Devon Share Value
1. **State the problem:** We want to find the expected value of a share of Devon on December 1, 2018, given that the first dividend of $0.45 will be paid on December 1, 2021, and dividends grow at 5.1% annually thereafter. The equity cost of capital is 11.1%.
2. **Identify the variables:**
- Dividend at 2021, $D_3 = 0.45$
- Growth rate, $g = 0.051$
- Cost of capital, $r = 0.111$
- We want the price at 2018, which is 3 years before 2021.
3. **Calculate the price at 2021 (just before dividend):**
The price at 2021, $P_3$, is the value of all future dividends starting from 2022, growing at rate $g$:
$$
P_3 = \frac{D_4}{r - g} = \frac{D_3 (1+g)}{r - g} = \frac{0.45 \times (1 + 0.051)}{0.111 - 0.051} = \frac{0.45 \times 1.051}{0.06} = \frac{0.47295}{0.06} = 7.8825
$$
4. **Calculate the price at 2018, $P_0$:**
Since 2018 is 3 years before 2021, discount $P_3$ and $D_3$ back 3 years:
$$
P_0 = \frac{D_3}{(1+r)^3} + \frac{P_3}{(1+r)^3} = \frac{0.45}{(1.111)^3} + \frac{7.8825}{(1.111)^3}
$$
Calculate $(1.111)^3$:
$$
(1.111)^3 = 1.111 \times 1.111 \times 1.111 \approx 1.371
$$
So,
$$
P_0 = \frac{0.45}{1.371} + \frac{7.8825}{1.371} = 0.328 + 5.75 = 6.078
$$
5. **Final answer:** The expected value of a share of Devon on December 1, 2018, is approximately **6.08**.