Present value models are based on a fundamental tenet of economics stating that individuals defer consumption in order to reap future benefits. Therefore, the value of an investment today should be worth the present value of expected future benefits, defined as dividends or free cash flow.

## Dividend Discount Model

The dividend discount model looks at cash flows from the investor’s perspective in which cash is received from distributions during the holding period and the final sale price upon liquidation of the security.

$$ V_0=\sum_{t=1}^n\frac{D_t}{(1+r)^t}+\frac{P_n}{(1+r)^n}$$

*V _{0}* = present value of a share of the stock today

*D _{t}* = expected dividend in year

*t*

*r* = required rate of return on the stock

The first part of the equation is simply the sum of the next dividend payments that will occur at some point in the future, each discounted back at the required rate of return so that we arrive at a present value today.

The second part of the equation is the discounted terminal stock value or the expected selling price at the end of the investment horizon.

## Free-cash-flow-to-equity Models

Instead of measuring expected dividends, the free-cash-flow-to-equity (FCFE) model is based on the company’s expected dividend-paying capacity. The calculation of FCFE starts with the cash flows from operations (CFO):

$$ CFO = \text{Net income} + \text{Noncash expenses} -\text{Working capital} $$

Then, we can come up with the free-cash-flow-to-equity (FCFE) calculation:

$$ FCFE = CFO – \text{Fixed capital investment} + \text{Net borrowing} $$

Where *Net borrowing* is simply *Borrowings* minus *Repayments*.

QuestionThe following is taken from an analyst’s valuation of CBA, Inc:

$$

\begin{array}{l|r}

\text{Current Price} & \$8.50 \\

\hline

\text{Expected Year 1 Dividend} & \$1.00 \\

\hline

\text{Expected Year 2 Dividend} & \$1.15 \\

\hline

\text{Expected Sale Price (End of Year 2)} & \$8.75 \\

\end{array}

$$The analyst’s required return is 8%. Based on the analyst’s estimates and using the dividend discount model, the stock price of CBA, Inc. is currently:

A. Fairly valued

B. Overvalued

C. Undervalued

SolutionThe correct answer is C.

Based on the given inputs, the stock’s estimated value is equal to year 1 cash flows ($1.00/1.08 = $0.93) plus year 2 cash flows (($8.75 + $1.15)/1.08

^{2}= $8.49), or approximately $9.41. Because the stock’s estimated value exceeds its current price, the stock is undervalued.

*Reading 41 LOS 41e:*

*Explain the rationale for using present value models to value equity and describe the dividend discount and free-cash-flow-to-equity models*