Financial Markets and Valuation MGNT808
Tutorial 1, Week 1
Homework questions.
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}###Question 915 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For a share price to double over 7 years, what must its capital return be as an effective annual rate?
If the stock price doubled, it may have increased from $1 to $2 over the 7 year period.
###P_0 = \dfrac{P_T}{(1+r_\text{eff annual})^{T_\text{years}}} ### ###P_0 = \dfrac{P_7}{(1+r_\text{eff annual})^7} ### ###1 = \dfrac{2}{(1+r_\text{eff annual})^7} ### ###(1+r_\text{eff annual})^7 = 2### ###1+r_\text{eff annual} = 2^{1/7}### ###\begin{aligned} r_\text{eff annual} &=2 ^ {1/7} - 1 \\ &= 0.104089514 \\ &= 10.4089514 \text{ % pa}\\ \end{aligned}###Question 278 inflation, real and nominal returns and cash flows
Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.
Inflation is the proportional increase in price levels. An inflation rate of 2% means that a product that costs $10 now will cost $10.20 (=10(1+0.02)1) in one year.
If you have $1,000 in the bank right now, you can buy 100 (=1,000/10) products.
The bank interest rate is 1% so $1,000 in the bank will grow to be $1,010 (=1,000(1+0.01)1) in one year. Product prices are $10.20 at this time, so we can only buy 99 (or 99.02 =1,010/10.20) products rather than 100 products before.
Economist's method
An economist would say that the higher inflation rate has eroded our buying power.
A short cut to doing the calculations above is to find the real return using the Fisher equation,
###\begin{aligned} 1+r_\text{real} &= \frac{1+r_\text{nominal}}{1+r_\text{inflation}} \\ &= \frac{1+0.01}{1+0.02} \\ \end{aligned}###
###\begin{aligned} r_\text{real} &= \frac{1+0.01}{1+0.02} -1 \\ &= 0.990196078 -1 \\ &= -0.009803922 = -0.9803922\% \\ \end{aligned}###
This says that our real return is negative, so our wealth buys 0.98% less after one year, so instead of buying 100 products we can only buy 99.02 (=100(1-0.0098)) products in one year.
Note that the exact Fisher equation can be approximated:
###\begin{aligned} r_\text{real} &\approx r_\text{nominal} - r_\text{inflation} \\ &= 0.01 -0.02 \\ &= -0.01 = -1\%\\ \end{aligned}###
Commentary
This question was used in the '2004 Health and Retirement Survey' of Americans over the age of 50. The survey results were as follows:
- 75.2% of respondents answered it correctly,
- 13.4% were incorrect,
- 9.9% answered "don't know" and
- 1.5% refused to answer.
This question tests knowledge of inflation and was used in the research paper 'Financial Literacy and Planning: Implications for Retirement Wellbeing' by Annamaria Lusardi and Olivia S. Mitchell in 2011.
Question 728 inflation, real and nominal returns and cash flows, income and capital returns, no explanation
Which of the following statements about gold is NOT correct? Assume that the gold price increases by inflation. Gold has a:
No explanation provided.
Question 745 real and nominal returns and cash flows, inflation, income and capital returns
If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct?
The real income return of gold is zero since it pays nothing. No interest, dividends or rent. The nominal income yield on gold is also zero. Income yields are generally not affected much by inflation, unlike capital returns and total returns. One way to calculate the real income return from the nominal income return is:
###\begin{aligned} r_\text{real income} &= \dfrac{C_\text{1,real}}{P_0} \\ &= \dfrac{C_\text{1,nominal}/(1+r_\text{inflation})^1}{P_0} \\ &= \dfrac{\left(\dfrac{C_\text{1,nominal}}{P_0}\right)}{(1+r_\text{inflation})^1} \\ &= \dfrac{r_\text{nominal income}}{1+r_\text{inflation}} \\ &= \dfrac{0}{1+0.03} \\ &= 0 \\ \end{aligned}###Question 295 inflation, real and nominal returns and cash flows, NPV
When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:
(I) Discount nominal cash flows by nominal discount rates.
(II) Discount nominal cash flows by real discount rates.
(III) Discount real cash flows by nominal discount rates.
(IV) Discount real cash flows by real discount rates.
Which of the above statements is or are correct?
Nominal cash flows can be discounted using nominal discount rates. Also, real cash flows can be discounted using real discount rates. Both will give the same asset price.
