Due to unfavorable economic conditions,EFB Company's earnings and dividends are expected to remain unchanged for the next 3 years.After 3 years,dividends are expected to grow at a 10 percent annual rate forever.The last dividend was $2.00,and the required rate of return is 20 percent.What should be the current market value of EFB stock?
A) $13.46
B) $14.51
C) $15.22
D) $16.03
E) $16.94

Question

Quizplus · Accepted Answer

The current market value of EFB stock can be calculated using the Dividend Discount Model (DDM) for a stock with dividends that grow at a constant rate. Since the dividends are expected to remain unchanged for the next 3 years, we first calculate the present value of these dividends. Then, we calculate the present value of the stock price at the end of year 3, which is when the dividends start growing at a constant rate.1. Calculate the present value of dividends for the first 3 years:$$PV = \frac{D}{(1+r)^1} + \frac{D}{(1+r)^2} + \frac{D}{(1+r)^3}$$Where $D = \$2.00$ (dividend), and $r = 0.20$ (required rate of return).$$PV = \frac{2}{(1+0.20)^1} + \frac{2}{(1+0.20)^2} + \frac{2}{(1+0.20)^3}$$$$PV = \frac{2}{1.20} + \frac{2}{1.44} + \frac{2}{1.728}$$$$PV = 1.67 + 1.39 + 1.16 = \$4.22$$2. Calculate the stock price at the end of year 3 using the Gordon Growth Model (since dividends grow at a constant rate after year 3):$$P_3 = \frac{D_4}{r - g}$$Where $D_4 = D \times (1+g) = 2 \times (1+0.10) = \$2.20$, $g = 0.10$, and $r = 0.20$.$$P_3 = \frac{2.20}{0.20 - 0.10} = \frac{2.20}{0.10} = \$22.00$$3. Calculate the present value of $P_3$:$$PV_{P3} = \frac{P_3}{(1+r)^3} = \frac{22}{(1+0.20)^3} = \frac{22}{1.728} = \$12.73$$4. Add the present value of the dividends for the first 3 years to the present value of $P_3$:$$PV_{total} = PV + PV_{P3} = 4.22 + 12.73 = \$16.95$$Rounding to two decimal places, the current market value of EFB stock is approximately \$16.94.

Due to Unfavorable Economic Conditions,EFB Company's Earnings and Dividends Are