Principles of Finance ACST603
Tutorial 11, Week 11 Dividends and dividend policy
Homework questions.
To receive the dividend you must own the stock when the market closes on which date?
To receive the cash dividend on the payment date, you must be the owner of the stock when the market closes on the last cum-dividend date. This is the trading day before the ex-dividend date.
On which date would the stock price increase if the dividend and earnings are higher than expected?
Earnings and dividends are usually announced at the same time. If earnings and dividends are higher than the market expected then the share price will usually rise on this positive news.
If the market is already open then the share price will rise the moment that the announcement is made .
If the announcement is made after the market has closed, then the stock price would rise at the open of the next trading day.
A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.
The share price is expected to fall during the:
The stock price will fall overnight between the market close (4pm in Australia) on the last with-dividend date and the market open (10am in Australia) on the ex-dividend date. This is because the dividend will only be paid to the shareholder who owns the share when the market closes on the last with-dividend date.
The dividend payment date is irrelevant. A share holder who held the share on the close of the last with-dividend date could sell the share before the dividend payment date and would still be paid the dividend.
All shareholders receive one new extra share for every one share they already owned in a 2-for-1 stock split, a 1-for-1 bonus issue and a 100% stock dividend. This will double the number of shares and halve the share price. Neither the company pays money to shareholders or vice versa.
All shareholders receive one new extra share for every two shares they already owned in a 3-for-2 stock split, a 1-for-2 bonus issue and a 50% stock dividend. This will increase the number of shares by 50% and reduce the share price by one third. Neither the company pays money to shareholders or vice versa.
All shareholders receive one new extra share for every four shares they already owned in a 1-for-4 bonus issue, a 5-for-4 stock split and a 25% stock dividend. This will increase the number of shares by 25% and reduce the share price by one fifth. Neither the company pays money to shareholders or vice versa.
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
To find the change in the stock price, remember that the stock split creates no wealth for shareholders, and no money changes hands between shareholders and the company.
###\text{WealthBefore} = \text{WealthAfter} ### ###n_0.P_0 = n_1.P_1 ### ###3 \times P_0 = 4 \times P_1 ### ###\dfrac{P_1}{P_0} = \dfrac{3}{4} ###To find the proportional change in the stock price from the stock split:
###\begin{aligned} r_P &= \dfrac{P_1 - P_0}{P_0} \\ &= \dfrac{P_1}{P_0} - 1\\ &= \dfrac{3}{4} - 1\\ &=-0.25 \\ \end{aligned}###The 4 for 3 stock split will:
- Decrease the share price by 25%;
- Increase the number of shares by 33.33% ##(=1/3)##.
- Cause no change in the market capitalisation of equity.
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
A 10 for 3 stock split means that for every 3 shares owned, 7 new shares will be gifted so that the investor ends up with 10 shares. Since no money is given by the investor to the company or vice versa, a stock split is neither an equity capital raising or a payout, it's nothing. The number of shares ##(n)## will increase by 7/3 (=2.3333).
Based on the idea that the assets and market capitalisation of equity ##(E)## remain unchanged, we can calculate the proportional change in the share price ##(r_E)##.
###E_\text{before} = E_\text{after}### ###n_\text{before}.P_\text{before} = n_\text{after}.P_\text{after}### ###n_\text{before}.P_\text{before} = n_\text{after}.P_\text{before}.(1+r_E)^1### ###3 \times P_\text{before} = 10 \times P_\text{before}.(1+r_E)### ###1+r_E = \dfrac{3 \times P_\text{before}}{10 \times P_\text{before}}### ###r_E = -0.7###Therefore the share price must fall by 70%.
A firm conducts a two-for-one stock split. Which of the following consequences would NOT be expected?
No explanation provided.
Question 625 dividend re-investment plan, capital raising
Which of the following statements about dividend re-investment plans (DRP's) is NOT correct?
