Question

Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $10.90, but management expects to reduce the payout by 5 percent per year indefinitely. If you require a return of 10 percent on this stock, what will you pay for a share today?

Answer 1

Answer:

$69.033

Explanation:

As per dividend growth model, the current market price of a stock is given by the following equation:

$P_{0} = \frac{D_{0}(1\ +\ g) }{R\ -\ g}$

wherein, $P_{0}$ = current market price of a stock

             R = Required rate of return

             g = Annual growth rate in dividends

            $D_{0}$ = Dividend just paid

Hence, in the given case, since the dividend is reducing by 5% every year, we have,

$P_{0} =$ $\frac{10.9(1\ -\ .05)}{.10\ -\ (-5)}$

$P_{0} =$ $\frac{10.355}{.15}$  = $69.033

The given case corresponded to negative growth model wherein dividend paid is consistently falling till perpetuity. Hence, in the formula, g is deducted in the numerator and added in the denominator owing to negative sign.