Question

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 year and, beginning with the fourth year, should attain a 10% growth rate that it will sustain thereafter. The first dividend (D1) to be paid at the end of the first year is expected to be $0.50 per share. Investors require a 15% rate of return on Club's stock. What will Club's stock price be at the end of the first year ()?

Answer 1

P1=$8.43

Step-by-step explanation:

`D1= 0.5\\D2=0.5\\D3=D2(1+g3) = 0.5(1.05)=0.525\\D4=D3(1+g4) = 0.5(1.05)(1.1) =0.5775\\`

The value of the stock is equal to the present value of all cash-flows expected from holding the stock. At the end of year 1, the value of the stock is found by calculating the present value of the remaining dividends i.e D2, D3, D4, D5 etc till infinity.

Therefore price equals
`P1=(D2)/(1+ke) + (D3)/((1+ke)^(2) )  +(D4)/((ke-g)(1+ke)^(3) )`

given the values of Dividends calculated above and ke= 15% :

`P1=(0.5)/(1.15^(1) ) +(0.525)/(1.15^(2)) +(0.5775)/((0.15-0.1)(1.15^(3) ) = <strong>$8.43</strong>`