False

(10-5) Constant growth model F G Answer: a EASY10. The constant growth DCF model used to evaluate the prices of common

stocks is conceptually similar to the model used to find the price of perpetual preferred stock or other perpetuities.

a. Trueb. False

(10-6) Nonconstant growth model F G Answer: a EASY11. According to the nonconstant growth model discussed in the textbook, the

discount rate used to find the present value of the expected cash flows during the initial growth period is the same as the discount rate used to find the PVs of cash flows during the subsequent constant growth

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period.

a. Trueb. False

(10-7) Corporate valuation model F G Answer: b EASY12. The corporate valuation model can be used only when a company doesn't

pay dividends.

a. Trueb. False

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(10-7) Corporate valuation model F G Answer: b EASY13. The corporate valuation model cannot be used unless a company pays

dividends.

a. Trueb. False

(10-7) Free cash flows and valuation F G Answer: a EASY14. Projected free cash flows should be discounted at the firm's weighted

average cost of capital to find the firm’s total corporate value.

a. Trueb. False

(10-8) Preferred stock F G Answer: b EASY15. Preferred stock is a hybrid--a sort of cross between a common stock and

a bond--in the sense that it pays dividends that normally increase annually like a stock but its payments are contractually guaranteed like interest on a bond.

a. Trueb. False

(10-8) Preferred stock F G Answer: a EASY16. From an investor's perspective, a firm's preferred stock is generally

considered to be less risky than its common stock but more risky than its bonds. However, from a corporate issuer's standpoint, these risk relationships are reversed: bonds are the most risky for the firm, preferred is next, and common is least risky.

a. Trueb. False

Multiple Choice: Conceptual

Some of the questions require calculations.

(10-5) Constant growth model C G Answer: c EASY17. Which of the following statements is CORRECT?

13. (10-7) Corporate valuation model F G Answer: b EASY

14. (10-7) Free cash flows and valuation F G Answer: a EASY

15. (10-8) Preferred stock F G Answer: b EASY

Preferred dividends don't normally grow, and they are not guaranteed.

16. (10-8) Preferred stock F G Answer: a EASY

17. (10-5) Constant growth model C G Answer: c EASY

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a. The constant growth model is often appropriate for evaluating start-up companies that do not have a stable history of growth but are expected to reach stable growth within the next few years.

b. If a stock has a required rate of return rs = 12% and its dividend is expected to grow at a constant rate of 5%, this implies that the stock’s dividend yield is also 5%.

c. The stock valuation model, P0 = D1/(rs - g), can be used to value firms whose dividends are expected to decline at a constant rate, i.e., to grow at a negative rate.

d. The price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.

e. The constant growth model cannot be used for a zero growth stock, where the dividend is expected to remain constant over time.

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(10-5) Required return C G Answer: e EASY18. An increase in a firm’s expected growth rate would cause its required

rate of return to

a. increase.b. decrease.c. fluctuate less than before.d. fluctuate more than before.e. possibly increase, possibly decrease, or possibly remain constant.

(10-5) Required return C G Answer: c EASY19. If in the opinion of a given investor a stock’s expected return exceeds

its required return, this suggests that the investor thinks

a. the stock is experiencing supernormal growth.b. the stock should be sold.c. the stock is a good buy.d. management is probably not trying to maximize the price per share.e. dividends are not likely to be declared.

(10-1) Preemptive right C G Answer: d MEDIUM20. The preemptive right is important to shareholders because it

a. allows managers to buy additional shares below the current market price.

b. will result in higher dividends per share.c. is included in every corporate charter.d. protects the current shareholders against a dilution of their

ownership interests.e. protects bondholders, and thus enables the firm to issue debt with a

relatively low interest rate.

(10-2) Classified stock C G Answer: e MEDIUM21. Companies can issue different classes of common stock. Which of the

following statements concerning stock classes is CORRECT?

a. All common stocks fall into one of three classes: A, B, and C.b. All common stocks, regardless of class, must have the same voting

rights.c. All firms have several classes of common stock.d. All common stock, regardless of class, must pay the same dividend.e. Some class or classes of common stock are entitled to more votes per

share than other classes.

18. (10-5) Required return C G Answer: e EASY

19. (10-5) Required return C G Answer: c EASY

20. (10-1) Preemptive right C G Answer: d MEDIUM

21. (10-2) Classified stock C G Answer: e MEDIUM


(10-5) Required return C G Answer: b MEDIUM22. Stocks A and B have the following data. Assuming the stock market is

efficient and the stocks are in equilibrium, which of the following statements is CORRECT?

A B Required return 10% 12%Market price $25 $40Expected growth 7% 9%

a. These two stocks should have the same price.b. These two stocks must have the same dividend yield.c. These two stocks should have the same expected return.d. These two stocks must have the same expected capital gains yield.e. These two stocks must have the same expected year-end dividend.

(10-5) Required return C G Answer: e MEDIUM23. Stocks A and B have the following data. Assuming the stock market is


A B Price $25 $40Expected growth 7% 9%Expected return 10% 12%

a. The two stocks should have the same expected dividend.

22

?. (10-5) Required return C G Answer: b MEDIUM

The following calculations show that answer b is correct. The others are all wrong.

A B Expected return 10% 12%Expected growth 7% 9%Dividend yield 3% 3%

23. (10-5) Required return C G Answer: e MEDIUM

The following calculations show that answer e is correct. The others are all wrong.

A B Price $25 $40Expected growth 7% 9%Expected return 10% 12%A = P0 = D1/(r – g) = D1=P0(r) – P0(g) = $0.75B = P0 = D1/(r – g) = D1=P0(r) – P0(g) = $1.20


b. The two stocks could not be in equilibrium with the numbers given in the question.

c. A's expected dividend is $0.50.d. B's expected dividend is $0.75.e. A's expected dividend is $0.75 and B's expected dividend is $1.20.

(10-5) Dividend yield and g C G Answer: a MEDIUM24. Stocks A and B have the same price and are in equilibrium, but Stock A

has the higher required rate of return. Which of the following statements is CORRECT?

a. If Stock A has a lower dividend yield than Stock B, its expected capital gains yield must be higher than Stock B’s.

b. Stock B must have a higher dividend yield than Stock A.c. Stock A must have a higher dividend yield than Stock B.d. If Stock A has a higher dividend yield than Stock B, its expected

capital gains yield must be lower than Stock B’s.e. Stock A must have both a higher dividend yield and a higher capital

gains yield than Stock B.


(10-5) Dividend yield and g C G Answer: b MEDIUM25. Two constant growth stocks are in equilibrium, have the same price, and

have the same required rate of return. Which of the following statements is CORRECT?

a. The two stocks must have the same dividend per share.b. If one stock has a higher dividend yield, it must also have a lower

dividend growth rate.c. If one stock has a higher dividend yield, it must also have a higher

dividend growth rate.d. The two stocks must have the same dividend growth rate.e. The two stocks must have the same dividend yield.