If all shareholders participated in the DRP, it is true that there would be no dividend payments but there would be lots of new shares issued which will result in a share price fall. The share price fall from issuing new shares without payment to the company is sometimes called dilution. Shareholder wealth would be unaffected since the fall in share price will be offset by the higher number of shares owned.
In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.
###P_0=\dfrac{C_1}{r-g}###
Which of the following statements about the DDM is NOT correct?
Dividends are expected to grow by the capital return ‘g’, not the total return 'r'. So the dividend at time 2 (##C_2##) is equal to the dividend at time 1 (##C_1##) multipled by (1+g)^1:
###C_2=C_1(1+g)^1### ###C_3=C_1(1+g)^2=C_2(1+g)^1### ###C_4=C_1(1+g)^3=C_2(1+g)^2=C_3(1+g)^1###For certain shares, the forward-looking Price-Earnings Ratio (##P_0/EPS_1##) is equal to the inverse of the share's total expected return (##1/r_\text{total}##). For what shares is this true?
Use the general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS) and assume that all cash flows, earnings and rates are real rather than nominal.
A company's forward-looking PE ratio will be the inverse of its total expected return on equity when it has a:
Companies that pay out all of their earnings as dividends are not re-investing and are likely to have zero real growth in earnings, dividends and share price. Therefore next year's expected earnings per share (##EPS_1##) is equal to next year's expected dividends (##C_1##) and the real capital returns will be zero.
For these firms the forward looking PE ratio will be the inverse of the real total expected return:
###\begin{aligned} \text{PE ratio} &= \frac{P_0}{EPS_1} = \frac{P_0}{C_1} = \frac{1}{\left( \dfrac{C_1}{P_0}\right)} = \frac{1}{\left( r_\text{income} \right)} \\ &= \frac{1}{\left( r_\text{total} - r_\text{capital} \right)} = \frac{1}{\left( r_\text{total} - 0 \right)} = \frac{1}{r_\text{total}} \\ \end{aligned}###A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.
Which of the following statements is NOT correct?
No explanation provided.
Which firms tend to have high forward-looking price-earnings (PE) ratios?
Forward-looking PE ratios can be calculated on a per-share basis as the current share price divided by next year's expected earnings per share. Or by multiplying by the number of shares, the current market capitalisation of equity (E as in V=D+E) divided by next year's total expected earnings (also called net income (NI) or net profit after tax (NPAT)):
###\text{forward looking PE ratio} = \dfrac{\text{share price}_0}{\text{EPS}_1} = \dfrac{\text{market cap of equity}_0}{\text{Net Income}_1} ###PE ratios are best thought about by remembering that the current share price equals the present value of future dividend payments. For simple unlevered firms, dividends will equal earnings if there is: no debt; a 100% payout ratio; no change in net working capital; and minimal accrual items such as depreciation. Simple firms like this will have low forward-looking PE ratios when next year's expected earnings are temporarily high, or when the share price is low. Factors that lead to low share prices include:
- Low levels of future earnings such as negative growth firms;
- High discount rates from high levels of systematic risk; or
- Illiquidity, such as when trying to sell a small business which has few potential buyers.
Firms with a high proportion of cash as assets will have a low level of systematic risk, and therefore a low required return, making their share price high, so the numerator of the PE ratio will be large. Next year's expected earnings will be low since a large part of their earnings are from cash which has a low interest rate, therefore the denominator of the PE ratio will be low. Therefore firms with a lot of cash tend to have high PE ratios.
Another way of looking at this is to consider again a company that pays out all of its earnings as dividends and is therefore not re-investing and is likely to have zero real growth in earnings, dividends and share price. Therefore next year's expected earnings per share (##EPS_1##) is equal to next year's expected dividends (##C_1##) and the real capital return will be zero.
