# Stocks: Questions

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• Published : August 28, 2010

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A. The common stockholders are the owners of a corporation, and as such, they have certain rights and privileges as described below.

1.Ownership implies control.

2.Common stockholders often have the right, called the preemptive right, to purchase any additional shares sold by the firm.

B:The value of any stock is the present value of its expected dividend stream: ￼ ￼

However, some stocks have dividend growth patterns which allow them to be valued using short-cut formulas.

B2:A constant growth stock is one whose dividends are expected to grow at a constant rate forever. Many companies have dividends which are expected to grow steadily into the foreseeable future, and such companies are valued as constant growth stocks.

For a constant growth stock:

D1 = D0(1 + g), D2 = D1(1 + g) = D0(1 + g)2, and so on.

With this regular dividend pattern, the general stock valuation model can be simplified to the following very important equation:

￼ = ￼ = ￼.

B3:The model is derived mathematically, and the derivation requires that rs > g. If g is greater than rs, the model gives a negative stock price. The model simply cannot be used unless (1) rs > g, (2) g is expected to be constant, and (3) g can reasonably be expected to continue indefinitely. Stocks may have periods of supernormal growth, where gs > rs; however, this growth rate cannot be sustained indefinitely. In the long-run, g < rs. C:The SML is used to calculate temp force’s required rate of return:

rs= rRF + (rM – rRF)bTemp Force = 7% + (12% - 7%)(1.2)
= 7% + (5%)(1.2) = 7% + 6% = 13%.

D1:Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 6 percent per year. Expressed as a time line, we have the following setup. Just enter 2 in your calculator; then keep multiplying by 1 + g = 1.06 to get D1, D2, and D3:

0 1 2 3 4 | | | | |

g=6%
D0 = 2.00 2.12 2.247 2.382

1.88 (Year 1)
1.76 (Year 2)
1.65 (Year 3)

D2:Since the stock is growing at a constant rate, its value can be estimated using the constant growth model:

￼ = ￼ = ￼ = ￼ = \$30.29.

D3:
￼ = ￼ = ￼ = ￼ = \$32.10.

D4:The expected dividend yield in any year n is

Dividend Yield = ￼,

While the expected capital gains yield is

Capital Gains Yield = ￼ = r - ￼.

Total return = 13.0% Dividend yield = \$2.12/\$30.29 = 7.0%
Capital gains yield = 6.0%

E:Constant growth model - Rearranged

￼s= ￼.

Expected Return:
￼s= \$2.12/\$30.29 + 0.060 = 0.070 + 0.060 = 13%.

F:

0 1 2 3 | | | |

2.00 2.00 2.00
1.77 (Year 1)
1.57 (Year 2)
1.39 (Year 3)
.
.
.
P0 = 15.38

P0 = PMT/r = \$2.00/0.13 = \$15.38.

G:Temp Force is no longer a constant growth stock, so the constant growth model is not applicable. The easiest way to value such non-constant growth stocks is to set the situation up on a time line as shown below:

0 1 2 3 4 | | | | |

2.600 3.380 4.394 4.658

2.301 (Year 1)
2.647 (Year 2)
3.045 (Year 3)
46.116 (Year 4)
54.109

P0 = \$54.109.
The dividend yield in year 1 is 4.80 percent, and the capital gains yield is 8.2 percent:

Dividend yield = ￼ = 0.0480 = 4.8%.

Capital gains yield = 13.00% - 4.8% = 8.2%.

After year 3, the stock becomes a constant growth stock, with g...