The saying "buy low, sell high" suggests that investors should make a:
If an investor buys at a low price and then sells at a higher price, then she has made a positive capital return. This is the answer to the question.
The equation that breaks total returns into income and capital returns is:
###\begin{aligned} r_\text{total}&=r_\text{income}+r_\text{capital} \\ &=\dfrac{C_1}{P_0} +\dfrac{P_1-P_0}{P_0} \\ \end{aligned}###The capital return is the last term:
###\begin{aligned} r_\text{capital} &= \dfrac{P_1-P_0}{P_0} = \dfrac{P_1}{P_0} - 1\\ \end{aligned}###The capital return will be positive when the sale price in one year ##(P_1)## is higher than the buy price now ##(P_0)##.
Commentary
The saying 'buy low, sell high' implies that capital returns are the best way to make money. While positive capital returns are certainly desirable, positive income returns are equally valuable, disregarding tax differences. Income cash flows ##(C_1)## occur in the form of dividends from stocks, rent from land or interest from debt.
The most important performance metric is the total return which is the sum of the capital and income returns. Investors seek high total returns on their wealth.
Given a constant total return, higher income returns actually reduce capital returns and vice versa. This can be seen when share prices fall following the payment of a dividend.
Question 490 expected and historical returns, accounting ratio
Which of the following is NOT a synonym of 'required return'?
There are many synonyms of required return, but the accounting rate of return is not one of them. Accounting rate of return is defined as:
###\begin{aligned} \text{Accounting rate of return} &= \dfrac{\text{Average net income}}{\text{Average investment}} \\ \end{aligned}###The average investment is often the business's average book assets. The accounting rate of return is not very useful since it uses book figures (historical cost) rather than market figures (current values). It also uses profit rather than cash flow which includes non-cash items such as depreciation, and it also ignores opportunity costs and the time value of money.
Some other types of often-used accounting returns which have the above problems are the accounting return on equity (ROE) and accounting return on assets (ROA):
###ROE = \dfrac{NI}{OE}### ###ROA = \dfrac{NI}{A}###Where NI is net income, OE is book owners' equity and A is book assets as in the balance sheet equation A = L + OE.
Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?
Shares pay dividends. Note that paying a dividend is a form of 'equity payout' from the dividend-paying firm's perspective. From the shareholder's perspective the dividend is income.
Which of the following equations is NOT equal to the total return of an asset?
Let ##p_0## be the current price, ##p_1## the expected price in one year and ##c_1## the expected income in one year.
All except answer d are mathematically equal to the total required return.
###\begin{aligned} r_\text{total} &= \dfrac{c_1+p_1-p_0}{p_0} \\ &= \dfrac{c_1}{p_0} + \dfrac{p_1-p_0}{p_0} \\ &= \dfrac{c_1}{p_0} + \dfrac{p_1}{p_0} - 1 \\ &= \dfrac{c_1+p_1}{p_0} - 1 \\ \end{aligned}###An asset's total expected return over the next year is given by:
###r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0} ###
Where ##p_0## is the current price, ##c_1## is the expected income in one year and ##p_1## is the expected price in one year. The total return can be split into the income return and the capital return.
Which of the following is the expected capital return?
The expected capital return is shown in answer d: ##r_\text{capital} = \dfrac{p_1}{p_0} - 1 = \dfrac{p_1-p_0}{p_0}##.
Answer a is the expected dollar income: ##c_1##.
Answer b is the expected dollar capital gain rather than return: ##p_1 - p_0##.
Answer c is the expected income return: ##\dfrac{c_1}{p_0}##.
Answer e is sometimes called the expected gross capital return: ##\dfrac{p_1}{p_0}##. Note that the gross return minus one equals the net capital return. Capital return and net capital return are used interchangeably. So ##r_\text{capital} = r_\text{net capital} = r_\text{gross capital} - 1##.
A stock was bought for $8 and paid a dividend of $0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year).
What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.