(10-5) Dividend yield and g C G Answer: a MEDIUM26. Which of the following statements is CORRECT, assuming stocks are in

equilibrium?

a. The dividend yield on a constant growth stock must equal its expected total return minus its expected capital gains yield.

b. Assume that the required return on a given stock is 13%. If the stock’s dividend is growing at a constant rate of 5%, its expected dividend yield is 5% as well.

c. A stock’s dividend yield can never exceed its expected growth rate.d. A required condition for one to use the constant growth model is that

the stock’s expected growth rate exceeds its required rate of return. e. Other things held constant, the higher a company’s beta coefficient,

the lower its required rate of return.

(10-5) Declining constant growth C G Answer: e MEDIUM27. A stock is expected to pay a year-end dividend of $2.00, i.e., D1 =

$2.00. The dividend is expected to decline at a rate of 5% a year forever (g = -5%). If the company is in equilibrium and its expected and required rate of return is 15%, which of the following statements is CORRECT?

a. The company’s current stock price is $20.b. The company’s dividend yield 5 years from now is expected to be 10%.c. The constant growth model cannot be used because the growth rate is

negative.d. The company’s expected capital gains yield is 5%.e. The company’s expected stock price at the beginning of next year is

$9.50.


(10-5) Constant growth model C G Answer: a MEDIUM28. Which of the following statements is CORRECT?

a. The constant growth model takes into consideration the capital gains investors expect to earn on a stock.

b. Two firms with the same expected dividend and growth rate must also have the same stock price.

c. It is appropriate to use the constant growth model to estimate a stock's value even if its growth rate is never expected to become constant.

d. If a stock has a required rate of return rs = 12%, and if its dividend is expected to grow at a constant rate of 5%, this implies that the stock’s dividend yield is also 5%.

e. The price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.

(10-5) Constant growth model C G Answer: e MEDIUM29. If a stock’s dividend is expected to grow at a constant rate of 5% a

year, which of the following statements is CORRECT? The stock is in equilibrium.

a. The expected return on the stock is 5% a year.b. The stock’s dividend yield is 5%.c. The price of the stock is expected to decline in the future.d. The stock’s required return must be equal to or less than 5%.e. The stock’s price one year from now is expected to be 5% above the

current price.

(10-5) Constant growth model C G Answer: a MEDIUM30. Stocks A and B have the following data. Assuming the stock market is


A B Price $25 $25Expected growth (constant) 10% 5%Required return 15% 15%

a. Stock A's expected dividend at t = 1 is only half that of Stock B.b. Stock A has a higher dividend yield than Stock B.c. Currently the two stocks have the same price, but over time Stock B's

price will pass that of A.d. Since Stock A’s growth rate is twice that of Stock B, Stock A’s

future dividends will always be twice as high as Stock B’s.e. The two stocks should not sell at the same price. If their prices

are equal, then a disequilibrium must exist.


(10-5) Constant growth model C G Answer: c MEDIUM31. Stocks X and Y have the following data. Assuming the stock market is


X Y Price $30 $30Expected growth (constant) 6% 4%Required return 12% 10%

a. Stock X has a higher dividend yield than Stock Y.b. Stock Y has a higher dividend yield than Stock X.c. One year from now, Stock X’s price is expected to be higher than

Stock Y’s price.d. Stock X has the higher expected year-end dividend.e. Stock Y has a higher capital gains yield.

(10-5) Constant growth model C G Answer: b MEDIUM32. Stock X has the following data. Assuming the stock market is efficient

and the stock is in equilibrium, which of the following statements is CORRECT?

Expected dividend, D1 $3.00Current Price, P0 $50Expected constant growth rate 6.0%

a. The stock’s required return is 10%.b. The stock’s expected dividend yield and growth rate are equal.c. The stock’s expected dividend yield is 5%.d. The stock’s expected capital gains yield is 5%.e. The stock’s expected price 10 years from now is $100.00.

(10-5) Constant growth model C G Answer: b MEDIUM33. Stocks X and Y have the following data. Assuming the stock market is


X Y Price $25 $25Expected dividend yield 5% 3%Required return 12% 10%

a. Stock Y pays a higher dividend per share than Stock X.b. Stock X pays a higher dividend per share than Stock Y.c. One year from now, Stock X should have the higher price.d. Stock Y has a lower expected growth rate than Stock X.e. Stock Y has the higher expected capital gains yield.


(10-5) Constant growth model C G Answer: d MEDIUM34. The expected return on Natter Corporation’s stock is 14%. The stock’s

dividend is expected to grow at a constant rate of 8%, and it currently sells for $50 a share. Which of the following statements is CORRECT?

a. The stock’s dividend yield is 7%.b. The stock’s dividend yield is 8%.c. The current dividend per share is $4.00.d. The stock price is expected to be $54 a share one year from now.e. The stock price is expected to be $57 a share one year from now.

(10-5) Constant growth model and CAPM C G Answer: b MEDIUM35. Stocks A and B have the following data. The market risk premium is 6.0%

and the risk-free rate is 6.4%. Assuming the stock market is efficient and the stocks are in equilibrium, which of the following statements is CORRECT?

A B Beta 1.10 0.90Constant growth rate 7.00% 7.00%

a. Stock A must have a higher stock price than Stock B.b. Stock A must have a higher dividend yield than Stock B.c. Stock B’s dividend yield equals its expected dividend growth rate.d. Stock B must have the higher required return.e. Stock B could have the higher expected return.

(10-7) Corporate valuation model C G Answer: b MEDIUM36. Which of the following statements is NOT CORRECT?

a. The corporate valuation model can be used both for companies that pay dividends and those that do not pay dividends.

b. The corporate valuation model discounts free cash flows by the required return on equity.

c. The corporate valuation model can be used to find the value of a division.

d. An important step in applying the corporate valuation model is forecasting the firm's pro forma financial statements.

e. Free cash flows are assumed to grow at a constant rate beyond a specified date in order to find the horizon, or continuing, value.

(10-7) Corporate valuation model C G Answer: a MEDIUM37. Which of the following statements is CORRECT?

a. To implement the corporate valuation model, we discount projected free cash flows at the weighted average cost of capital.

b. To implement the corporate valuation model, we discount net operating profit after taxes (NOPAT) at the weighted average cost of capital.

c. To implement the corporate valuation model, we discount projected net income at the weighted average cost of capital.

d. To implement the corporate valuation model, we discount projected free cash flows at the cost of equity capital.

e. The corporate valuation model requires the assumption of a constant growth rate in all years.



(10-8) Preferred stock concepts C G Answer: b MEDIUM38. Which of the following statements is CORRECT?

a. Preferred stockholders have a priority over bondholders in the event of bankruptcy to the income, but not to the proceeds in a liquidation.

b. The preferred stock of a given firm is generally less risky to investors than the same firm’s common stock.

c. Corporations cannot buy the preferred stocks of other corporations.d. Preferred dividends are not generally cumulative.e. A big advantage of preferred stock is that dividends on preferred

stocks are tax deductible by the issuing corporation.

