Question

The required return for Williamson Heating's stock is 12%, and the stock sells for $40 per share. The firm just paid a dividend of $1.00, and the dividend is expected to grow by 30% per year for the next 4 years, so D4 = $1.00(1.30)4 = $2.8561. After t = 4, the dividend is expected to grow at a constant rate of X% per year forever. What is the stock's expected constant growth rate after t = 4, i.e., what is X?

A: 5.17%
B: 5.44%
C: 5.72%
D: 6.02
E: 6.34

Answer 1

Answer:

E: 6.34

Explanation:

First we solve for the PV of the next years dividends using the lump sum PV formula:

$\frac{Dividends}{(1 + rate)^{time} } = PV$

rate = 12%

$\left[\begin{array}{ccc}Year&dividends&PV\\1&1.3&1.1607\\2&1.69&1.3473\\3&2.197&1.5638\\4&2.8561&1.8151\\\end{array}\right]$

Total of 5.8869

Then, this with the PV of the future dividends usign the gordon model should match 40 dollars.

so the PV of the indefinite sum of dividends should be: 40 - 5.8869 = 34.1131

\frac{Dividends_1}{return - growth} = Value

This is four years into the future thus, we discount as well for the rate of return We want ot knwo the value at the fourth year to solve for the grow rate:

34.1131 x 1.12^4 = 53.67762328

Now the formual for the gordon model requires next year dividends thus D0 x 1 + g and we don't know g so we have to operate to solve  it:

$\frac{2.8561 \times (1+g)}{0.12-g} =53.67762328\\2.8561 + 2.8561g = 53.67762328 / (0.12 - g)\\g ( 1 + 2.8561/53.67762328) = 0.12 - \frac{2.8561}{53.67762328} \\g = 0.066791608 \div 1.053208392= 0.063417277$

The correct answer would be E