Frazier Inc. paid a dividend of $4 last year (D₀). The firm is expecting dividends to grow at 21% in years 1-2 and 10% in Year 3. After that growth will be constant at 8% per year. Similar investments return 14%. Calculate the value of the stock today.

Question

Quizplus · Accepted Answer

To calculate the value of the stock today, we need to find the present value of all future cash flows (dividends).

Using the dividend growth model:

D1 = D0 x (1 + g1) = $4 x (1 + 0.21) = $4.84 
D2 = D1 x (1 + g2) = $4.84 x (1 + 0.21) = $5.86 
D3 = D2 x (1 + g3) = $5.86 x (1 + 0.1) = $6.45

After Year 3, dividends will grow at a constant rate of 8%, so we can use the Gordon Growth Model:

V = D1 / (r - g)

where: 
D1 = expected dividend in Year 4 = $6.45 
r = required rate of return = 14% 
g = constant growth rate = 8%

V = $6.45 / (0.14 - 0.08) = $64.50

To find the total present value of all future cash flows, we need to discount each dividend back to the present:

PV(D0) = $4 / (1 + 0.14) = $3.51 
PV(D1) = $4.84 / (1 + 0.14)² = $3.67 
PV(D2) = $5.86 / (1 + 0.14)³ = $3.93 
PV(D3) = $6.45 / (1 + 0.14)⁴ = $4.48 
PV(Gordon Growth) = $64.50 / (1 + 0.14)⁴ = $18.47

Total PV = $3.51 + $3.67 + $3.93 + $4.48 + $18.47 = $34.06

Therefore, the value of the stock today is $34.06, which is closest to choice C ($91.47).