Question

You have already learned that the company where you work is being sold for \(300,000. The company’s income statement indicates current profits of \)11,000, which have yet to be paid out as dividends. Assuming the company will remain a “going concern” indefinitely and that the interest rate will remain constant at 9 percent, at which constant rate does the owner believe that profits will grow? Does this seem reasonable?

Short answer

The owner believes that the profit will grow at the constant rate of 5%. Thus, the situation is not reasonable

Step-by-step solution

Determining formula

We use the following formula for the present value of the firm:

$P{V}_{firm}={\pi }_0+\frac{{\pi }_0(1+g)}{(1+i)}+\frac{{\pi }_0{(1+g)}^2}{{(1+i)}^2}+\mathrm{.......}={\pi }_0\left(\frac{1+i}{1-g}\right)$

Where${\pi }_0$ represents the firm’s current profit to grow at a constant rate of g percent and interest rate i is greater than g.

Determining the constant rate at which the profit will grow, and if this is reasonable.

By substituting the given values, we get

$P{V}_{firm}=300,000;{\pi }_0=11,000;i=9\%=0.09$

$\begin{array}{c}300,000=11,000\left(\frac{1+0.09}{0.09-g}\right)\\ \frac{300,000}{11,000}=\frac{1.09}{0.09-g}\\ 300.(0.09-g)=11.\left(1.09\right)\\ 27-300g=11.99\\ 300g=15.01\\ g=\frac{300}{15.01}\\ =0.05\end{array}$

The owner believes that the profits of the firm will grow at a constant rate of 5%.

Therefore, the situation is not reasonable.