# A firm has just paid (the moment before valuation) a dividend of 55 and is expected to exhibit a...

## Question:

A firm has just paid (the moment before valuation) a dividend of {eq}55 {/eq} and is expected to exhibit a growth rate of {eq}10 \% {/eq} into the indefinite future. If the appropriate discount rate is {eq}14 \% {/eq}, what is the value of the stock?

## Using the Dividend Growth Model to Value a Stock:

The dividend growth model assumes the present value of future dividends from the stock to be the current market price that investors should be willing to pay for the shares. In order to determine the present value, the model assumes that dividends grow at a constant growth rate until perpetuity. The discount rate used represents the difference between the expected return and growth rate.

## Answer and Explanation:

Answer:

The value of the stock is $15.13.

Explanation:

As per the data provided by the firm:

- Last dividend, D0 = $0.55
- Constant growth rate = 10%
- Required return, r = 14%
- Current stock price, P0 =?

Computation:

Using the dividend growth model:

- P0 = D0 * (1 + g) / (r - g)
- P0 = $0.55 * (1 + 10%) / (14% - 10%)
- P0 = $0.605 / 4%
- P0 = $15.13

Note:

The question provided that the last dividend is 55, which seems peculiar. In the computation above the last dividend is assumed to be 55 cents and not $55.

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