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

Answer:

$56.20

Explanation:

We know,

Under constant growth model, value of stock, $P_{0}$ = $\frac{D_{1}}{r - g}$

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,

$P_{0}$ = $\frac{2.36025}{0.091 - 0.049}$

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