Question

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 $5.40, it is exactly one quarter until the first quarterly dividend from that $5.40, 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? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

expected quarterly dividend = expected annual dividend/no.of quarters in a year = $5.40/4 = $1.35‬

quarterly required rate of return = annual required rate of return/no.of quarters in a year = 12%/4 = 3%

stock's worth = expected 1st quarter dividend/(1+quarterly required rate of return)no. of months/12 + expected 2nd quarter dividend/(1+quarterly required rate of return)no. of months/12 + expected 3rd quarter dividend/(1+quarterly required rate of return)no. of months/12 + expected 4th quarter dividend/(1+annual required rate of return) + terminal value/(1+annual required rate of return)

dividend paid at the end of 1st quarter will be discounted back for 3 months, 2nd quarter for 6 months, 3rd quarter for 9 months and 4th quarter for 12 months or a year.

terminal value is calculated at the end of year. so, it will be discounted back only for one year.

terminal value = expected annual dividend*(1+dividend growth rate)/(annual required rate of return - dividend growth rate) = $5.40*(1+0.04)/(0.12 - 0.04) = $5.40*1.04/0.08 = $5.616‬/0.08 = $70.2‬

stock's worth = $1.35/(1+0.03)3/12 + $1.35/(1+0.03)6/12 + $1.35/(1+0.03)9/12​​​​​​​ + $1.35/(1+0.03)​​​​​​​ + $70.2‬/(1+0.03)

stock's worth = $1.35/1.030.25 + $1.35/1.030.5​​​​​​​ + $1.35/1.030.75​​​​​​​ + $1.35/1.03 + $70.2/1.03

stock's worth = $1.35/1.0074170717777329521051879550209‬ + $1.35/1.0148891565092219468648520118936‬ + $1.35/1.0224166622294936979509681615748‬ + $1.35/1.03 + $70.2/1.03

stock's worth = $1.3400606737959383419745699205107‬ + $1.3301945255217957555995633165595‬ + $1.3204010164077082381961201352216‬ + $1.3106796116504854368932038834951‬ + $68.155339805825242718446601941748‬ = $73.46

this stock will be worth $73.46.