Dividends Set Annually Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly payments. If the next...

Dividends Set Annually
Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly payments. If the next such “annual” dividend has been announced as $6, it is exactly one quarter until the first quarterly dividend from that $6, the effective annual required rate of return on the company’s stock is 12 percent, and all future “annual” dividends are expected to grow at 4 percent per year indefinitely,
how much will this stock be worth?

Since dividends come quarterly, first convert the 12 percent into an effective quarterly rate, then EAR:

i
quarterly

=
√?+??−?

Use the annuity equation or App, to calculate the present value of the first year’s dividends. It will be the present value of a four-period annuity with payments of $1.50.

Using this Dividend, we can value the stock’s dividends as the present value of a growing perpetuity due:

PV = PV (D
0
) +

[(
PV (D
0
)
)/(
i – g
)]