Question

Consider the following three stocks: Stock A is expected to provide a dividend of $10 a share forever. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4% a year forever. 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?

Answer 1

Answer:

Value of stock =$100

Value of stock B=$83.33

Value of stock C = $104.51

Explanation:

Stock A

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

PV of a perpetuity =$\frac{CF}{ke}$

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 = $\frac{10}{0.1}$ =$100

Stock B

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

PV=$\frac{D_1}{ke-g}$

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= $\frac{5}{0.1-0.04}$ = $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 = $\frac{D1}{(1+ke)^1}+\frac{D2}{(1+ke)^2}+\frac{D3}{(1+ke)^3}+\frac{D4}{(1+ke)^4}+\frac{D5}{(1+ke)^5}+\frac{D6}{(1+ke)^6}+\frac{P6}{(1+ke)^6}$

where P6= $\frac{D7}{ke}=\frac{D6}{ke}$

Price of the stock C = $\frac{5}{(1+0.1)^1}+\frac{5(1.2)}{(1+0.1)^2}+\frac{5(1.2)^2}{(1+0.1)^3}+\frac{5(1.2)^3}{(1+0.1)^4}+\frac{5(1.2)^4}{(1+0.1)^5}+\frac{5(1.2)^5}{(1+0.1)^6}+\frac{5(1.2)^5}{0.1*(1+0.1)^6}$

= $34.2755+\frac{5(1.2)^5}{0.1*(1+0.1)^6}$ =$104.51

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

Answer 2

Answer:

If the market capitalization rate of each stock is $10 \%$, Stock $C$ is most valuable.

Explanation:

Calculation of price of the stock if market capitalization rate (ke) is $10 \%$Price of Stock $A=Dividend/ \mathrm{ke}$

$=10 / 0.10$

$=\ 100$

Price of Stock $B=D 1 / k e-g$

$=5 /(0.10- 0.04)$

$=\ 83.33$

Price of Stock $C=5 /(1.10)+6 /(1.10)^2+7.2 /(1.10)^ 3+8.64 /(1.10)^4+10.37 / (1.10)^ 5+\left(12.44 / 0.10 \times 1 /1.10^6\right)$

$=\ 104.50$

So, if the capitalization rate of each stock is $10 \%$, Stock $C$ is most valuable.

Learn more about capitalization, refer:

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