(10-8) Preferred stock concepts C G Answer: b MEDIUM39. Which of the following statements is CORRECT?

a. A major disadvantage of financing with preferred stock is that preferred stockholders typically have supernormal voting rights.

b. Preferred stock is normally expected to provide steadier, more reliable income to investors than the same firm’s common stock, and, as a result, the expected after-tax yield on the preferred is lower than the after-tax expected return on the common stock.

c. The preemptive right is a provision in all corporate charters that gives preferred stockholders the right to purchase (on a pro rata basis) new issues of preferred stock.

d. One of the disadvantages to a corporation of owning preferred stock is that 70% of the dividends received represent taxable income to the corporate recipient, whereas interest income earned on bonds would be tax free.

e. One of the advantages to financing with preferred stock is that 70% of the dividends paid out are tax deductible to the issuer.

(Comp.) Common stock concepts C G Answer: c MEDIUM40. Which of the following statements is CORRECT?

a. If a company has two classes of common stock, Class A and Class B, the stocks may pay different dividends, but under all state charters the two classes must have the same voting rights.

b. The preemptive right gives stockholders the right to approve or disapprove of a merger between their company and some other company.

c. The preemptive right is a provision in the corporate charter that gives common stockholders the right to purchase (on a pro rata basis) new issues of the firm's common stock.

d. The stock valuation model, P0 = D1/(rs - g), cannot be used for firms that have negative growth rates.

e. The stock valuation model, P0 = D1/(rs - g), can be used only for firms whose growth rates exceed their required return.


(Comp.) Common stock concepts C G Answer: a MEDIUM41. The required returns of Stocks X and Y are rX = 10% and rY = 12%. Which

of the following statements is CORRECT?

a. If the market is in equilibrium, and if Stock Y has the lower expected dividend yield, then it must have the higher expected growth rate.

b. If Stock Y and Stock X have the same dividend yield, then Stock Y must have a lower expected capital gains yield than Stock X.

41. (Comp.) Common stock concepts C G Answer: a MEDIUM

Since X has the lower required return, if Y has a lower dividend yield it must have a higher expected growth rate.

5. (10-2) Founders' shares F G Answer: a EASY

6. (10-4) Total stock returns F G Answer: b EASY

7. (10-4) Common stock cash flows F G Answer: a EASY

8. (10-4) Stock valuation F G Answer: b EASY

9. (10-4) Marginal investor and price F G Answer: a EASY

10. (10-5) Constant growth model F G Answer: a EASY

11. (10-6) Nonconstant growth model F G Answer: a EASY

12. (10-7) Corporate valuation model F G Answer: b EASY

24. (10-5) Dividend yield and g C G Answer: a MEDIUM

Statement a is true, because if the required return for Stock A is higher than that of Stock B, and if the dividend yield for Stock A is lower than Stock B’s, the growth rate for Stock A must be higher to offset this.

25. (10-5) Dividend yield and g C G Answer: b MEDIUM

26. (10-5) Dividend yield and g C G Answer: a MEDIUM

27. (10-5) Declining constant growth C G Answer: e MEDIUM

Note that P0 = $2/(0.15 + 0.05) = $10. That price is expected to decline by 5% each year, so P1 must be $10(0.95) = $9.50. Therefore, answer e is correct, while the others are all false.

28. (10-5) Constant growth model C G Answer: a MEDIUM

Statement a is true, because the expected growth rate is also the expected capital gains yield. All the other statements are false.

29. (10-5) Constant growth model C G Answer: e MEDIUM

Statement e is true, because the stock price is expected to grow at the dividend growth rate.

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c. If Stock X and Stock Y have the same current dividend and the same expected dividend growth rate, then Stock Y must sell for a higher price.

d. The stocks must sell for the same price.e. Stock Y must have a higher dividend yield than Stock X.

Multiple Choice: Problems

Most of these problems are straightforward and only moderately difficult. However, a few of the later ones are relatively difficult and should be used primarily on take-home exams for students with some experience with Excel. Problems with * in the topic line are nonalgorithmic.

30. (10-5) Constant growth model C G Answer: a MEDIUM

Statement a is correct, because if both stocks have the same price and the same required return, and A’s growth rate is twice that of B, then A’s dividend and dividend yield must be half that of B. This point is illustrated with the following example.

A B Price $25 $25g 10% 5%r 15% 15%Div. Yield = r – g = 5% 10%D1 = P(Div Yield) = $1.25 $2.50

31. (10-5) Constant growth model C G Answer: c MEDIUM

The correct answer is statement c. Both prices are currently the same, but X's price should grow at 6% vs. 4% for Y, so X's price should be higher a year from now.

32. (10-5) Constant growth model C G Answer: b MEDIUM

The correct answer choice is b. One could quickly calculate the dividend yield and see that it equals the growth rate, but here are some numbers that provide more information.

D1 $3.00 D1/P0 6.0%P0 $50.00 rX 12.0%g 6.0%

33. (10-5) Constant growth model C G Answer: b MEDIUM

Dividend = Yield × Price: X dividend = $1.25 Y dividend = $0.75

Stock X has a dividend yield of 5% versus a dividend yield of 3% for Y. Since they both have the same stock price, X must pay a higher dividend.

34. (10-5) Constant growth model C G Answer: d MEDIUM

P1 = P0(1 + g) = $54. Therefore, d is correct. All the other answers are false. P1 = $54.00

35. (10-5) Constant growth model and CAPM C G Answer: b MEDIUM

Statement b is true, because Stock A has a higher required return but the stocks have the same growth rate, so Stock A must have the higher dividend yield. Here are some calculations to demonstrate the point.

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(10-5) Constant growth valuation C G Answer: c EASY42. A stock is expected to pay a dividend of $0.75 at the end of the year.

The required rate of return is rs = 10.5%, and the expected constant growth rate is g = 6.4%. What is the stock's current price?

a. $17.39b. $17.84c. $18.29d. $18.75e. $19.22

(10-5) Constant growth valuation C G Answer: e EASY43. A stock just paid a dividend of D0 = $1.50. The required rate of return

is rs = 10.1%, and the constant growth rate is g = 4.0%. What is the current stock price?

a. $23.11b. $23.70c. $24.31d. $24.93e. $25.57

r RF beta RP M r Stock A 6.40% + 1.10 × 6.00% = 13.00%B 6.40% + 0.90 × 6.00% = 11.80%

Div. Yld. g r Stock A D1/P0 + 7.00% = 13.00% D1/P0 = r g = 6.00%B D1/P0 + 7.00% = 11.80% D1/P0 = r g = 4.80%

36. (10-7) Corporate valuation model C G Answer: b MEDIUM

37. (10-7) Corporate valuation model C G Answer: a MEDIUM

38. (10-8) Preferred stock concepts C G Answer: b MEDIUM

39. (10-8) Preferred stock concepts C G Answer: b MEDIUM

40. (Comp.) Common stock concepts C G Answer: c MEDIUM

Statement a is false—a number of companies have different classes of stock with different voting rights. Statement b is simply false. Statement c is true. Statements d and e are false, because the constant growth model can be used anytime as long as the constant growth rate is less than the required return (even if the growth rate is negative).

