Question

1) 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 (20%) 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 8% 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 50%. Last year's earnings were $2.00 per share (E0) and the firm's cost of equity is 10%. What should be the current price of the common stock?

Answer 1

$ 71.83

Explanation:

This year's earnings=last year's earnings*(1+growth rate)=$2*(1+20%)=$2.4

This year's dividend=2.4 *payout ratio=2.4 *20%=$0.48

Next year's earnings=$2.4*1.2=$2.88

Next year's dividend=2.88 *0.2=$ 0.58

Year 3 earnings=$2.88*1.2=$ 3.46

Year three dividend= 3.46*0.2=$0.69

year 4 earnings =$3.46*1.08=$ 3.74

Dividend from year 4 onward= 3.74 *0.5=1.87

From year 4 terminal value=1.87 /(cost of equity-growth rate)=1.87/(10%-8%)=$93.5

Share price is present value of the above dividends amnd terminal value=0.48/(1+0.1)^0+0.58/(1+0.1)^1+0.69/(1+0.1)^2+93.5/(1+0.1)^3=$ 71.83