Question

2) The Club Auto Parts Company has just recently been organized. It is expected to experience no growth for the next 2 years as it identifies its market and acquires its inventory. However, Club will grow at an annual rate of 5% in the third and fourth years and, beginning with the fifth year, should attain a 10% growth rate which it will sustain thereafter. The last dividend paid was $0.50 per share. Club has a cost of capital of 12%. What should be the present price per share of Club common stock?

Answer 1

$20.84

Explanation:

div 1 = $0.50

div 2 = $0.50

div 3 = $0.50 x 1.05 = $0.525

div 4 = $0.525 x 1.05 = $0.55125

years 5 and beyond we need to use the growing perpetuity formula:

stock price = [div 4 x (1 + g)] / (r - g) = ($0.55125 x 1.1) / (12% - 10%) = $30.32

now to determine the current value of the stocks we must calculate the present value of the future dividends and stock price:

stock price = $0.50/1.12 + $0.50/1.12² + $0.525/1.12³ + $0.55125/1.12⁴ + $30.32/1.12⁴ = $0.45 + $0.40 + $0.37 + $0.35 + $19.27 = $20.84