42. (10-5) Constant growth valuation C G Answer: c EASY

D1 $0.75rs 10.5%g 6.4%P0 = D1/(rs − g) $18.29


(10-5) Constant growth valuation C G Answer: d EASY44. A share of common stock just paid a dividend of $1.00. If the expected

long-run growth rate for this stock is 5.4%, and if investors' required rate of return is 11.4%, what is the stock price?

a. $16.28b. $16.70c. $17.13d. $17.57e. $18.01

(10-5) Expected dividend yield C G Answer: d EASY45. If D1 = $1.25, g (which is constant) = 4.7%, and P0 = $26.00, what is the

stock’s expected dividend yield for the coming year?

a. 4.12%b. 4.34%c. 4.57%d. 4.81%e. 5.05%

(10-5) Expected dividend yield C G Answer: b EASY46. If D0 = $2.25, g (which is constant) = 3.5%, and P0 = $50, what is the

stock’s expected dividend yield for the coming year?

a. 4.42%b. 4.66%c. 4.89%d. 5.13%e. 5.39%

(10-5) Expected cap. gains yield C G Answer: a EASY47. If D1 = $1.50, g (which is constant) = 6.5%, and P0 = $56, what is the

stock’s expected capital gains yield for the coming year?

a. 6.50%b. 6.83%c. 7.17%d. 7.52%e. 7.90%

(10-5) Expected total return C G Answer: e EASY48. If D1 = $1.25, g (which is constant) = 5.5%, and P0 = $44, what is the

stock’s expected total return for the coming year?

a. 7.54%b. 7.73%c. 7.93%d. 8.13%e. 8.34%

(10-5) Expected total return C G Answer: e EASY


49. If D0 = $1.75, g (which is constant) = 3.6%, and P0 = $32.00, what is the stock’s expected total return for the coming year?

a. 8.37%b. 8.59%c. 8.81%d. 9.03%e. 9.27%


(10-5) Constant growth rate C G Answer: e EASY50. Gay Manufacturing is expected to pay a dividend of $1.25 per share at

the end of the year (D1 = $1.25). The stock sells for $32.50 per share, and its required rate of return is 10.5%. The dividend is expected to grow at some constant rate, g, forever. What is the equilibrium expected growth rate?

a. 6.01%b. 6.17%c. 6.33%d. 6.49%e. 6.65%

50. (10-5) Constant growth rate C G Answer: e EASY

Expected dividend (D1) $1.25Stock price $32.50Required return 10.5%Dividend yield 3.85%Growth rate = rs − D1/P0 = 6.65%

43. (10-5) Constant growth valuation C G Answer: e EASY

D0 $1.50rs 10.1%g 4.0%D1 = D0(1 + g) = $1.56P0 = D1/(rs − g) $25.57

44. (10-5) Constant growth valuation C G Answer: d EASY

Last dividend (D0) $1.00Long-run growth rate 5.4%Required return 11.4%D1 = D0(1 + g) = $1.054P0 = D1/(rs − g) $17.57

45. (10-5) Expected dividend yield C G Answer: d EASY

D1 $1.25g 4.7%P0 $26.00Dividend yield = D1/P0 = 4.81%

46. (10-5) Expected dividend yield C G Answer: b EASY

D0 $2.25g 3.5%P0 $50.00D1 = D0(1 + g) = $2.329Dividend yield = D1/P0 = 4.66%

47. (10-5) Expected cap. gains yield C G Answer: a EASY

D1 $1.50g 6.5%P0 $56.00


(10-5) Constant growth: future price C G Answer: e EASY51. Reddick Enterprises' stock currently sells for $35.50 per share. The

dividend is projected to increase at a constant rate of 5.50% per year. The required rate of return on the stock, rs, is 9.00%. What is the stock's expected price 3 years from today?

a. $37.86b. $38.83c. $39.83d. $40.85e. $41.69

(10-5) Constant growth: future price C G Answer: e EASY52. Whited Inc.'s stock currently sells for $35.25 per share. The dividend

is projected to increase at a constant rate of 4.75% per year. The required rate of return on the stock, rs, is 11.50%. What is the stock's expected price 5 years from now?

a. $40.17b. $41.20c. $42.26d. $43.34e. $44.46

(10-7) Corporate valuation model C G Answer: c EASY53. Mooradian Corporation’s free cash flow during the just-ended year (t =

0) was $150 million, and its FCF is expected to grow at a constant rate of 5.0% in the future. If the weighted average cost of capital is 12.5%, what is the firm’s total corporate value, in millions?

a. $1,895b. $1,995c. $2,100d. $2,205e. $2,315

Capital gains yield = g = 6.50%

48. (10-5) Expected total return C G Answer: e EASY

D1 $1.25g 5.5%P0 $44.00Total return = rs = D1/P0 + g 8.34%

49. (10-5) Expected total return C G Answer: e EASY

D0 $1.75g 3.6%P0 $32.00D1 = D0(1 + g) = $1.81Total return = rs = D1/P0 + g 9.27%


(10-7) Corporate valuation model C G Answer: d EASY54. Suppose Boyson Corporation’s projected free cash flow for next year is

FCF1 = $150,000, and FCF is expected to grow at a constant rate of 6.5%. If the company’s weighted average cost of capital is 11.5%, what is the firm’s total corporate value?

a. $2,572,125b. $2,707,500c. $2,850,000d. $3,000,000e. $3,150,000

(10-8) Preferred stock valuation C G Answer: e EASY55. Molen Inc. has an outstanding issue of perpetual preferred stock with an

annual dividend of $7.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell?

a. $104.27b. $106.95c. $109.69d. $112.50e. $115.38

(10-5) Constant growth valuation: CAPM C G Answer: a MEDIUM56. The Francis Company is expected to pay a dividend of D1 = $1.25 per

share at the end of the year, and that dividend is expected to grow at a

54. (10-7) Corporate valuation model C G Answer: d EASY

FCF1 $150,000g 6.50%WACC 11.50%Total corporate value = FCF1/(WACC – g) = $3,000,000

51. (10-5) Constant growth: future price C G Answer: e EASY

Stock price $35.50Growth rate 5.50%Years in the future 3P3 = P0(1 + g)3 = $41.69

52. (10-5) Constant growth: future price C G Answer: e EASY

Growth rate 4.75%Years in the future 5Stock price $35.25P5 = P0(1 + g)5 = $44.46

53. (10-7) Corporate valuation model C G Answer: c EASY

FCF0 $150g 5.0%WACC 12.5%FCF1 = FCF0(1 + g) = $157.50Total corporate value = FCF1/(WACC – g) = $2,100.00


constant rate of 6.00% per year in the future. The company's beta is 1.15, the market risk premium is 5.50%, and the risk-free rate is 4.00%. What is the company's current stock price?

