Question

IBM just paid a $5 dividend and dividends are expected to grow at a perpetual rate of 8% for the foreseeable future. What is the value of the stock if investors require a 16% return?

Answer 1

Current price=D1/(Required return-Growth rate)

=(5*1.08)/(0.16-0.08)

which is equal to

=$67.50

Answer 2

Solution:

Given:

• Dividend just paid (D₀): $5

• Dividend growth rate (g): 8% (0.08)

• Required return (r): 16% (0.16)

Objective:
Calculate the value of the stock using the Gordon Growth Model (Dividend Discount Model for perpetual growth).

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Step 1: Calculate Next Year's Dividend (D₁)

Since dividends grow at 8%, the next dividend (D₁) is:

$$D_1=D_0\times (1+g)=5\times (1+0.08)=\mathrm{\$}5.40$$

Step 2: Apply the Gordon Growth Model

The stock value ($P_0$) is given by:

$$P_0=\frac{D_1}{r-g}$$

Plug in the values:

$$P_0=\frac{5.40}{0.16-0.08}=\frac{5.40}{0.08}=\mathrm{\$}67.50$$

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Final Answer:

The value of the stock is $\boxed{{\displaystyle 67.50}}$.