Question

National Trucking has paid an annual dividend of $1 per share on its common stock for the past 15 years and is expected to continue paying a dollar a share long into the future. Given this, one share of the firm's stock is:
A) basically worthless as it offers no growth potential.
B) equal in value to the present value of $1 paid one year from today.
C) priced the same as a $1 perpetuity.
D) valued at an assumed growth rate of 1 percent.
E) worth $1 a share in the current market.

Answer 1

Answer:

C) priced the same as a $1 perpetuity.

Explanation:

If this company has been paying $1 and continues paying that indefinitely, Gordon growth model describes that a constant growth dividend. However, In this case, it is a constant growth rate of zero.  You use time value concept of perpetuity to price this stock using the infinite constant dividend as your cashflow at a certain required rate of return.

Assuming that the investors in National Trucking stock require a return of 5%, the price of this stock will be done as follows;

Price = $\frac{Div1}{r}$

where Div1 = next year's dividend = $1

r = required return which we assumed as being 5%

Price is therefore;

Price = $\frac{1}{0.05} \\ \\ = 20$

This stock will therefore be sold at $20