a. $28.90b. $29.62c. $30.36d. $31.12e. $31.90

(10-5) Constant growth valuation: CAPM C G Answer: a MEDIUM57. The Isberg Company just paid a dividend of $0.75 per share, and that

dividend is expected to grow at a constant rate of 5.50% per year in the future. The company's beta is 1.15, the market risk premium is 5.00%, and the risk-free rate is 4.00%. What is the company's current stock price, P0?

a. $18.62b. $19.08c. $19.56d. $20.05e. $20.55


(10-5) Constant growth valuation: CAPM C G Answer: a MEDIUM58. Schnusenberg Corporation just paid a dividend of D0 = $0.75 per share,

and that dividend is expected to grow at a constant rate of 6.50% per year in the future. The company's beta is 1.25, the required return on the market is 10.50%, and the risk-free rate is 4.50%. What is the company's current stock price?

a. $14.52b. $14.89c. $15.26d. $15.64e. $16.03

(10-5) Constant growth dividend C G Answer: b MEDIUM59. Goode Inc.'s stock has a required rate of return of 11.50%, and it sells

for $25.00 per share. Goode's dividend is expected to grow at a constant rate of 7.00%. What was the last dividend, D0?

a. $0.95b. $1.05c. $1.16d. $1.27e. $1.40

(10-5) Constant growth dividend C G Answer: b MEDIUM60. Francis Inc.'s stock has a required rate of return of 10.25%, and it

sells for $57.50 per share. The dividend is expected to grow at a constant rate of 6.00% per year. What is the expected year-end dividend, D1?

a. $2.20b. $2.44c. $2.69d. $2.96e. $3.25

58. (10-5) Constant growth valuation: CAPMC G Answer: a MEDIUM

D0 $0.75b 1.25rRF 4.5%rM 10.5%g 6.5%D1 = D0(1 + g) = $0.7988rs = rRF + b(rM − RRF) = 12.0%P0 = D1/(rs − g) $14.52

59. (10-5) Constant growth dividend C G Answer: b MEDIUM

Stock price $25.00Required return 11.50%Growth rate 7.00%P0 = D1/(rs − g), so D1 = P0(rs − g) = $1.1250Last dividend = D0 = D1/(1 + g) $1.05


(10-5) Constant growth: future price C G Answer: a MEDIUM61. Sorenson Corp.’s expected year-end dividend is D1 = $1.60, its required

return is rs = 11.00%, its dividend yield is 6.00%, and its growth rate is expected to be constant in the future. What is Sorenson's expected stock price in 7 years, i.e., what is ?

a. $37.52b. $39.40c. $41.37d. $43.44e. $45.61


(10-7) Corporate valuation model C G Answer: e MEDIUM62. Gupta Corporation is undergoing a restructuring, and its free cash flows

are expected to vary considerably during the next few years. However, the FCF is expected to be $65.00 million in Year 5, and the FCF growth rate is expected to be a constant 6.5% beyond that point. The weighted average cost of capital is 12.0%. What is the horizon (or continuing) value (in millions) at t = 5?

a. $1,025b. $1,079c. $1,136d. $1,196e. $1,259

(10-7) Corporate valuation model C G Answer: a MEDIUM63. Misra Inc. forecasts a free cash flow of $35 million in Year 3, i.e., at

t = 3, and it expects FCF to grow at a constant rate of 5.5% thereafter. If the weighted average cost of capital (WACC) is 10.0% and the cost of equity is 15.0%, what is the horizon, or continuing, value in millions at t = 3?

a. $821b. $862c. $905d. $950e. $997

(10-7) Corporate valuation model C G Answer: c MEDIUM64. You must estimate the intrinsic value of Noe Technologies’ stock. The

end-of-year free cash flow (FCF1) is expected to be $27.50 million, and it is expected to grow at a constant rate of 7.0% a year thereafter. The company’s WACC is 10.0%, it has $125.0 million of long-term debt plus preferred stock outstanding, and there are 15.0 million shares of common stock outstanding. What is the firm's estimated intrinsic value per share of common stock?

a. $48.64b. $50.67c. $52.78d. $54.89e. $57.08

(10-7) Corporate valuation model C G Answer: c MEDIUM65. You have been assigned the task of using the corporate, or free cash

flow, model to estimate Petry Corporation's intrinsic value. The firm's WACC is 10.00%, its end-of-year free cash flow (FCF1) is expected to be $75.0 million, the FCFs are expected to grow at a constant rate of 5.00% a year in the future, the company has $200 million of long-term debt and preferred stock, and it has 30 million shares of common stock outstanding. What is the firm's estimated intrinsic value per share of common stock?

a. $40.35b. $41.82


c. $43.33d. $44.85e. $46.42

(10-7) Corporate valuation model C G Answer: b MEDIUM66. Kedia Inc. forecasts a negative free cash flow for the coming year, FCF1

= -$10 million, but it expects positive numbers thereafter, with FCF2 = $25 million. After Year 2, FCF is expected to grow at a constant rate of 4% forever. If the weighted average cost of capital is 14.0%, what is the firm’s total corporate value, in millions?

a. $200.00b. $210.53c. $221.05d. $232.11e. $243.71

(10-7) Corporate valuation model C G Answer: a MEDIUM67. Kale Inc. forecasts the free cash flows (in millions) shown below. If

the weighted average cost of capital is 11.0% and FCF is expected to grow at a rate of 5.0% after Year 2, what is the firm’s total corporate value, in millions?

Year 1 2 Free cash flow -$50 $100

a. $1,456b. $1,529c. $1,606d. $1,686e. $1,770

(10-7) Corporate valuation model C G Answer: e MEDIUM68. Ryan Enterprises forecasts the free cash flows (in millions) shown

below. The weighted average cost of capital is 13.0%, and the FCFs are expected to continue growing at a 5.0% rate after Year 3. What is the firm’s total corporate value, in millions?

Year 1 2 3 FCF -$15.0 $10.0 $40.0

a. $314.51b. $331.06c. $348.48d. $366.82e. $386.13

(10-7) Corporate valuation model C G Answer: d MEDIUM69. Based on the corporate valuation model, Wang Inc.’s total corporate

value is $750 million. Its balance sheet shows $100 million notes payable, $200 million of long-term debt, $40 million of common stock (par plus paid-in-capital), and $160 million of retained earnings. What is the best estimate for the firm’s value of equity, in millions?


a. $386b. $406c. $428d. $450e. $473


(10-7) Corporate valuation model C G Answer: b MEDIUM70. Based on the corporate valuation model, Gay Entertainment's total

corporate value is $1,200 million. The company’s balance sheet shows $120 million of notes payable, $300 million of long-term debt, $50 million of preferred stock, $180 million of retained earnings, and $800 million of total common equity. If the company has 30 million shares of stock outstanding, what is the best estimate of its price per share?

a. $21.90b. $24.33c. $26.77d. $29.44e. $32.39

(10-7) Corporate valuation model C G Answer: c MEDIUM71. Based on the corporate valuation model, the total corporate value of

Chen Lin Inc. is $900 million. Its balance sheet shows $110 million in notes payable, $90 million in long-term debt, $20 million in preferred stock, $140 million in retained earnings, and $280 million in total common equity. If the company has 25 million shares of stock outstanding, what is the best estimate of its stock price per share?

