CHAPTER 8

STOCK VALUATION

Only one correction â€“ Q 5 in solutions

Answers to Concepts Review and Critical Thinking Questions

1. The value of any investment depends on its cash flows; i.e., what investors will actually receive. The cash

flows from a share of stock are the dividends.

2. Investors believe the company will eventually start paying dividends (or be sold to another company).

3. In general, companies that need the cash will often forgo dividends since dividends are a cash expense. Young,

growing companies with profitable investment opportunities are one example; another example is a company

in financial distress. This question is examined in depth in a later chapter.

4. The general method for valuing a share of stock is to find the present value of all expected future dividends.

The dividend growth model presented in the text is only valid (i) if dividends are expected to occur forever,

that is, the stock provides dividends in perpetuity, and (ii) if a constant growth rate of dividends occurs forever.

A violation of the first assumption might be a company that is expected to cease operations and dissolve itself

some finite number of years from now. The stock of such a company would be valued by the methods of this

chapter by applying the general method of valuation. A violation of the second assumption might be a start-up

firm that isnâ€™t currently paying any dividends, but is expected to eventually start making dividend payments

some number of years from now. This stock would also be valued by the general dividend valuation method of

this chapter.

5. The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the

preferred. However, the preferred is less risky because of the dividend and liquidation preference, so it is

possible the preferred could be worth more, depending on the circumstances.

6. The two components are the dividend yield and the capital gains yield. For most companies, the capital gains

yield is larger. This is easy to see for companies that pay no dividends. For companies that do pay dividends,

the dividend yields are rarely over five percent and are often much less.

7. Yes. If the dividend grows at a steady rate, so does the stock price. In other words, the dividend growth rate

and the capital gains yield are the same.

8. In a corporate election, you can buy votes (by buying shares), so money can be used to influence or even

determine the outcome. Many would argue the same is true in political elections, but, in principle at least, no

one has more than one vote.

9. It wouldnâ€™t seem to be. Investors who donâ€™t like the voting features of a particular class of stock are under no

obligation to buy it.

10. Investors buy such stock because they want it, recognizing that the shares have no voting power. Presumably,

investors pay a little less for such shares than they would otherwise.

Solutions to Questions and Problems

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NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to

space and readability constraints, when these intermediate steps are included in this solutions manual, rounding

may appear to have occurred. However, the final answer for each problem is found without rounding during any

step in the problem.

Basic

1. The constant dividend growth model is:

Pt = Dt Ã— (1 + g) / (R â€“ g)

So the price of the stock today is:

P0 = D0 (1 + g) / (R â€“ g) = $1.40 (1.06) / (.12 â€“ .06) = $24.73

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 â€“ g) = D0 (1 + g)4 / (R â€“ g) = $1.40 (1.06)4 / (.12 â€“ .06) = $29.46

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 â€“ g) = D0 (1 + g)16 / (R â€“ g) = $1.40 (1.06)16 / (.12 â€“ .06) = $59.27

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 = $24.73(1 + .06)3 = $29.46

And the stock price in 15 years will be:

P15 = P0(1 + g)15 = $24.73(1 + .06)15 = $59.27

2. We need to find the required return of the stock. Using the constant growth model, we can solve the equation

for R. Doing so, we find:

R = (D1 / P0) + g = ($3.10 / $48.00) + .05 = 11.46%

3. The dividend yield is the dividend next year divided by the current price, so the dividend yield is:

Dividend yield = D1 / P0 = $3.10 / $48.00 = 6.46%

The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:

Capital gains yield = 5%

4. Using the constant growth model, we find the price of the stock today is:

P0 = D1 / (R â€“ g) = $3.60 / (.13 â€“ .045) = $42.35

5. 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:

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R = Dividend yield + Capital gains yield = .039 +.06 = 9.90%

6. We know the stock has a required return of 12 percent, and the dividend and capital gains yield are equal, so:

Dividend yield = 1/2(.12) = .06 = 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 = .06($70) = $4.20

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:

D1 = $4.20(1 + .06)

D0 = $4.20 / 1.06 = $3.96

7. The price of any financial instrument is the PV of the future cash flows. The future dividends of this stock are

an annuity for eight years, so the price of the stock is the PVA, which will be:

P0 = $12.00(PVIFA10%,8) = $64.02

8. The price 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 = $8.25/$113 = 7.30%

Intermediate

9. This stock has a constant growth rate of dividends, but the required return changes twice. To find the value of

the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate

and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7,

divided by the required return minus the growth rate in dividends. So:

P6 = D6 (1 + g) / (R â€“ g) = D0 (1 + g)7 / (R â€“ g) = $3.00 (1.05)7 / (.11 â€“ .05) = $70.36

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 = $3.00(1.050)4 / 1.14 + $3.00(1.050)5 / 1.142 + $3.00(1.05)6 / 1.143 + $70.36 / 1.143

P3= $56.35

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:

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