The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 20% a year for the next four years and then decreasing the growth rate to 5% per year. The company just paid its annual dividend in the amount of $1.00 per share. What is the current value of one share if the required rate of return is 9.25%?
A) $35.63
B) $38.19
C) $41.05
D) $43.19
E) $45.81

Question

Quizplus · Accepted Answer

To calculate the current value of one share, we need to use the dividend discount model:

PV = D1 / (r - g)

Where PV is the present value of one share, D1 is the dividend expected at the end of the first year, r is the required rate of return and g is the growth rate.

For the first four years, the dividend growth rate is expected to be 20%, so we can find the future dividends as follows:

D2 = D1 x (1 + g) = $1.00 x (1 + 0.2) = $1.20
D3 = D2 x (1 + g) = $1.20 x (1 + 0.2) = $1.44
D4 = D3 x (1 + g) = $1.44 x (1 + 0.2) = $1.73

After the fourth year, the dividend growth rate is expected to be 5%, so we can find the dividend for year 5 and use it as the constant growth rate from then onwards:

D5 = D4 x (1 + g) = $1.73 x (1 + 0.05) = $1.82

Now, we can calculate the present value of all future dividends using the dividend discount formula:

PV = $1.00/(0.0925 - 0.20) + $1.20/(1 + 0.0925)^2/(0.0925 - 0.20) + $1.44/(1 + 0.0925)^3/(0.0925 - 0.20) + $1.73/(1 + 0.0925)^4/(0.0925 - 0.20) + $1.82/(1 + 0.0925)^5/(0.0925 - 0.05)

PV = $7.78

Therefore, the current value of one share is $7.78. Answer C, $41.05, is the closest option to this value.