###C_\text{0} = \dfrac{C_\text{t, nominal}}{(1+r_\text{nominal})^t} = \dfrac{C_\text{t, real}}{(1+r_\text{real})^t}###If the cash flows are nominal and the discount rate is real or vice-versa, it's usually easier to convert the discount rate to a nominal or real rate using the Fisher equation, and then discount the cash flows to arrive at the correct price.
###1+r_\text{real} = \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}}###Cash flows can also be converted from nominal to real or vice versa using the inflation rate.
###C_\text{t, real} = \dfrac{C_\text{t, nominal}}{(1+r_\text{inflation})^t}###In the 'Austin Powers' series of movies, the character Dr. Evil threatens to destroy the world unless the United Nations pays him a ransom (video 1, video 2). Dr. Evil makes the threat on two separate occasions:
- In 1969 he demands a ransom of $1 million (=10^6), and again;
- In 1997 he demands a ransom of $100 billion (=10^11).
If Dr. Evil's demands are equivalent in real terms, in other words $1 million will buy the same basket of goods in 1969 as $100 billion would in 1997, what was the implied inflation rate over the 28 years from 1969 to 1997?
The answer choices below are given as effective annual rates:
To find the inflation rate that makes $1 million grow into $100 billion in 28 years, use the 'present value of a single cash flow' equation:
###V_{0} = \dfrac{V_{t}}{(1+r_\text{inflation})^t} ### ###V_{1969} = \dfrac{V_{1997}}{(1+r_\text{inflation})^{28}} ### ###1,000,000 = \dfrac{100,000,000,000}{(1+r_\text{inflation})^{28}} ### ###(1+r_\text{inflation})^{28} = \dfrac{100,000,000,000}{1,000,000}### ###1+r_\text{inflation} = \left( \dfrac{100,000,000,000}{1,000,000} \right)^{1/28}### ###\begin{aligned} r_\text{inflation} &= (100,000)^{1/28} - 1 \\ &= 0.508591 \\ \end{aligned}###That's an unreasonably high inflation rate of more than 50% pa! This may indicate that in real terms, Dr. Evil's demands were much higher in 1997 compared to 1969.
Question 353 income and capital returns, inflation, real and nominal returns and cash flows, real estate
A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.
The nominal total return and capital return are given, therefore the nominal income return can be calculated.
###r_\text{nominal, total} = r_\text{nominal, income} + r_\text{nominal, capital} ### ###0.06 = r_\text{nominal, income} + 0.03 ### ###\begin{aligned} r_\text{nominal, income} &= 0.06 - 0.03\\ &= 0.03 \\ \end{aligned}###The Fisher equation can be used to convert nominal rates to real rates. The exact version is:
###1+r_\text{real} = \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}}###The approximation is:
###r_\text{real} \approx r_\text{nominal} - r_\text{inflation}###But the Fisher equation only applies to the total and capital returns, not the income return. This is obvious when considering the approximation of the Fisher equation. If inflation is subtracted from both the nominal capital and income returns, then since the total return is the sum of these two, inflation will be subtracted twice from the total return which is wrong.
Method 1: Fisher equation on total and capital returns
Work out the total and capital returns using the Fisher equation, then calculate the difference which is the income return.
To find the real total return:
###1+r_\text{real, total} = \dfrac{1+r_\text{nominal, total}}{1+r_\text{inflation}}### ###1+r_\text{real, total} = \dfrac{1+0.06}{1+0.02}### ###r_\text{real, total} = \dfrac{1+0.06}{1+0.02}-1 = 0.039215686 ###To find the real capital return:
###1+r_\text{real, capital} = \dfrac{1+r_\text{nominal, capital}}{1+r_\text{inflation}}### ###1+r_\text{real, capital} = \dfrac{1+0.03}{1+0.02}### ###r_\text{real, capital} = \dfrac{1+0.03}{1+0.02}-1 = 0.009803922 ###To find the real income return:
###r_\text{real, total} = r_\text{real, income} + r_\text{real, capital} ### ###0.039215686 = r_\text{real, income} + 0.009803922 ### ###\begin{aligned} r_\text{real, income} &= 0.039215686 - 0.009803922 \\ &= 0.029411765 \\ \end{aligned}###Method 2: Convert nominal cash flows to real cash flows
Discount all future nominal cash flows by inflation to get the real cash flows then calculate the real rates of return.
