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

$69.033

Step-by-step explanation:

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

`P_(0) = (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) =`
`(10.9(1\ -\ .05))/(.10\ -\ (-5))`

`P_(0) =`
`(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.