###### Supervised Machine Learning Algorithms

1. Penalized Regression Penalized regression is a technique that is useful for reducing/shrinking... **Read More**

The value of a stock can be evaluated as the sum of:

- The value of the company without earnings reinvestment, \((\text{E}_{1}/\text{r})\); plus
- The present value of growth opportunities (PVGO).

$$\text{V}_0= \frac{E_1}{\text{r}}+\text{PVGO}$$

Where:

\(\text{E}_{1}=\) Expected earnings at time, \(t = 1\).

\(\text{r} =\) Required rate of return.

The present value growth opportunities (PVGO) sums the present value of opportunities to reinvest future earnings profitably. Earnings growth may increase, remain unchanged, or reduce shareholder wealth depending on whether the growth results from earning returns above, equal to, or less than the opportunity cost of funds. The PVGO is determined by:

- The company’s options to invest, and
- The company’s options to start, scale, or abandon future projects.

Increases in shareholder wealth occur when reinvested earnings earn more than the opportunity cost of funds. Companies with no prospects for investing in positive NPV projects are referred to as no-growth companies. They should distribute their earnings to shareholders as dividends to redirect capital to more attractive areas.

The present value of growth opportunities can be restated in terms of the P/E ratio based on forecasted earnings:

$$\frac{V_o}{E_1}\ \text{or}\ \frac{P_0}{E_1}\ \text{or}\ \text{P⁄E}= \frac{1}{\text{r}}+ \frac{\text{PVGO}}{\text{E}_1}$$

The first term, \(\frac{1}{\text{r}}\), is the value of the P/E for a no-growth company. The second term, \( \frac{\text{PVGO}}{\text{E}_1}\), is the component of the P/E value that relates to growth opportunities.

XYZ Ltd shares sell for $60 on future earnings per share of $2.00. Suppose that the required return is 10%. The PVGO is *closest* to:

$$\begin{align*}\text{V}_0&=\frac{\text{E}_1}{\text{r}}+\text{PVGO}\\ \\60&=\frac{2}{0.01}+\text{PVGO}\\ \\ \text{PVGO}&= \$60-\$20 = \$40\end{align*}$$

The market assigns 66.67% of the price \(\bigg(\frac{$40}{$60}\bigg)\) to future growth.

## Question

Suppose a company’s earnings per share is expected to be $1.50. If its required rate of return is 12% and its share market price is $36, its PVGO is

closestto:

- $12.
- $23.
- $36.
## Solution

The correct answer is B.$$\begin{align*}36&= \frac{1.50}{0.12}+\text{PVGO}\\ \\4.32&=1.50 +0.12(\text{PVGO})\\ \\2.82&= 0.12(\text{PVGO})\\ \\ \text{PVGO}&=23\end{align*}$$

Reading 23: Discounted Dividend Valuation

*LOS 23 (f) C**alculate and interpret the present value of growth opportunities (PVGO) and the component of the leading price-to-earnings ratio (P/E) related to PVGO.*