a. $22.03b. $24.48c. $27.20d. $29.92e. $32.91

(10-7) Corporate valuation model C G Answer: d MEDIUM72. Based on the corporate valuation model, Morgan Inc.’s total corporate

value is $300 million. The balance sheet shows $90 million of notes payable, $30 million of long-term debt, $40 million of preferred stock, and $100 million of common equity. The company has 10 million shares of stock outstanding. What is the best estimate of the stock’s price per share?

a. $12.00b. $12.64c. $13.30d. $14.00e. $14.70

(10-8) Preferred required return C G Answer: e MEDIUM73. Carter's preferred stock pays a dividend of $1.00 per quarter. If the

price of the stock is $45.00, what is its nominal (not effective) annual rate of return?

a. 8.03%b. 8.24%c. 8.45%d. 8.67%e. 8.89%


(10-8) Preferred required return C G Answer: e MEDIUM74. Rebello's preferred stock pays a dividend of $1.00 per quarter, and it

sells for $55.00 per share. What is its effective annual (not nominal) rate of return?

a. 6.62%b. 6.82%c. 7.03%d. 7.25%e. 7.47%

(10-6) Nonconstant growth valuation C G Answer: d MEDIUM/HARD75. Nachman Industries just paid a dividend of D0 = $1.32. Analysts expect

the company's dividend to grow by 30% this year, by 10% in Year 2, and at a constant rate of 5% in Year 3 and thereafter. The required return on this low-risk stock is 9.00%. What is the best estimate of the stock’s current market value?

a. $41.59b. $42.65c. $43.75d. $44.87e. $45.99

(10-6) Nonconstant growth valuation C G Answer: c HARD76. Church Inc. is presently enjoying relatively high growth because of a

surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 25% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company’s last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock?

a. $26.77b. $27.89c. $29.05d. $30.21e. $31.42

(10-6) Nonconstant growth valuation C G Answer: b HARD77. The Ramirez Company's last dividend was $1.75. Its dividend growth rate

is expected to be constant at 25% for 2 years, after which dividends are expected to grow at a rate of 6% forever. Its required return (rs) is

74. (10-8) Preferred required return C G Answer: e MEDIUM

Periods per year = 4Pref. quarterly dividend $1.00Preferred stock price $55.00Eff % required return = (1+ (Qt Div/P))N − 1 = 7.47%


12%. What is the best estimate of the current stock price?

a. $41.58b. $42.64c. $43.71d. $44.80e. $45.92


(10-6) Nonconstant growth valuation C G Answer: a HARD78. Ackert Company's last dividend was $1.55. The dividend growth rate is

expected to be constant at 1.5% for 2 years, after which dividends are expected to grow at a rate of 8.0% forever. The firm's required return (rs) is 12.0%. What is the best estimate of the current stock price?

a. $37.05b. $38.16c. $39.30d. $40.48e. $41.70

(10-6) Nonconstant growth valuation C G Answer: d HARD79. Huang Company's last dividend was $1.25. The dividend growth rate is

expected to be constant at 15% for 3 years, after which dividends are expected to grow at a rate of 6% forever. If the firm's required return (rs) is 11%, what is its current stock price?

a. $30.57b. $31.52c. $32.49d. $33.50e. $34.50

(10-6) Nonconstant growth valuation C G Answer: d HARD80. Agarwal Technologies was founded 10 years ago. It has been profitable

for the last 5 years, but it has needed all of its earnings to support growth and thus has never paid a dividend. Management has indicated that it plans to pay a $0.25 dividend 3 years from today, then to increase it at a relatively rapid rate for 2 years, and then to increase it at a constant rate of 8.00% thereafter. Management's forecast of the future dividend stream, along with the forecasted growth rates, is shown below. Assuming a required return of 11.00%, what is your estimate of the stock's current value?

Year 0 1 2 3 4 5 6 Growth rate NA NA NA NA 50.00% 25.00% 8.00%Dividends $0.000 $0.000 $0.000 $0.250 $0.375 $0.469 $0.506

78. (10-6) Nonconstant growth valuation C G Answer: a HARD

Last dividend (D0) $1.55Short-run growth rate 1.50%Long-run growth rate 8.00%Required return 12.00%

Year 0 1 2 3 1.50% 1.50% 8.00%

Dividend $1.5500 $1.5733 $1.5968 $1.7246Horizon value = D3/(rs − g3) = 43 .1149 Total CFs $1.5733 $44.7118PV of CFs $1.4047 $35.6439

Price = Sum of PVs = $37.05


a. $ 9.94b. $10.19c. $10.45d. $10.72e. $10.99


(10-7) Corporate valuation model C G Answer: b HARD81. Wall Inc. forecasts that it will have the free cash flows (in millions)

shown below. If the weighted average cost of capital is 14% and the free cash flows are expected to continue growing at the same rate after Year 3 as from Year 2 to Year 3, what is the firm’s total corporate value, in millions?

Year 1 2 3 Free cash flow -$20.00 $48.00 $54.00

a. $2,650.00b. $2,789.47

81. (10-7) Corporate valuation model C G Answer: b HARD

Year 1 2 3 Free cash flow -$20.00 $48.00 $54.00WACC = 14.00%

First, find the growth rate: g = FCF3/FCF2 − 1 = 12.500%Second, find the horizon, or continuing, value, at Year 2:HV2 = FCF3/(WACC – g) = $3,600.00Now find the PV of the FCFs and the horizon value:Total corporate value = FCF1/(1.14) + (FCF2 + HV2)/(1.14)2 = $2,789.47

55. (10-8) Preferred stock valuation C G Answer: e EASY

Preferred dividend $7.50Required return 6.5%Preferred price = DP/rP = $115.38


D1 $1.25b 1.15rRF 4.00%RPM 5.50%g 6.00%rs = rRF + b(RPM) = 10.33%P0 = D1/(rs − g) $28.90


D0 $0.75b 1.15rRF 4.0%RPM 5.0%g 5.5%D1 = D0(1 + g) = $0.7913rs = rRF + b(RPM) = 9.75%


c. $2,928.95d. $3,075.39e. $3,229.16

(10-6) Nonconstant growth rate* C G Answer: e VERY HARD82. Savickas Petroleum’s stock has a required return of 12%, and the stock

sells for $40 per share. The firm just paid a dividend of $1.00, and the dividend is expected to grow by 30% per year for the next 4 years, so D4 = $1.00(1.30)4 = $2.8561. After t = 4, the dividend is expected to grow at a constant rate of X% per year forever. What is the stock’s expected constant growth rate after t = 4, i.e., what is X?

