Implied Cost of Equity

EXERCISE 01

The share price is €25.00, the next dividend is €3.000, and subsequent annual growth is 0.00%.

r_E=\frac{D_1}{P_0}+g

r_E=\frac{3}{25}+0

12.00%

EXERCISE 02

The share price is €10.00, the next dividend is €2.000, and subsequent annual growth is 2.00%.

r_E=\frac{D_1}{P_0}+g

r_E=\frac{2}{10}+0.02

22.00%

EXERCISE 03

The share price is €43.75, the next dividend is €2.205, and subsequent annual growth is 5.00%. The last dividend was €2.10.

r_E=\frac{D_1}{P_0}+g

g=\frac{2.205}{2.1}-1=0.05

r_E=\frac{2.205}{43.75}+0.05

10.04%

EXERCISE 04

The share price is €35.00, the next dividend is €1.120, and subsequent annual growth is 5.00%.

r_E=\frac{D_1}{P_0}+g

r_E=\frac{1.12}{35}+0.05

8.20%

EXERCISE 05

The stock traded at $18.87 last year and trades at $20 today. The current dividend is $2. Assume dividends and prices grow at the same constant rate.

g=20/18.87-1,\quad D_1=2(1+g),\quad r_E=D_1/20+g

Expected return = 16.587%.

EXERCISE 06

The stock trades at €60 and has just paid a €1 dividend. ROE is 12% and payout is 30%, both constant forever.

g=0.70(0.12)=8.4\%,\quad D_1=1.084

r_E=1.084/60+0.084=10.2067\%

EPS_1=1.084/0.30

\frac{PVGO}{P_0}=1-\frac{1.084/0.30}{60(0.084+1.084/60)}\approx40.9972\%

PVGO / price = 40.997%.

Use forward earnings EPS₁ = D₁ / payout when computing no-growth value.