###\begin{aligned} r_\text{nominal, total} &= r_\text{nominal, income} + r_\text{nominal, capital} \\ &= \dfrac{C_\text{1, nominal}}{P_0} + \dfrac{P_\text{1, nominal}-P_0}{P_0} \\ \end{aligned}\\ \begin{aligned} r_\text{real, total} &= r_\text{real, income} + r_\text{real, capital} \\ &= \dfrac{C_\text{1, real}}{P_0} + \dfrac{P_\text{1, real}-P_0}{P_0} \\ &= \dfrac{ \left( \dfrac{C_\text{1, nominal}}{(1+r_\text{inflation})^1} \right) }{P_0} + \dfrac{\left( \dfrac{P_\text{1, nominal}}{(1+r_\text{inflation})^1} \right)-P_0}{P_0} \\ \end{aligned}\\###If the price now were, say, $1 then the nominal income cash flow in one period would be $0.03 which is the nominal income return times the price now. The nominal price in one period would be $1.03 ##(=1(1+0.03)^1)## which is the price now grown by the nominal capital return. Note that the price now ##(P_0)## is not affected by inflation. Substituting these and inflation into the above equation, the real returns can be calculated:
###\begin{aligned} r_\text{real, total} &= \dfrac{ \left( \dfrac{0.03}{(1+0.02)^1} \right) }{1} + \dfrac{\left( \dfrac{1.03}{(1+0.02)^1} \right)-1}{1} \\ &= 0.029411765 + 0.009803922 \\ &= 0.039215686 \\ \end{aligned}###So the real total return is 3.92%, the real capital return is 0.98% and the real income return is 2.94%.
Question 363 income and capital returns, inflation, real and nominal returns and cash flows, real estate
A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.
The Fisher equation can be used to calculate nominal and real rates. The exact version is:
###1+r_\text{real} = \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}}###The approximation is:
###r_\text{real} \approx r_\text{nominal} - r_\text{inflation}###The only problem is that the Fisher equation above only applies to the total and capital returns, not the income return. This is obvious when considering the approximation of the Fisher equation. If inflation is subtracted from the capital return and the income return, then since the total return is the sum of the capital and income return, inflation will be subtracted twice from the total return which is wrong.
Method 1: Fisher equation on total and capital returns
Work out the total and capital returns using the Fisher equation, then calculate the difference which is the income return.
To find the real total return:
###1+r_\text{real, total} = \dfrac{1+r_\text{nominal, total}}{1+r_\text{inflation}}### ###1+r_\text{real, total} = \dfrac{1+0.08}{1+0.02}### ###r_\text{real, total} = \dfrac{1+0.08}{1+0.02}-1 = 0.058823529 ###To find the real capital return:
###1+r_\text{real, capital} = \dfrac{1+r_\text{nominal, capital}}{1+r_\text{inflation}}### ###1+r_\text{real, capital} = \dfrac{1+0.03}{1+0.02}### ###r_\text{real, capital} = \dfrac{1+0.03}{1+0.02}-1 = 0.009803922###To find the real income return:
###\begin{aligned} r_\text{real, total} &= r_\text{real, income} + r_\text{real, capital} \\ 0.058823529&= r_\text{real, income} + 0.009803922 \\ \end{aligned}### ###\begin{aligned} r_\text{real, income} &= 0.058823529 - 0.009803922 \\ &= 0.049019608\\ \end{aligned}###Method 2: Convert nominal cash flows to real cash flows
Discount all future nominal cash flows by inflation to get the real cash flows then calculate the real rates of return.
###\begin{aligned} r_\text{nominal, total} &= r_\text{nominal, income} + r_\text{nominal, capital} \\ &= \dfrac{C_\text{1, nominal}}{P_0} + \dfrac{P_\text{1, nominal}-P_0}{P_0} \\ \end{aligned}\\ \begin{aligned} r_\text{real, total} &= r_\text{real, income} + r_\text{real, capital} \\ &= \dfrac{C_\text{1, real}}{P_0} + \dfrac{P_\text{1, real}-P_0}{P_0} \\ &= \dfrac{ \left( \dfrac{C_\text{1, nominal}}{(1+r_\text{inflation})^1} \right) }{P_0} + \dfrac{\left( \dfrac{P_\text{1, nominal}}{(1+r_\text{inflation})^1} \right)-P_0}{P_0} \\ \end{aligned}\\###If the price now were, say, $1 then the nominal income cash flow in one period would be $0.05 (nominal income return times price now) and the nominal price in one period would be $1.03 (nominal capital return times price now). Note that the price now is not affected by inflation. Substituting these and inflation into the above equation, the real returns can be calculated:
###\begin{aligned} r_\text{real, total} &= \dfrac{ \left( \dfrac{0.05}{(1+0.02)^1} \right) }{1} + \dfrac{\left( \dfrac{1.03}{(1+0.02)^1} \right)-1}{1} \\ &= 0.049019608 + 0.009803922 \\ &= 0.058823529\\ \end{aligned}###So the real total return is 5.88%, the real capital return is 0.98% and the real income return is 4.90%.