P0 = D1/(rs − g) $18.62

62. (10-7) Corporate valuation model C G Answer: e MEDIUM

CF5 $65.00g 6.5%WACC 12.0%FCF6 = FCF5(1 + g) = $69.2250HV5 = FCF6/(WACC – g) = $1,258.64


FCF3 $35.00g 5.5%WACC 10.0%FCF4 = FCF3(1 + g) = $36.9250HV3 = FCF4/(WACC – g) = $820.56

64. (10-7) Corporate valuation model C G Answer: c MEDIUM

FCF1 $27.50Constant growth rate 7.0%WACC 10.0%Debt & preferred stock $125Shares outstanding 15Total firm value = FCF1/(WACC − g) = $916.67Less: Value of debt & preferred -$125.00Value of equity $791.67Number of shares 15Value per share = Equity value/Shares = $52.78


FCF1 $75.00Constant growth rate 5.0%WACC 10.0%Debt & preferred stock $200Shares outstanding 30Total firm value = FCF1/(WACC − g) = $1,500.00Less: Value of debt & preferred -$200.00Value of equity $1,300.00Number of shares 30Value per share = Equity value/Shares = $43.33


a. 5.17%b. 5.44%c. 5.72%d. 6.02%e. 6.34%


FCF1 -$10FCF2 $25g 4%WACC 14%

First, find the horizon, or continuing, value at t = 2:HV2 = FCF2(1 + g)/(WACC – g) = $25(1.04)/(0.14 – 0.04) = $26.0/0.10 = $260.00

Then find the PV of the free cash flows and the horizon value:Total corporate value = -$10/(1.14)1 + ($25 + $260)/(1.14)2

Total corporate value = -$8.772 + $219.298 = $210.53


FCF1 -$50FCF2 $100g 5%WACC 11%

First, find the horizon, or continuing, value:HV2 = FCF2(1 + g)/(WACC – g) = $100(1.05)/(0.11 – 0.05) = $1,750.00

Then find the PV of the free cash flows and the horizon value:Total corporate value = -$50/(1.11) + ($100 + $1,750)/(1.11)2 =$1,456.46

68. (10-7) Corporate valuation model C G Answer: e MEDIUM

g 5%WACC 13%

Year 1 2 3 4 FCF -$15.00 $10.00 $40.00 $42.00Horizon, or continuing, value $525 .00 = FCF3(1 + g)/(WACC – g)Annual FCF -$15.00 $10.00 $565.00PVs at 13% -$13.27 $7.83 $391.57

Total corporate value = Sum = $386.13


(10-6) Nonconstant valuation--use Excel* C G L Answer: d VERY HARD83. Your boss, Sally Maloney, treasurer of Fred Clark Enterprises (FCE),

asked you to help her estimate the intrinsic value of the company's stock. FCE just paid a dividend of $1.00, and the stock now sells for $15.00 per share. Sally asked a number of security analysts what they believe FCE's future dividends will be, based on their analysis of the company. The consensus is that the dividend will be increased by 10% during Years 1 to 3, and it will be increased at a rate of 5% per year in Year 4 and thereafter. Sally asked you to use that information to estimate the required rate of return on the stock, rs, and she provided you with the following template for use in the analysis.

69. (10-7) Corporate valuation model C G Answer: d MEDIUM

Assuming that the book value of debt is close to its market value, the total market value of the company is:Total corporate value $750Notes payable -$100Long-term debt -$200Value of equity = $450

The book value of equity figures are irrelevant for this problem.


Assuming that the book value of debt is close to its market value, the total market value of the firm’s equity is:Total corporate value $1,200Notes payable -$120Long-term debt -$300Preferred stock -$50MV equity $730Shares outstanding 30Stock price = Value of equity/Shares outstanding = $24.33



Assuming that the book value of debt is close to its market value, the total market value of the firm’s equity is:Total corporate value $900Notes payable -$110Long-term debt -$90Preferred stock -$20MV equity $680Shares outstanding 25Stock price = Value of equity/Shares outstanding = $27.20


Estimated rs = 10.00% (must be changed to force Calculated Price to equal the Actual Market Price)$15.00

Year 0 1 2 3 4 5Dividend growth rate (insert correct values) 10% 10% 10% 5% 5%Calculated dividends (D0 has been paid) $1.00 ? ? ? ? ?HV3 = P3 = D4/(rs − g4). Find using Estimated rs. ?Total CFs ? ? ?PVs of CFs when discounted at Estimated rs ? ? ?Calculated Price = P0 = Sum of PVs = $0.00 A positive number will be here when dividends are estimated.

The Calculated Price will equal the Actual Market Price once the correct rs has been found.

Normal growthRapid growthActual Market Price, P0:


72. (10-7) Corporate valuation model C G Answer: d MEDIUM

Assuming that the book value of debt is close to its market value, the total market value of the firm’s equity is:Total corporate value $300Notes payable -$90Long-term debt -$30Preferred stock -$40MV equity $140Shares outstanding 10Stock price = Value of equity/Shares outstanding = $14.00

The book value of equity figures are irrelevant for this problem

73. (10-8) Preferred required return C G Answer: e MEDIUM

Pref. quarterly dividend $1.00Annual dividend = Qtrly dividend × 4 = $4.00Preferred stock price $45.00Nom. required return = Annual dividend/Price = 8.89%

75. (10-6) Nonconstant growth valuation C G Answer: d MEDIUM/HARD

rs = 9.0%Year 0 1 2 3 Growth rates: 30.0% 10.0% 5.0%Dividend $1.32 $1.716 $1.888 $1.982Horizon value = D3/(rs − g3) = 49 .550 Total CFs $1.716 $51.437PV of CFs $1.574 $43.294

Stock price = $44.87

76. (10-6) Nonconstant growth valuation C G Answer: c HARD

Last dividend (D0) $1.25Short-run growth rate 25%Long-run growth rate 0%Beta 1.20Market risk premium 5.50%Risk-free rate 3.00%Required return = rs = rRF + b(RPM) = 9.60%


Sally told you that the growth rates in the template were just put in as a trial, and that you must replace them with the analysts' forecasted rates to get the correct forecasted dividends and then the estimated HV. She also notes that the estimated value for rs, at the top of the template, is also just a guess, and you must replace it with a value that will cause the Calculated Price shown at the bottom to equal the Actual Market Price. She suggests that, after you have put in the correct dividends, you can manually calculate the price, using a series of guesses as to the Estimated rs. The value of rs that causes the calculated price to equal the actual price is the correct one. She notes, though, that this trial-and-error process would be quite tedious, and that the correct rs could be found much faster with a simple Excel model, especially if you use Goal Seek. What is the value of rs?

a. 11.84%b. 12.21%c. 12.58%d. 12.97%e. 13.36%

Year 0 1 2 3 4 5 25% 25% 25% 25% 0%

Dividend $1.2500 $1.5625 $1.9531 $2.4414 $3.0518 $3.0518Horizon value = D5/(rs − g5) = 31 .7891 Total CFs $1.5625 $1.9531 $2.4414 $34.8409PV of the CFs $1.4256 $1.6260 $1.8544 $24.1461


79. (10-6) Nonconstant growth valuation C G Answer: d HARD

Required return 11.0%Short-run growth rate 15.0%Long-run growth rate 6.0%Last dividend (D0) $1.25

Year 0 1 2 3 4 Dividend $1.2500 $1.4375 $1.6531 $1.9011 $2.0152Horizon value = P2 = D3/(rs − g3) = 40 .3032 Total CFs $1.4375 $1.6531 $42.2043PV of CFs $1.2950 $1.3417 $30.8594



(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)

Note that there is some overlap between the T/F and the multiple choice questions, as some T/F statements are used in the MC questions. See the preface for information on the AACSB letter indicators (F, M, etc.) on the subject lines.

