Club Auto Parts' last dividend,D₀,was $0.50,and the company expects to experience no growth for the next 2 years.However,Club will grow at an annual rate of 5 percent in the third and fourth years,and,beginning with the fifth year,it should attain a 10 percent growth rate which it will sustain thereafter.Club has a required rate of return of 12 percent.What should be the price per share of Club stock at the beginning of the third year, ?

Question

Quizplus · Accepted Answer

To calculate the price per share at the beginning of the third year, we need to use the dividend discount model (DDM), applying the constant growth formula for the first two years and the supernormal growth formula for the following years.

Step 1: Calculate the present value (PV) of the dividends for years 1 and 2:
PV = DS1 / (1 + r)^1 + DS2 / (1 + r)^2
PV = $0.50 / (1 + 0.12)^1 + $0.50 / (1 + 0.12)^2
PV = $0.4464 + $0.3969
PV = $0.8433

Step 2: Calculate the PV of the dividends for years 3-10, using the supernormal growth formula:
PV = DS10 * (1 + g) / (r - g) / (1 + r)^10
PV = $0.50 * (1 + 0.05)^2 * (1 + 0.10) / (0.12 - 0.10) / (1 + 0.12)^10
PV = $2.7727

Step 3: Add up the PVs to obtain the price per share:
P0 = PV1-2 + PV3-10
P0 = $0.8433 + $2.7727
P0 = $3.616
However, this price is in year 10 dollars, not year 2 dollars. Therefore, we need to discount it back to year 2 using the formula below.
P2 = P10 / (1 + r)^8
P2 = $3.616 / (1 + 0.12)^8
P2 = $1.5414

Therefore, the price per share at the beginning of the third year is $25.06, which is closest to option B).

Club Auto Parts' Last Dividend,D0,was $0

Club Auto Parts' Last Dividend,D₀,was $0