Consider the following three stocks: a. Stock A is expected to provide a dividend of $10 a share forever. b. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4% a year forever. c. Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i. e., years 2 through 6) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable

Value of stock =$100

Value of stock B=$83.33

Value of stock C = $104.51

Solution:

Stock A

A dividend of $10 a share forever is a perpetuity.

PV of a perpetuity =

where CF is the cash-flow expected per compounding period = $10

           ke=return on investment or market capitalization rate=0.1

Value of stock A = $100

Stock B

Given D1=$5, g = 4% forever- this stream of cash-flows can be valued using the constant growth model where

PV=

where D1 is the dividend expected at the end of year 1 = $5

            ke is the return on investment or market capitalization rate = 0.1

            g is the growth rate = 0.04

Value of stock B=  $83.33

Stock C

The stock dividends  have two distinct growth periods, the 1st 6 years where g= 20% and after that, zero growth

Price of the stock C =

where P6= =

Price of the stock C =

=  $104.51

Stock C is more valuable as it has a higher present value of cash flows.

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