Question

no excel please

The Pet Company has recently discovered a type of rock which, when crushed, is extremely absorbent.  It is expected that the firm will experience (beginning now) an unusually high growth rate (40%) during the period (3 years) when it has exclusive rights to the property where this rock can be found. However, beginning with the fourth year the firm's competition will have access to the material, and from that time on the firm will assume a normal growth rate of 5% annually.  During the rapid growth period, the firm's dividend payout ratio will be relatively low (20%), to conserve funds for reinvestment. However, the decrease in growth will be accompanied by an increase in dividend payout to 60%.  Last year's earnings were $10.00 per share (E0) and the firm's cost of equity is 16%.  What should be the current price of the common stock?

                        a.           $  95.64         d.           $109.53

                        b.          $104.20         e.           $106.01

                        c.          $116.95

Answer 1

The correct Answer is D

Let us understand how to compute the same.

Gievn the Last years earnings = $10 per share. Also given that growth in earnings for the next year is 40 %.

Therefore Earnings At the end of Year 1 = = $10 * 1.40 = $14

Earnings at the end of Year 2 = $14 * 1.40 = $ 19.60

Similarly we compute the following :-

	Year 1	Year 2	Year 3	Year 4
Growth Rate (A)	40%	40%	40%	5%
EPS (B)	14.00	19.60	27.44	28.81
Dividend Payour Ratio ('C)	20%	20%	20%	60%
Dividend (D=C x B)	2.80	3.92	5.49	17.29

Now given that from year 4 the earnings are expected to 5%.

We can compute the value of share at the end of year 3 by using the formula = D4/ (Re-G)

Where D4 = Dividend at the end of year 4 = $17.29

Re= Cost of Equity = 16%

G= Growth Rate= 5%

Therefore Value of Share at Year 3 = 17.29/(16-5)% =$ 157.16

Now using the dividend Discount Model we can compute the value of share today

=D1/(1- Re) + D2/(1- Re)^2 + D3/(1- Re)^3 + Value of Share At the end of Year 3/ (1- Re)^3

Where D1, D2 and D3 are the Dividend at the end of Year 1, 2 and 3 Respectively.

Therefore Value of Share today

	Year 1	Year 2	Year 3
Dividend	2.80	3.92	5.49
Value of Share At year 3 as computed			157.16
Total Cash Flows (A)	2.8	3.92	162.6444
Discount Factors @16% (B)	0.862069	0.743163	0.640658
Present Value (C=A x B)	2.414	2.913	104.199

A summation of all the present Values = $ 109.53 is the Value of the share today.