###### Takeovers

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When estimating the terminal value, analysts use price multiples such as P/Es and P/Bs to estimate terminal values. There are two significant approaches to computing terminal values based on multiples:

The terminal value is computed as the product of the justified multiple and the estimate of earnings.

$$\begin{align*}\text{Terminal value}_{\text{n}}&=\text{Justified leading P⁄E}\times \text{Forecasted earnings}_{(\text{n}+1)}\\ \text{Terminal value}_{\text{n}}&=\text{Justified trailing P⁄E}\times \text{Forecasted earnings}_ {(\text{n})}\end{align*}$$

The terminal value is computed as the product of the benchmark multiple and the estimate of earnings.

$$\begin{align*}\text{Terminal value}_{\text{n}}&=\text{Benchmark leading P⁄E}\times \text{Forecasted earnings}_{(\text{n}+1)}\\ \text{Benchmark value}_{\text{n}}&=\text{Justified leading P⁄E}\times \text{Forecasted earnings}_ {(\text{n})}\end{align*}$$

The benchmark value could be the:

- Median industry P/E.
- Average industry P/E.
- Average of own past P/E.

An advantage of the price multiples approach is that it is grounded in market data, unlike the Gordon growth model that is based on multiple estimates and is very sensitive to changes in these estimates.

A disadvantage is that if the benchmark value is mispriced, the estimate of the terminal value will also reflect this mispricing.

Consider the following information:

$$\small{\begin{array}{l|l}\textbf{Values for subject firm} & \\ \hline\text{Required rate of return} & 10\% \\ \hline\text{EPS forecast in year five} & 1.4\\ \end{array}}$$

$$\small{\begin{array}{l|l}\textbf{Values for peer group} & \\ \hline \text{Mean dividend payout ratio} & 0.35 \\ \hline \text{Mean ROE} & 6\% \\ \hline \text{Median P/E} & 8\\ \end{array}}$$

Using P/Es to determine terminal value using the Gordon Growth model:

$$\begin{align*}\text{D}_5&= \text{EPS}_5\times\text{Dividend payout ratio}\\&=1.4 \times0.35\\&=0.49\end{align*}$$

$$\begin{align*}\text{Retention ratio}&=1-\text{Dividend payout ratio}\\&=1-0.35\\&=0.65\end{align*}$$

$$\begin{align*}\text{g}&=\text{Retention ratio} \times\text{ROE}\\&=0.65 ×6\%\\&=3.9\%\end{align*}$$

$$\begin{align*}\text{V}_5&=\frac{\text{D}_5(1+\text{g})}{\text{r}-\text{g}}\\&=\frac{0.49(1.039)}{0.10-0.039}\\&=8.35\end{align*}$$

Using P/Es to determine terminal value using comparables:

$$\begin{align*}\text{V}_5&= \text{P⁄E}\times\text{EPS}_5\\&=8×1.4\\&=11.20\end{align*}$$

## Question

Consider the following information:

$$\small{\begin{array}{l|l}\textbf{The required rate of return} & 14\% \\ \hline\text{EPS forecast for year six} & 2.5 \\ \hline\text{ROE} & 7\% \\ \hline\text{Dividend payout ratio} & 30\%\\ \end{array}}$$

The terminal value in year value is

closest to:

- 75.
- 9.
- 24.
## Solution

The correct answer is C.$$\begin{align*}\text{g}&=\text{Retention ratio}\times\text{ROE}\\ \\ \text{Retention ratio}&=1-\text{Dividend payout ratio}\\ &=1-0.30=0.70\\ \\ \text{g}&=0.70\times0.07\\&=4.9\%\\ \\ \text{D}_6&= 2.5 \times0.30\\&=0.75\\ \\ \text{V}_5&=\frac{0.75}{0.14-0.049}\\&=8.24\end{align*}$$

Reading 25: Market-Based Valuation: Price and Enterprise Value Multiples

*LOS 25 (l) Calculate and explain the use of price multiples in determining terminal value in a multistage discounted cash flow (DCF) model.*