Question

A stock just paid a dividend of Do = $3.125/year. This dividend is expected to grow at: g1 = 20%/year for the next 3 years after that (i.e., Years 1, 2, & 3); and then grows at a constant rate of g2 = 5% after 3 years (i.e., Year 4 to infinity). Assume required rate of return r = 12%. What is the value of this stock? $63.28 $68.48 $73.47 $79.26

Answer 1

Step 1:

Dividend at year 1 = Current year dividend ( 1+growth rate) = $3.125 (1+20%) = $3.75

Dividend at year 2 = Dividend at year 1 (1+growth rate) = $3.75 (1+20%) = $ 4.5

Dividend at year 3 = Dividend at year 2 (1+growth rate ) = $4.5 (1+20%) = $5.4

Step 2:

Dividend value after 3 years to infinity at year 3 = Dividend at year 4 / (rate of return - growth rate)

= [$5.4 *(1+5%)] / [12%-5%]

= $5.67 / 7%

= $81

Step 3:

Value of stock is present value of dividends paid for all years. Discounting all dividend cash flows at required rate of return will give value of stock

Value of stock = [$3.75 / (1+12%)^1] + [$4.5 / (1+12%)^2] +[$5.4 / (1+12%)^3] + [$81 / (1+12%)^3]

= [$3.75 /1.12] + [$4.5 / 1.2544] + [$5.4 / 1.404928] + [$81/1.404928]

= $3.35 + $3.59 + $3.87 + $57.66

= $68.47

Therefore, the value of stock is $68.48

Second option is correct