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Stock Valuation. FIL 341 Prepared by Keldon Bauer. Introduction. The valuation of all financial securities is based on the expected PV of future cash flows. Equity Valuation.

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## Stock Valuation

FIL 341

Prepared by Keldon Bauer

### Introduction

• The valuation of all financial securities is based on the expected PV of future cash flows.

### Equity Valuation

• Because equity has no stated maturity, the value of the security can be seen as the present value of a kind of perpetuity:

### Equity Valuation

• To use the equation above, one would have to forecast every dividend (or cash flow) forever, which is not realistic.

• To estimate the equity value, simplifying assumptions can be made.

• If we allow dividends (cash flows) to grow at a constant rate.

• If ks is fixed over the life of the stock.

[1]

[2]

### Equity Valuation

• The Gordon Constant Growth Model:

### Gordon Constant Growth Model

• Subtracting [2] from [1]:

### Gordon Constant Growth Model

• Solving for PV:

### Gordon Constant Growth Model

• Assumptions:

• g must be less than ks (or P0 = ¥)

• ks must be fixed

• Dividend growth must be smooth (constant)

• Note that this model works for any growth rate less than ks - including g=0

### Gordon Growth Model-Example

• If a share currently pays \$1.50 in annual dividends, is expected to grow at a rate of 5% per year, and has a required return of 14%, what should its share price be?

### Equity Valuation

• The Gordon Growth Model suggests that valuation is a function of:

• Dividend (or free cash flow),

• Growth in dividends (or free cash flows),

• Discount rate.

• How does current stock news affect the market’s estimates of these three measures?

### Equity Valuation

• Some have suggested that a company should not just have one constant growth rate.

• As a partial answer to that problem the same solution has been solved (virtually the same way) for a two stage growth valuation model.

• The solution is as follows:

### Two-Stage Dividend Growth Model

Where: P0 = Price of stock today.

D0= Most recent dividend (or cash flow).

g1 = Growth rate over the first growth period.

k = Required rate of return for common equity.

T = Length of time the first growth rate is expected to last.

g2 = Growth rate over the second growth period.

### Non-Constant Growth Valuation

• Since constant growth is unlikely, we will now consider how to value stock under non-constant growth.

• First, project dividends (or free cash flows) as far as practical.

• From there estimate a constant growth rate.

• Then take the PV as in chapter 6.

### Non-Constant Growth - Example

• If Buford’s Bulldozer is expected to pay the following dividends, and then grow indefinitely at 4.5% (assuming a discount rate of 14.50%), what would its stock value be?

### Non-Constant Growth - Example

• First we consider the price of the stock at time five.

### Non-Constant Growth - Example

• Next we sum all period cash flows.

\$ 1.09

2

3

4

5

0

1

14.5%

\$ 2.10

\$ 1.00

\$ 1.63

\$1.25

\$2.75

\$1.50

\$2.80

\$36.64

\$18.62

### Non-Constant Growth - Example

\$24.44 = Present Value

### Non-Constant Growth Valuation

• If the cash flows or dividends can be estimated for a short-term, after which a two-stage growth model is appropriate, then a similar procedure can be employed to estimate the value, only using a two-stage formula in the terminal cash flow, rather than the Gordon Growth Model.