Question

PerfectlySoft Corp. is experiencing rapid growth. Dividends are expected to grow at 21 percent per year during the next three years, 13 percent over the following year, and then 5 percent per year thereafter indefinitely. The required return on this stock is 11.11 percent, and the stock currently sells for $65.02 per share. What is the projected dividend (in $) for the coming year? Answer to two decimals, carry intermediate calcs. to four decimals.

please show steps******

Answer 1

D0	X
For the first three years
g1	0.21
D1	X*(1.21)
D2	X*(1.21)^2
D3	X*(1.21)^3
g2	0.13
D4	(X*(1.21)^3)*(1.13)
g3	0.05
D5	(X*(1.21)^3)*(1.13)*(1.05)
The price of the stock in year 5
According to the dividend growth model.
P5 = D5/(R-g3)
where R is .1111
P5	(X*(1.21)^3)*(1.13)*(1.05)/(.1111-.05)
The value of the stock today = sum of present value of future cash flows.
Using R = .1111
Year	1	2	3	4	5
Cash flow	X*(1.21)	X*(1.21)^2	X*(1.21)^3	(X*(1.21)^3)*(1.13)	(X*(1.21)^3)*(1.13)*(1.05)/(.1111-.05)
Present value	1.21X/(1.1111)	1.4641X/1.234543	(1.771561X/1.371701)	2.001864X/1.524097	2.101957X/.0611
Present value	1.089011X	1.19X	1.29X	1.31X	34.40192X
sum of present values	X*(1.089+1.19+1.29+1.31+34.402)
sum of present values	X*(39.281)
The value of the stock today is equal to $65.02.
X*(39.281) = 65.02
X = (65.02/39.281)
X = 1.65525
The projected dividend in the coming year is equal to $1.66.