###### Pricing and Valuing Interest Rate Swap ...

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Valuing a stock involves assuming that its growth rate will slow down to a long-term rate comparable to the economy. The value projected at the end of the high-growth stages based on the long-term growth rate is known as the * terminal value* of the stock (or continuing value).

The terminal value may be calculated :

- Using the Gordon growth model.
- Applying a multiple, e.g., P/E to an estimated fundamental, e.g., EPS at the terminal date.

Consider the following information:

- Recently paid annual dividend = $0.40.
- Dividend growth rate = 12% for the next 5 years.
- The growth rate will stabilize to a long-term rate of 4%.
- Trailing P/E ratio at the end of the initial high-growth period = 6.
- Retention ratio = 25%.
- Required rate of return = 12%.

Using the Gordon growth model, the terminal value is calculated as:

$$\begin{align*}\text{Year 5 dividends}&=0.40(1.12)^{5}\\&=0.70\\ \\ \text{Terminal value}&=\frac{0.70(1.04)}{12\%-4\%}\\&=\frac{0.728}{0.08}\\&=9.16\end{align*}$$

Using a P/E multiple, the terminal value is calculated as:

$$\begin{align*}\text{Year 5 dividends}&=0.70\\ \\ \text{Year 5 EPS}&=\frac{0.70}{0.75}=0.9333\end{align*}$$

Applying the trailing P/E of 6 based on year 5 EPS of 2.8, the terminal value is:

$$\text{V}_{0}=0.9333\times6=5.6$$

## Question

A company’s current EPS of $2.50 is expected to grow at 12% for 8 years. After that, it will decline to a long-term rate of 4%. If the trailing P/E at the end of the high growth stage is 9, the terminal value is

closestto:

- $22.55.
- $57.80.
- $55.70.
## Solution

The correct answer is C.$$\begin{align*}\text{EPS}_{8}&=2.50(1.12)^{8}=6.19\\ \\ \text{Terminal value}&=6.19\times9=55.71\end{align*}$$

Reading 23: Discounted Dividend Valuation

*LOS 23 (k) D**escribe the terminal value and explain alternative approaches to determining the terminal value in a DDM.*