UTS Corporate Finance Theory and Practice 25557
Tutorial 5, Week 6
Homework questions.
A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns.
What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain.
Since dividends are expected to grow in perpetuity and the share is fairly priced, the dividend discount model (DDM) applies. The dividends and share price will grow at the same rate of 5% pa. For an explanation of why see question 3.
Let the dividend cash flow be ##c##, the price be ##p##, the capital return be ##r_\text{capital}## and the total return be ##r_\text{capital}##.
###\begin{aligned} c_2 &= c_1(1+r_\text{capital})^1 \\ &= 1(1+0.05)^1 \\ &= 1.05 \\ \end{aligned}###To find the capital gain from just after the first dividend (t=1) to just after the second dividend (t=2), find the price increase between time 1 and 2.
###\begin{aligned} p_1 &= p_0(1+r_\text{capital})^1 \\ &= 4(1+0.05)^1 \\ &= 4.2 \\ \end{aligned}### ###\begin{aligned} p_2 &= p_0(1+r_\text{capital})^2 \\ &= 4(1+0.05)^2 \\ &= 4.41 \\ \end{aligned}###The capital gain is the price increase which is the difference between ##p_2## and ##p_1##. ###\begin{aligned} \text{Capital gain over second year} &= p_2 - p_1 \\ &= 4.41 - 4.2 \\ &= 0.21 \\ \end{aligned}###
Another method which gives the same expected share prices is to grow by the total return and subtract the dividends at the appropriate time.
###\begin{aligned} p_1 &= p_0(1+r_\text{total})^1 - c_1 \\ &= 4(1+0.3)^1 - 1 \\ &= 5.2 - 1 \\ &= 4.2 \\ \end{aligned}### ###\begin{aligned} p_2 &= \left( p_1 - c_1 \right)(1+r_\text{total})^1 - c_2 \\ &= \left( p_0(1+r_\text{total})^1 - c_1 \right)(1+r_\text{total})^1 - c_1(1+r_\text{capital})^1 \\ &= \left( 4(1+0.3)^1 - 1 \right)(1+0.3)^1 - 1(1+0.05)^1 \\ &= (5.2 - 1) \times 1.30 - 1.05 \\ &= 4.41 \\ \end{aligned}###Question 442 economic depreciation, no explanation
A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa. All rates are effective annual returns.
What is the expected dividend cash flow, economic depreciation, and economic income and economic value added (EVA) that will be earned over the second year (from t=1 to t=2) and paid at the end of that year (t=2)?
No explanation provided.