we assume x=8

Probably Company's last dividend was $4. The dividend growth rate is expected to be constant at Ix % for 3 years, after which dividends are expected to grow at a rate of x % forever. If the firm's required return (r.) is 12%, what is its current stock price?

~ Assumption of x = 8 is given.

~ Expected Dividends:

"Dn" = Dividend for the year "n"

Dn = Previous dividend  x (1+growth rate)

D0 = Dividend for the year 0 = $4 (given)

Dividends will grow at the rate of 18% (1x%) for the next 3 years:

Therefore,

D1 = $4 x 1.18 = $4.72

D2 = $4.72 x 1.18 = $5.57

D3 = $5.57 x 1.18 = $6.57

After year 3, dividends will grow at 8% (x%) forever:

Therefore, D4 = $6.57 x 1.08 = $7.10

~ Terminal Value at the end of year 3:

= D4 / (r - g)

where,

r = required rate of return

g = growth rate

= $7.10 / (0.12 - 0.08)

= $177.50

~ Current stock price:

= D1/(1+r)¹ + D2/(1+r)² + (D3 + Terminal value)/(1+r)³

= $4.72/1.12¹ + $5.57/1.12² + ($6.57 + $177.50)/1.12³

= $4.21 + $4.44 + $131.02

= $139.67

Answer: Current stock price = $139.67