Question

Wayne, Inc.'s outstanding common stock is currently selling in the market for ​$54. Dividends of ​$1.99 per share were paid last​ year, return on equity is 32 ​percent, and its retention rate is 28 percent.

a. What is the value of the stock to​ you, given a required rate of return of 14 ​percent?

b. Should you purchase this​ stock?

c. Given a required rate of return of 14 ​percent, the value of the stock to you is ​($)?

Answer 1

Value of stock = D1 / (Re - g)

D1 = Dividend for year 1

g = Growth rate

Re = Required rate of return

a.

Step 1 = Calculation of Growth rate

g = b * r

b = Retention rate

r = Return on equity

g = 0.28 * 0.32

= 0.0896 or 8.96%

Step 2 - Calculation of D1

D1 = D0 (1+g)

= $1.99 * (1 + 0.0896)

= $1.99 * 1.0896

= $2.168304

Step 3 - Value of stock

= D1 / (Re - g)

= $2.168304 / (0.14 - 0.0896)

= $2.168304 / 0.0504

= $43.02190

The value of the stock is $43.02190

b. The value of the stock is $43.02190 but it currently sells in the market at $54. This means that the stock is overpriced and we should not purchase it.

c. Value of stock

= D1 / (Re - g)

= $2.168304 / (0.14 - 0.0896)

= $2.168304 / 0.0504

= $43.02190

The value of the stock is $43.02190

Note -

14% can be written as 0.14

8.96% can be written as 0.0896