For these firms the forward looking PE ratio will be the inverse of the real total expected return:
###\begin{aligned} \text{PE ratio} &= \frac{P_0}{EPS_1} = \frac{P_0}{C_1} = \frac{1}{\left( \dfrac{C_1}{P_0}\right)} = \frac{1}{\left( r_\text{income} \right)} \\ &= \frac{1}{\left( r_\text{total} - r_\text{capital} \right)} = \frac{1}{\left( r_\text{total} - 0 \right)} = \frac{1}{r_\text{total}} \\ \end{aligned}###Since cash has zero systematic risk it has a very low total return (the risk free rate) and therefore firms with a lot of cash will have low total returns and their PE ratios will be high.
Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.
Firms in a declining industry with very low or negative earnings growth will have low stock prices, and therefore low forward looking price-to-earnings ratios.
Forward-looking PE ratios can be calculated on a per-share basis as the current share price divided by next year's expected earnings per share. Or by multiplying by the number of shares, the current market capitalisation of equity (E as in V=D+E) divided by next year's total expected earnings (also called net income (NI) or net profit after tax (NPAT)):
###\text{forward looking PE ratio} = \dfrac{\text{share price}_0}{\text{EPS}_1} = \dfrac{\text{market cap of equity}_0}{\text{Net Income}_1} ###PE ratios are best thought about by remembering that the current share price equals the present value of future dividend payments. For simple unlevered firms, dividends will equal earnings if there is: no debt; a 100% payout ratio; no change in net working capital; and minimal accrual items such as depreciation.
Simple firms like this will have high forward-looking PE ratios when next year's expected earnings are temporarily low, or when the share price is high. Factors that lead to high share prices include:
- High levels of future earnings such as high growth tech firms;
- Low discount rates from low levels of systematic risk; or
- High liquidity, such as when trying to sell big listed companies' shares which have lots of potential buyers.
Question 455 income and capital returns, payout policy, DDM, market efficiency
A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.
The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.
What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?
Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.
The firm is fairly priced, so its required return (cost of capital) of 8% must equal its expected return (or internal rate of return). Since the new projects' risks are the same as the old projects, the required return must also be 8%.
###r_\text{total, new} = r_\text{total, old} = 0.08###The new projects' expected return is 8% too, so the new projects must be fairly priced, therefore they have a zero net present value. Another way of looking at this is that the cost of capital (total required return or deserved return) equals the internal rate of return (expected return) therefore the NPV is zero.
The share price must not change since the NPV of the projects is zero and there is no new money raised or paid by the firm. Also, payout policy is irrelevant to firm value. So the new share price ##P_{0, \text{new}}## must equal the old share price ##P_{0, \text{old}}##. The old 3% growth rate in the dividend must be equal to the old growth rate in the share price which is the old capital return ##P_\text{capital old}##, according to the theory of the perpetuity equation. Applying the perpetuity with growth formula:
###\begin{aligned} P_{0, \text{new}} &= P_{0, \text{old}} \\ &= \dfrac{C_\text{1 old}}{r_\text{total old} - r_\text{capital old}} \\ &= \dfrac{1}{0.08 - 0.03} \\ &= 20 \\ \end{aligned}###The new dividend ##C_\text{1 new}## will be only $0.90, so the new long term capital return in the perpetuity formula can be calculated:
###\begin{aligned} P_{0, \text{new}} &= \dfrac{C_\text{1 new}}{r_\text{total new} - r_\text{capital new}} \\ 20 &= \dfrac{0.9}{0.08 - r_\text{capital new}} \\ \end{aligned}### ###\begin{aligned} r_\text{capital new} &= 0.08 - \dfrac{0.9}{20} \\ &= 0.08 - 0.045 \\ &= 0.035 \\ \end{aligned}###This new 3.5% pa growth rate in the dividends is also the long term capital return of the stock. Therefore the stock price should increase 3.5% each year, faster than the old 3% pa rate. This makes sense since the firm is re-investing more money and should be able to generate higher growth in assets, dividends and the stock price.
Note that the instantaneous capital return is zero since there was no price-sensitive news released, just a change in payout policy. All of the new projects that will be invested in have zero NPV. So there is no reason for the stock price to increase straightaway.
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
One hundred year case
To find the NPV of the investment when the 15% pa total return lasts for 100 years, subtract the price now and add the present value of the growing dividends and the capital price in 100 years.
