Springboro Tech is a young start-up company.No dividends will be paid on the stock over the next 15 years,because the firm needs to plow back its earnings to fuel growth.The company will pay a $15 per share dividend in 16 years and will increase the dividend by 4 percent per year thereafter.What is the current share price if the required return on this stock is 8 percent?
A)$118.22
B)$119.19
C)$120.00
D)$164.59
E)$240.00

Question

Quizplus · Accepted Answer

The current share price can be calculated using the dividend discount model for a stock that starts paying dividends at a future date and then grows at a constant rate. The first dividend ($15) will be paid in 16 years, and it will grow at a rate of 4% thereafter. The required return is 8%.First, calculate the present value of the first dividend:$$ PV = \frac{D_1}{(1 + r)^{t}} = \frac{15}{(1 + 0.08)^{16}} $$Then, since the dividends grow at a constant rate (g = 4% or 0.04) after the first payment, we use the Gordon Growth Model (also known as the Dividend Growth Model) to find the present value of all future dividends starting from year 16 onwards:$$ P_{16} = \frac{D_{17}}{r - g} = \frac{15 \times (1 + 0.04)}{0.08 - 0.04} $$$$ P_{16} = \frac{15 \times 1.04}{0.04} = \frac{15.6}{0.04} = 390 $$Now, we need to discount $P_{16}$ back to the present value:$$ PV = \frac{390}{(1 + 0.08)^{15}} $$$$ PV = \frac{390}{(1.08)^{15}} \approx 118.22 $$Therefore, the current share price is approximately $118.22.

Springboro Tech Is a Young Start-Up Company