Multiple Choice: True/False

80. (10-6) Nonconstant growth valuation C G Answer: d HARD

Required return = 11%

Year 0 1 2 3 4 5 6 50.00% 25.00% 8.00%

Dividend $0.000 $0.000 $0.000 $0.250 $0.375 $0.469 $0.506Horizon value = P5 = D6/(rs − g6) = 16.875 Total CFs $0.000 $0.000 $0.250 $0.375 $17.344PV of CFs $0.000 $0.000 $0.183 $0.247 $10.293

Price = $10.72

82. (10-6) Nonconstant growth rate* C G Answer: e VERY HARD

Stock price $40.00Paid dividend (D0) $1.00Short-run growth rate 30.0%Required return 12.0%Forecasted LR growth rate, X 6.34% Arbitrarily set at 5% initially.

Year 0 1 2 3 4 5 30.0% 30.0% 30.0% 30.0% 6.34%

Dividend $1.0000 $1.3000 $1.6900 $2.1970 $2.8561 $3.0372Horizon value = P4 = D5/(rs − g5): 53 .6777 Total CFs $1.3000 $1.6900 $2.1970 $56.5338PV of CFs $1.1607 $1.3473 $1.5638 $35.9282

Stock price = $40.00 Must equal $40. Change the forecasted growth rate till reach $40.

Page 352 Conceptual M/C Appendix 10A: Stock Market Equilibrium

APPENDIX 10ASTOCK MARKET EQUILIBRIUM

(10A) Stock market equilibrium F G Answer: a EASY84. If a stock's expected return as seen by the marginal investor exceeds

this investor's required return, then the investor will buy the stock until its price has risen enough to bring the expected return down to equal the required return.

a. Trueb. False

(10A) Stock market equilibrium F G Answer: a EASY85. If a stock's market price exceeds its intrinsic value as seen by the

We must solve for the long-run growth rate. We can forecast the dividends in Years 1-4, so they are inserted in the time line. We need a growth rate to find D5 and the HV. We begin with a guess of say 5.0%, which we insert in the forecast cell. We then find the PV of the forecasted CFs and sum them. If the sum equals the given price, then our growth rate would be correct. If not, we need to substitute in different g's until we find the one that works. We used Excel's Goal Seek function to simplify the process, but one could use trial and error.

60. (10-5) Constant growth dividend C G Answer: b MEDIUM

Stock price $57.50Required return 10.25%Growth rate 6.00%P0 = D1/(rs − g), so D1 = P0(rs − g)Expected dividend = D1 = P0(rs − g) = $2.44

Appendix 10A: Stock Market Equilibrium True/False Page 353© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

marginal investor, then the investor will sell the stock until its price has fallen down to the level of the investor's estimate of the intrinsic value.

a. Trueb. False

(10A) Stock market equilibrium F G Answer: a EASY86. For a stock to be in equilibrium, two conditions are necessary: (1) The

stock's market price must equal its intrinsic value as seen by the marginal investor and (2) the expected return as seen by the marginal

61. (10-5) Constant growth: future price C G Answer: a MEDIUM

Next expected dividend = D1 = $1.60Required return 11.0%Dividend yield = D1/P0 = 6.0%Find the growth rate: g = rs − yield = 5.0%Find P0 = D1/(rs − g) = $26.67Years in the future 7

= P0(1 + g)7 $37.52

77. (10-6) Nonconstant growth valuation C G Answer: b HARD

Last dividend (D0) $1.75Short-run growth rate 25%Long-run growth rate 6%Required return 12%

Year 0 1 2 3 25.00% 25.00% 6.00%

Dividend $1.7500 $2.1875 $2.7344 $2.8984Horizon value = D3/(rs − g3) = 48 .3073 Total CFs $2.1875 $51.0417PV of CFs $1.9531 $40.6901


83. (10-6) Nonconstant valuation--use Excel*C G L Answer: d VERY HARD

Finding the discount rate when we know the dividends and the actual stock price is complicated if the growth rate is not constant, and an iterative solution is required.

Estimated rs = 12.97%Actual Market Price, P0: $15.00


investor must equal this investor's required return.

a. Trueb. False

(10A) Stock market equilibrium F G Answer: b EASY87. Two conditions are used to determine whether or not a stock is in

equilibrium: (1) Does the stock's market price equal its intrinsic value as seen by the marginal investor, and (2) does the expected return on the stock as seen by the marginal investor equal this investor's required return? If either of these conditions, but not necessarily both, holds, then the stock is said to be in equilibrium.

a. Trueb. False

Rapid Growth Normal Growth Year 0 1 2 3 4 5

4 5Dividend growth rate 10% 10% 10% 5% 5%Dividends (D0 has been paid) $1.00 $1.100 $1.210 $1.331 $1.398HV3 = P3 = D4/(rs – g4). Use Estimated rs. $17 .527 Total CFs $1.100 $1.210 $18.858PVs of CFs discounted at Estimated rs $0.974 $0.948 $13.078

Calculated Price = P0 = Sum of PVs = $15.00

84. (10A) Stock market equilibrium F G Answer: a EASY



Appendix 10A: Stock Market Equilibrium True/False Page 355© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Multiple Choice: Conceptual

(10A) Market equilibrium C G Answer: b EASY88. If markets are in equilibrium, which of the following conditions will

exist?

a. Each stock’s expected return should equal its realized return as seen by the marginal investor.

b. Each stock’s expected return should equal its required return as seen by the marginal investor.

c. All stocks should have the same expected return as seen by the marginal investor.

d. The expected and required returns on stocks and bonds should be equal.

e. All stocks should have the same realized return during the coming year.

(10A) Market equilibrium C G Answer: e MEDIUM89. For a stock to be in equilibrium, that is, for there to be no long-term

pressure for its price to depart from its current level, then

a. the expected future return must be less than the most recent past realized return.

b. the past realized return must be equal to the expected return during the same period.

c. the required return must equal the realized return in all periods.d. the expected return must be equal to both the required future return

and the past realized return.e. the expected future return must be equal to the required return.

87. (10A) Stock market equilibrium F G Answer: b EASY

If one condition holds, then the other must also hold.

88. (10A) Market equilibrium C G Answer: b EASY

Statement b is true, because if the expected return does not equal the required return, then markets are not in equilibrium and buying/selling will occur until the expected return equals the required return.

89. (10A) Market equilibrium C G Answer: e MEDIUM


Chapter 10: Stocks Answers Page 357© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

CHAPTER 10ANSWERS AND SOLUTIONS

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STOCKS AND THEIR VALUATION EXERCISE