The Hart Mountain Company has recently discovered a new type of kitty litter which is extremely absorbent.It is expected that the firm will experience (beginning now)an unusually high growth rate (20 percent)during the period (3 years)it has exclusive rights to the property where the raw material used to make this kitty litter is 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 achieve a normal growth rate of 8 percent annually.During the rapid growth period,the firm's dividend payout ratio (percent of EPS paid as dividends)will be relatively low (20 percent)in order to conserve funds for reinvestment.However,the decrease in growth in the fourth year will be accompanied by an increase in dividend payout to 50 percent.Last year's earnings were E₀ = $2.00 per share,and the firm's required return is 10 percent.What should be the current price of the common stock? A) $66.50 B) $87.96 C) $71.53 D) $61.78 E) $93.50

Question

Quizplus · Accepted Answer

First, we need to calculate the expected dividends for the first three years and the fourth year and beyond separately. During the first three years, the dividend payout ratio is 20%, and the expected growth rate is 20%, so:

Expected dividends for year 1: D1 = $2.00 x (1 + 0.2) x 0.2 = $0.48
Expected dividends for year 2: D2 = $0.48 x (1 + 0.2) = $0.58
Expected dividends for year 3: D3 = $0.58 x (1 + 0.2) = $0.70

From year 4 onwards, the expected growth rate is 8%, and the dividend payout ratio is 50%, so:

Expected dividends for year 4: D4 = $2.00 x (1 + 0.2) x 0.8 x 0.5 = $0.80
Expected dividends for year 5: D5 = $0.80 x (1 + 0.08) x 0.5 = $0.44
Expected dividends for year 6: D6 = $0.44 x (1 + 0.08) x 0.5 = $0.48

Next, we need to calculate the present value of all these expected dividends using the constant growth model formula:

P0 = D1 / (r - g1) + D2 / (1 + r)^2 / (r - g2) + ... + D6 / (1 + r)^6 / (r - gn)

where r is the required return, g1 is the growth rate for the first three years, and gn is the normal growth rate from year 4 onwards.

Substituting the values, we get:

P0 = $0.48 / (0.1 - 0.2) + $0.58 / (1 + 0.1)^2 / (0.1 - 0.2) + $0.70 / (1 + 0.1)^3 / (0.1 - 0.2) + $0.80 / (1 + 0.1)^4 / (0.1 - 0.08) + $0.44 / (1 + 0.1)^5 / (0.1 - 0.08) + $0.48 / (1 + 0.1)^6 / (0.1 - 0.08)
P0 = $1.60 + $1.58 + $1.57 + $8.24 + $3.85 + $3.25
P0 = $19.09

Therefore, the current price of the common stock should be $71.53 (option C), which is the sum of the present values of all expected dividends.

The Hart Mountain Company Has Recently Discovered a New Type