The Brigapenski Co. has just paid a cash dividend of $2 per share. Investors require a 16 percent return from investments such as this. If the dividend is expected to grow at a steady 8 percent per year, what is the current value of the stock? What will the stock be worth in five years?

Question

Accepted Answer

The last dividend, [latex]D_{0}[/latex], was $2. The dividend is expected to grow steadily at 8 percent. The required return is 16 percent. Based on the dividend growth model, we can say that the current price is:

[latex]P_{0} = D_{1}/(R – g) = D_{0} × (1 + g)/(R – g)[/latex]
= $2 × 1.08/(.16 – .08)
= $2.16/.08
= $27

We could calculate the price in five years by calculating the dividend in five years and then using the growth model again. Alternatively, we could recognize that the stock price will increase by 8 percent per year and calculate the future price directly. We’ll do both. First, the dividend in five years will be:

[latex]D_{5} = D_{0} × (1 + g)^5[/latex]
= $2 × [latex]1.08^5[/latex]
= $2.9387

The price in five years would therefore be:

[latex]P_{5} = D_{5} × (1 + g)/(R – g)[/latex]
= $2.9387 × 1.08/.08
= $3.1738/.08
= $39.67
Once we understand the dividend model, however, it’s easier to notice that:

[latex]P_{5} = P_{0} × (1 + g)^5[/latex]

= $27 × [latex]1.08^5[/latex]

= $27 × 1.4693
= $39.67

Notice that both approaches yield the same price in five years.

Question 8CRS-TP1: The Brigapenski Co. has just paid a cash dividend of $2 per ...

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