Question

A firm’s current profits are $400,000. These profits are expected to grow indefinitely at a constant annual rate of 4 percent. If the firm’s opportunity cost of funds is 6 percent, determine the value of the firm

(a)The instant before it pays out current profits as dividends.

(b) The instant after it pays out current profits as dividends.

Short answer

1. $P{V}_{firm}=\$21,200,000.$
   

2. $P{V}_{firm}^{dividend}=\$20,800,000.$

Step-by-step solution

(a) Determining the value of firm the instant before it pays out current profit as dividend. 

$$\begin{gathered} P_0=\$400,000, \\ g=4\%,i=6\%. \end{gathered}$$

To find the value of the firm, we substitute the given values in the equation:

$$\begin{gathered} P{V}_{firm}=P_0\left(\frac{1+i}{i-g}\right) \\ P{V}_{Firm}=\$400,000\left(\frac{1+0.06}{0.04-0.06}\right) \\ P{V}_{firm}=\$21,200,000 \end{gathered}$$

Therefore, the instant before is$\mathit{P}{\mathit{V}}_{\mathbf{f}\mathbf{i}\mathbf{r}\mathbf{m}}\mathbf{=}\mathbf{\$}\mathbf{21}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}$

(b) Determining the value of firm the instant after it pays out current profit as dividend.

$$\begin{gathered} P_0=\$400,000, \\ g=4\%,i=6\%. \end{gathered}$$

To find the value of the firm, we substitute the given values in the equation:

data-custom-editor="chemistry" $$\begin{gathered} {\mathrm{PV}}_{\mathrm{firm}}^{\mathrm{dividend}}={\mathrm{P}}_0\left(\frac{1+\mathrm{g}}{\mathrm{i}-\mathrm{g}}\right) \\ =\$400,000\left(\frac{1+0.04}{0.06-0.04}\right) \\ =\$20,800,000 \end{gathered}$$

Therefore, the instant after is$\mathit{P}{\mathit{V}}_{\mathbf{f}\mathbf{i}\mathbf{r}\mathbf{m}}^{\mathbf{d}\mathbf{i}\mathbf{v}\mathbf{i}\mathbf{d}\mathbf{e}\mathbf{n}\mathbf{d}}\mathbf{=}\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{800}\mathbf{,}\mathbf{000}\mathbf{.}$