Question

A company just paid out an annual dividend of $4. The dividend amount will grow at 5% annually forever. If you buy a share today and sell it at year 4, how much of a capital gain (not including the dividend yield) would you expect? Assume that the required rate of return for this stock is 20%.

Group of answer choices

$6.98

$6.03

$6.45

$5.77

Answer 1

Answer;

Option $ 6.03

Explanation:

Present Value of Stock Formula(Po) = D0 + G / (Ke- G)

D0 = Dividend at 0th year

G = Growth

Ke = Required Return

Po = Present value at 0th Year

So,

Step 1

Po = D0 + G / (Ke - G)

D0 = $4

Ke = 20%

G = 5%

Po = $4 + 5% / (20% - 5%)

= $4.2 / 15%

Po= $28

Step 2

P4 =D4 + G / (Ke- G)

P4 = Present value at 4th year

D4 Dividend paid in 4rd year

i.e. D0 x ( 1 + G)^n

D0 = $4

G = 5%

n = 4 years

D4 = $4 x (1.05)^4 = $4.86

So,

P4 = $4.86 + 5% / (20% - 5%)

= $5.11/ 15%

= $34.03

Step 3

Capital Gain = 4th year value - Today's Value

= $34.03 - $28

= $6.03

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