стр. 90 |

V = $50(PVIFA3%,10) $1,OOO(PVIF3%.io)

= $50(8.5302) + $1,000(0.7441) = $426.51 + $744.10 = $1,170.61

V = $50(PVIFA5%,lo)+ $1,˜0(PVIFs%,io)

= $50(7.7217) + $1,000(0.6139) = $386.09 + $613.90 = $999.99

V = $50(PVIFA6%,10)+ $1,000(PVIFs%,io)

= $50(7.3601) + $1,000(0.5584) = $368.01 + $558.40 = $926.41

Stock Valuation-Single Period. Mary Czech is considering the purchase of stock X at the

71

.5

beginning of the year. The dividend at year-end is expected to be $3.25, and the market price by

the end of the year is expected to be $25. If she requires a rate of return of 12 percent, what is

the value of the stock?

SOLUTION

- (1p r)

D1 +-= 1 $3.25 $25

P

O

+

=

(1 + r ) + (1 + 0.12) (1 f 0.12)

= $3.25(0.893) + $25(0.893) = $2.90 + $22.33 = $25.23

71

.6 Stock Valuation-Finite Periods. The Ohm Company paid a $2.50 dividend per share at the end

of the year. The dividend is expected to grow by 10 percent each year for the next 3 years, and

the stock's market price per share is expected to be $50 at the end of the third year. Investors

require a rate of return of 14 percent. At what price per share should the Ohm stock sell?

SOLUTION

po=z-+- D, p3

151

[CHAP. 7

192 RISK, RETURN, AND VALUATION

Do = $2.50

Note that

D = $2.50(1 + 0.10) = $2.50(1.10) = $2.75

1

D = $2.50(1+ 0.10)2 = $2.50(1.21) = $3.03

z

D3 = $2.50(1 + 0.10)3= $2.50(1.331) = $3.33

$2.75 $3.03 $3.33 $50

P=

O

+ + +

(1+ 0.14) (1 + 0.14)2 (1+ 0.14)3 (1+ 0.14)3

= $2.75(0.877) + $3.03(0.770)+ $3.33(0.675) + $50(0.675)

= $2.41 + $2.33 + $2.25 + $33.75 = $40.74

The stock should sell for $40.74 per share.

Stock Valuation-No Growth in Dividends. Susan O'Reilly invests in a stock of company X

7.17

which expects no growth in dividends. The company paid a $2.75 dividend per share. If Susan

requires a rate of return of 10 percent, what would be the value of the stock?

SOLUTION

D

P =-

O

r

Therefore,

$2.75

PO=-= $27.50

0.1

The Gordon Dividend Growth Model. Develop the Gordon growth model, assuming constant

7.18

growth of dividends, i.e., Dr = Do(l + g)'.

SOLUTlON

Since D, = Do(1 + g)'

+ g ) and then this is subtracted from the

If both sides of this expression are multiplied by (1 + r ) / ( l

product, the result is:

If r >g, which should normally be true, the term on the far right-hand side approaches zero. As a result,

If we assume dividends grow at a constant rate g, then

D,=Do(l +g)' and t =1

and

193

RISK, RETURN, AND VALUATION

CHAP. 71

71

.9 Stock Valuation. Investors require a rate of return of 12 percent. At what price will the stock sell

if the next expected dividend D 1is $1 per share and investors expect the dividends and earnings

to grow (a) at 8 percent; (b)at 10 percent; (c) at 12 percent; and (d) at 14 percent?

SOLUTION

P

O = $25

=

0.12 - 0.08

PO = = $50

0.12 - 0.1

P

O $' = undefined

=

0.12 - 0.12

The formula is invalid since a necessary condition is r >g.

PO $' =undefined

=

0.12 - 0.14

Beta and Stock Valuation. The risk-free rate is 6 percent, the required rate of return on the

7.20

market is 12 percent, and stock A has a beta coefficient of 1.2. If the dividend expected during

the coming year is $2 and the growth rate of dividends and earnings is 7 percent, at what price

should stock A sell?

SOLUTION

r = rf + b(rm- r,) = 6% + 1.2(12% - 6%) = 6% + 7.2% = 13.2%

Therefore,

PO=-=

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