Note that the fair total required return is 10% so ##r_\text{total} = 0.1## and the dividend yield is 7% so ##r_\text{div} = 0.07##. The growth rate in the dividend for the first 100 years must be 8% which is the 15% expected total return less the 7% dividend yield, so ##g_\text{div growth} = 0.08##.
###\begin{aligned} NPV &= -\text{Cost} + \text{Benefit} \\ &= -P_{\text{0, actual}} + P_{\text{0, fair}} \\ &= -P_{\text{0, actual}} + \text{PresentValueOfDividendsFor100Years} + \text{PresentValueOfFairPriceIn100Years} \\ &= -P_{\text{0, actual}} + \dfrac{C_1}{r_\text{total} - g_\text{div growth}} \left( 1 - \left( \dfrac{1+g_\text{div growth}}{1+r_\text{total}} \right)^{100} \right) + \dfrac{P_\text{100, fair}}{(1+r_\text{total})^{100}} \\ &= -P_{\text{0, actual}} + \dfrac{P_{\text{0, actual}} . r_\text{div}}{r_\text{total} - g_\text{div growth}} \left( 1 - \left( \dfrac{1+g_\text{div growth}}{1+r_\text{total}} \right)^{100} \right) + \dfrac{P_{\text{0, actual}}.(1+g_\text{div growth})^{100}}{(1+r_\text{total})^{100}} \\ &= -1,000 + \dfrac{1,000 \times 0.07}{0.1 - 0.08} \left( 1 - \left( \dfrac{1+0.08}{1+0.1} \right)^{100} \right) + \dfrac{1,000(1+0.08)^{100}}{(1+0.1)^{100}} \\ &=-1,000 + 3,100.93 \\ &=2,100.93 \\ \end{aligned}###Note that there's another way to calculate the fair price at time 100 ##P_\text{100, fair} = 1000(1+0.08)^{100} = 2,199,761.25634##, which is to value the stock as a perpetuity of the dividends from year 101 onwards:
###\begin{aligned} P_\text{100, fair} &= \dfrac{C_{101}}{r_\text{total} - g_\text{div growth low}} \\ &= \dfrac{C_{1}(1+g_\text{div growth high})^{100}}{r_\text{total} - g_\text{div growth low}} \\ &= \dfrac{P_\text{0, actual}.r_\text{div}(1+g_\text{div growth high})^{100}}{r_\text{total} - g_\text{div growth low}} \\ &= \dfrac{1,000 \times 0.07 \times (1+0.08)^{100}}{0.1 - 0.02} \\ &= \dfrac{70 \times (1+0.08)^{100}}{0.1 - 0.02} \\ &= 2,199,761.25634 \\ \end{aligned}###Perpetual case
To find the NPV of the investment when the 15% pa total return lasts forever, subtract the actual price now and add the present value of the fair price which is perpetuity of growing dividends using the DDM.
###\begin{aligned} NPV &= -\text{Cost} + \text{Benefit} \\ &= -P_{\text{0, actual}} + P_{\text{0, fair}} \\ &= -P_{\text{0, actual}} + \dfrac{C_\text{1}}{r_\text{total} - g_\text{div growth}} \\ &= -P_{\text{0, actual}} + \dfrac{P_{\text{0, actual}} . r_\text{div, actual}}{r_\text{total} - g_\text{div growth}} \\ &= -1,000 + \dfrac{1,000 \times 0.07}{0.1 - 0.08} \\ &= -1,000 + 3,500 \\ &=2,500 \\ \end{aligned}###| Actual and Fair Values and Returns | ||
| Actual | Fair Perpetual | |
| Total return pa | 0.15 | 0.10 |
| Capital return and dividend growth rate pa |
0.08 | 0.08 |
| Dividend return pa | 0.07 | 0.02 |
| Price ##(P_0)## | 1,000 | 3,500 |
Question 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct.
What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever):
No explanation provided.