###\begin{aligned} r_\text{total} =& r_\text{capital} + r_\text{income} \\ =& \frac{P_1 - P_0}{P_0} + \frac{C_1}{P_0} \\ =& \frac{7- 8}{8} + \frac{0.50}{8} \\ =& -\frac{1}{8} + \frac{0.5}{8} \\ =& -0.125 + 0.0625 \\ \end{aligned}### So the capital return was -0.125 and the income return was 0.0625. The total return is the sum: ### r_\text{total} = 0.0625###
A share was bought for $30 (at t=0) and paid its annual dividend of $6 one year later (at t=1).
Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates?
The choices are given in the same order:
##r_\text{total}## , ##r_\text{capital}## , ##r_\text{dividend}##.
###\begin{aligned} r_\text{total} =& r_\text{capital} + r_\text{income} \\ =& \frac{P_1 - P_0}{P_0} + \frac{C_1}{P_0} \\ =& \frac{27 - 30}{30} + \frac{6}{30} \\ =& \frac{-3}{30} + \frac{6}{30} \\ =& -0.1 + 0.2 \\ \end{aligned}### So the capital return was -0.1 and the income return was 0.2. The total return is the sum: ### r_\text{total} = 0.1###
A fixed coupon bond was bought for $90 and paid its annual coupon of $3 one year later (at t=1 year). Just after the coupon was paid, the bond price was $92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
###\begin{aligned} r_\text{total} =& r_\text{capital} + r_\text{income} \\ =& \frac{P_1 - P_0}{P_0} + \frac{C_1}{P_0} \\ =& \frac{92 - 90}{90} + \frac{3}{90} \\ =& \frac{2}{90} + \frac{3}{90} \\ =& 0.0222 + 0.0333 \\ \end{aligned}### So the capital return is 0.0222 and the income return is 0.0333. The total return is the sum, so: ### r_\text{total} = 0.0556 ###
One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.
The expected total return on Frank's residential property is 7% pa.
He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $18,617.27.
The future value of 12 months of rental payments one year in the future is $19,920.48.
What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.
The rental yield, also called the income return, of a property is calculated as the dollar income at the end of the period divided by the current market price.
The future value of the annual rent cash flow ($19,920) is used as the income cash flow ##C_1## since the income return (##r_\text{income}##) is supposed to be the cash income received at the end of the year (t=1) divided by the market price now (t=0):
###r_\text{rent} = r_\text{income} = \dfrac{C_1}{P_0} = \dfrac{19,920}{500,000} = 0.039841###Notice that the current market price is $500,000, compared to the old market price of $600,000. The old price of $600,000 could be called the historical cost or book value. The current market price is the best estimate of how much the asset is actually worth if it was sold right now. That's why financiers prefer to always know the current market price. However, accountants prefer to use book prices because they're more certain, despite the fact that they are old, stale and a little useless.
An Apple (NASDAQ:AAPL) stock was purchased by an investor for $120 and one year later was sold for $150. A dividend of $4 was also collected at the end of the year just before the stock was sold.
Which of the following statements about the stock investment is NOT correct? Ignore taxes.
Over the year, the investor made a:
.
The dividend yield is equal to the cash dividend divided by the buy price at the start, not the sell price at the end of the year:
###\begin{aligned} r_\text{dividend} &= \dfrac{C_1}{P_0} \\ &= \dfrac{4}{120} \\ &= 0.033333333 \\ &= 3.3333333\% \\ \end{aligned}###The total return is the sum of the capital return and dividend return:
###\begin{aligned} r_\text{total} &= r_\text{capital} + r_\text{dividend} \\ &= \dfrac{P_\text{sell at end} - P_\text{buy at start}}{P_\text{buy at start}} + \dfrac{C_\text{end}}{P_\text{buy at start}} \\ &= \dfrac{P_1 - P_0}{P_0} + \dfrac{C_1}{P_0} \\ &= \dfrac{150 - 120}{120} + \dfrac{4}{120} \\ &= 0.25 + 0.033333333 \\ &= 0.283333333 \\ &= 28.3333333\% \\ \end{aligned}###