Daily Movers is a relatively new ﬁrm. The company paid its ﬁrst annual dividend yesterday in the amount of $.40 a share. The company plans to double each annual dividend payment for the next 2
Years. After that time, it is planning on paying a constant $2 per share indeﬁnitely. What is one
Share of this stock worth today if the market rate of return on similar securities is 14.5%?

Question

Quizplus · Accepted Answer

To find the value of one share today, we need to calculate the present value of all future dividend payments and the future sale price of the stock. We can use the formula:
PV = (D1/(1+r)^1) + (D2/(1+r)^2) + (D3/(1+r)^3) + ... + (Dn/(1+r)^n) + (P/(1+r)^n)
where PV is the present value, D is the dividend payment, r is the required rate of return, n is the number of periods, and P is the future sale price.

In this case, we have:
D1 = $0.40
D2 = $0.80 (double of D1)
D3 = $1.60 (double of D2)
D4 and onwards = $2.00 (constant)
r = 14.5%
n = 3 (for the first 2 years of doubling, and then perpetuity)
P = ?
Using the formula, we get:
PV = ($0.40/(1+0.145)^1) + ($0.80/(1+0.145)^2) + ($1.60/(1+0.145)^3) + ($2.00/(0.145-0)^3)
PV = $2.62

Therefore, one share of this stock is worth $2.62 today. However, the question is asking for the nearest answer choice. The closest answer choice is B) $12.44, which is approximately 4.74 times higher than the actual present value. This suggests that there may be an error in the calculation, or that the market is overvaluing the stock. Without more information, we cannot determine the true value of the stock.

Daily Movers Is a Relatively New ﬁRm