Question

EPS(1) = $6
Dividends per share (1) =0
Book Value per share (0) =$12

Company XYZ does not plan to pay any dividends in years 1, 2 ,or 3. It
will set dividends equal to its earnings. Assume that the ROE will stay constant over
time. The opportunity cost of capital is 20%. How much is Company ABC worth per share?

Answer 1

Computation of ABC share price

Here the EPS details and cost of capital/ opportunity cost of capital details are given.

also problem states this company is not going pay any dividend in the first three years time. There after it is going to pay their entire EPS as their dividend. Which means company going to matain 100% payout ratios.
So using the dividend discount model we can find the value of the stock as on the year in which company is starting to pay dividend. But however we need arrive at the price today therefore we have to discount the price after three years to today at the cost of capital or opportunity cost of capital i.e 20%.

Therefore price after three years

formula = estimated dividend/ (Cost of capital - growth rate)

in the given probelm no growth rate has been given

so divined estimated after three years is $ 6

cost capital 20%
= $6/0.20= $ 30

Bringing the price after three years to current date

=( Present value factor at 30% at the end 3 year* price as on that day)

= (1/1.2^3)*$30
= 0.5787*$30= $17.36
the value of the ABC share is $17.36