Question

Michael's, Inc., just paid $2.25 to its shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 4.9 percent. If you require a rate of return of 9.1 percent, how much are you willing to pay today to purchase one share of the company's stock?

Answer 1

Using the Gordon Growth Model, an investor who requires a 9.1% rate of return would be willing to pay $53.57 for a share of Michael's, Inc. stock, expecting future dividends to grow at a rate of 4.9 percent.

Step-by-step explanation:

To determine the value of Michael's, Inc. stock given the dividend payment and growth rate, we will use the Gordon Growth Model. This model is used in financial analysis to determine the present value of a stock based on a future series of dividends that grow at a constant rate. Given that Michael's, Inc. paid an annual dividend of $2.25 and announced that future dividends will be increasing by 4.9%, and the investor requires a 9.1% rate of return, the calculation is as follows:

Present value of stock = Dividend per share / (Required rate of return - Growth rate)

Present value of stock = $2.25 / (0.091 - 0.049)

Present value of stock = $2.25 / 0.042

Present value of stock = $53.57

Therefore, an investor would be willing to pay $53.57 today for one share of Michael's, Inc. stock, expecting the dividends to increase at a constant rate of 4.9 percent.

Answer 2

$56.20

Step-by-step explanation:

We know,

Under constant growth model, value of stock,
`P_(0)` =
`(D_(1))/(r - g)`

Here,

`D_(1)` = Expected dividend/Next year dividend =
`D_(0)` × (1 + g)

`D_(0)` = Current year dividend = $2.25

g = dividend growth rate = 4.9% = 0.049

r = required rate of return = 9.1% = 0.091

Therefore,

`D_(1)` = Expected dividend/Next year dividend = $2.25 × (1 + 0.049) = $2.25 × 1.049 = 2.36025

Putting the values into the above formula, we can get,

`P_(0)` =
`(2.36025)/(0.091 - 0.049)`

or,
`P_(0)` = 2.36025 ÷ 0.042

Therefore, I am willing to pay today to purchase one share of the company's stock,
`P_(0)` = $56.20