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Solution:

Let s = the initial price of the stock on January 1, 2008. If the value of the stock falls 20 percent, then its price on January 1, 2009 will be

$\begin{array}{l}\Rightarrow \mathrm{F}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}\text{ Value =}\left(\mathrm{I}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\text{ Value}\right)\times \left(1-\frac{\mathrm{P}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\text{ Less Than}}{100}\right)\\ \Rightarrow 2009\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\mathrm{s}\right)\times \left[\text{1-}\left(\frac{20}{100}\right)\right]\\ \Rightarrow 2009\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\mathrm{s}\right)\times \left(\frac{80}{100}\right)\\ \Rightarrow 2009\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\frac{4}{5}\mathrm{s}\end{array}$

If the value of the stock then drops an additional 25 percent, then its price on January 1, 2010 will be

$\begin{array}{l}\Rightarrow \mathrm{F}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}\text{ Value =}\left(\mathrm{I}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}\text{ Value}\right)\times \left(1-\frac{\mathrm{P}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\text{ Less Than}}{100}\right)\\ \Rightarrow 2010\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\frac{4}{5}\mathrm{s}\right)\times \left[\text{1-}\left(\frac{25}{100}\right)\right]\\ \Rightarrow 2010\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\frac{4}{5}\mathrm{s}\right)\times \left(\frac{3}{4}\right)\\ \Rightarrow 2010\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\frac{3}{5}\mathrm{s}\\ \Rightarrow 2010\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\left(\frac{3}{5}\text{s}\times \text{100}\right)\to \text{60\% of s}\end{array}$

The final price of the stock is 60 percent of its original price s.

Alternatively, we could let value of the stock on January 1, 2008 be $100. Then on January 1, 2009, the price of the stock would have been $80. On January 1, 2010, the price of the stock would have been $60. Thus $\frac{60}{100}=\frac{6}{10}=60\mathrm{\%}$.