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 (begin¬ning 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 will be relatively low (20 percent) in order to conserve funds for reinvest¬ment. However, the decrease in growth in the fourth year will be accom¬panied 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

To find the current price, we need to use the dividend discount model:

P0 = D1 /(1 + r) + D2 /(1 + r)^2 + D3 /(1 + r)^3 + D4 /(1 + r)^3 + P4 /(1 + r)^3

where D1 = E0 × (1 - payout ratio) = $2.00 × (1 - 0.20) = $1.60
D2 = D1 × (1 + growth rate) = $1.60 × 1.20 = $1.92
D3 = D2 × (1 + growth rate) = $1.92 × 1.20 = $2.30
D4 = D3 × payout ratio = $2.30 × 0.50 = $1.15
P4 = D4 /(r - growth rate) = $1.15 /(0.10 - 0.08) = $57.50

Plugging in the numbers:
P0 = $1.60 /(1 + 0.10) + $1.92 /(1 + 0.10)^2 + $2.30 /(1 + 0.10)^3 + $1.15 /(1 + 0.10)^3 + $57.50 /(1 + 0.10)^3
P0 = $71.53

Therefore, the current price of the common stock should be $71.53, which is closest to choice C, $71.53.

The Hart Mountain Company Has Recently Discovered a New Type