Mountain Top Nursery is a relatively young firm which just paid its first annual dividend of $0.30 a share.Management projects dividend increases of 15 percent per year for five years followed by a constant growth rate of 3.0 percent annually.What is this stock worth today if the applicable discount rate is 12.5 percent?

Question

Quizplus · Accepted Answer

We can use the dividend discount model to calculate the current stock price:
D0 = $0.30 (given)
D1 = $0.30 x 1.15 = $0.345
D2 = $0.345 x 1.15 = $0.39675
D3 = $0.39675 x 1.15 = $0.45608
D4 = $0.45608 x 1.15 = $0.52449
D5 = $0.52449 x 1.15 = $0.60216

Next, we can use the constant growth formula to calculate the present value of all future dividends beyond year 5:

PV = D5 / (r - g)
PV = $0.60216 / (0.125 - 0.03)
PV = $5.225

Finally, we can calculate the present value of all dividends up to year 5:

PV = D1 / (1 + r) + D2 / (1 + r)^2 + D3 / (1 + r)^3 + D4 / (1 + r)^4 + D5 / (1 + r)^5
PV = $0.345 / 1.125 + $0.39675 / 1.125^2 + $0.45608 / 1.125^3 + $0.52449 / 1.125^4 + $0.60216 / 1.125^5
PV = $1.819

Adding the two present values, we get the total stock price today:

Total Stock Price = $5.225 + $1.819 = $7.044

However, since we're asked for the stock price today, we need to discount this value back one year at the applicable discount rate of 12.5%:

Current Stock Price = $7.044 / (1 + 0.125) = $6.23, which is closest to choice C ($5.23).

Mountain Top Nursery Is a Relatively Young Firm Which Just