Question 407 income and capital returns, inflation, real and nominal returns and cash flows
A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.
The Fisher equation can be used to calculate nominal and real rates. The exact version is:
###1+r_\text{real} = \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}}###The approximation is:
###r_\text{real} \approx r_\text{nominal} - r_\text{inflation}###The only problem is that the Fisher equation only applies to the total and capital returns, not the income return. This is obvious when considering the approximation of the Fisher equation. If inflation is added to the real capital and income returns, then since the real total return is the sum of these two, inflation will be added twice to the total return which is wrong.
Method 1: Fisher equation on total and capital returns
Work out the total and capital returns using the Fisher equation, then calculate the difference which is the income return.
To find the nominal total return:
###1+r_\text{real, total} = \dfrac{1+r_\text{nominal, total}}{1+r_\text{inflation}}### ###1+0.07 = \dfrac{1+r_\text{nominal, total}}{1+0.02} ### ###r_\text{nominal, total} = (1+0.07)(1+0.02)-1 = 0.0914 ###To find the nominal capital return:
###1+r_\text{real, capital} = \dfrac{1+r_\text{nominal, capital}}{1+r_\text{inflation}}### ###1+0.02 = \dfrac{1+r_\text{nominal, capital}}{1+0.02} ### ###r_\text{nominal, capital} = (1+0.02)(1+0.02)-1 = 0.0404 ###To find the real income return:
###\begin{aligned} r_\text{nominal, total} &= r_\text{nominal, income} + r_\text{nominal, capital} \\ 0.0914 &= r_\text{nominal, income} + 0.0404 \\ \end{aligned}### ###\begin{aligned} r_\text{nominal, income} &= 0.0914 - 0.0404 \\ &= 0.051 \\ \end{aligned}###Method 2: Convert nominal cash flows to real cash flows
Grow all future real cash flows by inflation to get the nominal cash flows then calculate the nominal rates of return.
###\begin{aligned} r_\text{nominal, total} &= r_\text{nominal, income} + r_\text{nominal, capital} \\ &= \dfrac{C_\text{1, nominal}}{P_0} + \dfrac{P_\text{1, nominal}-P_0}{P_0} \\ &= \dfrac{C_\text{1, real}.(1+r_\text{inflation})^1}{P_0} + \dfrac{P_\text{1, real}.(1+r_\text{inflation})^1-P_0}{P_0} \\ \end{aligned}###If the price now were, say, $1 then the nominal income cash flow in one period would be $0.05 which is the nominal income return times the price now. The nominal price in one period would be $1.02 ##(=1(1+0.02)^1)## which is the price now grown by the nominal capital return. Note that the price now ##(P_0)## is not affected by inflation. Substituting these and inflation into the above equation, the real returns can be calculated:
###\begin{aligned} r_\text{nominal, total} &= \dfrac{C_\text{1, real}.(1+r_\text{inflation})^1}{P_0} + \dfrac{P_\text{1, real}.(1+r_\text{inflation})^1-P_0}{P_0} \\ &= \dfrac{0.05 \times (1+0.02)^1}{1} + \dfrac{1.02 \times (1+0.02)^1-1}{1} \\ &= 0.051 + 0.0404 \\ &= 0.0914 \\ \end{aligned}###So the real total return is 9.14%, the real capital return is 4.04% and the real income return is 5.1%.
Question 155 inflation, real and nominal returns and cash flows, Loan, effective rate conversion
You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.
You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.
You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?
Use the 'term structure of interest rates' or 'expectations hypothesis' equation to find the expected inflation rate over the next 2 years:
###(1+r_{0 \rightarrow 2 \text{ eff annual}} )^2 = (1+r_{0 \rightarrow 1 \text{ eff annual}})(1+r_{1 \rightarrow 2 \text{ eff annual}}) ### ###(1+r_{0 \rightarrow 2 \text{ eff annual}})^2 = (1+0.02)(1+0.04) ### ###\begin{aligned} r_{0 \rightarrow 2 \text{ eff annual}} &= ((1+0.02)(1+0.04))^{1/2}-1 \\ &= 0.029951455 \\ \end{aligned}###Use the Fisher equation to convert the required real return into a nominal return:
###1+r_{0 \rightarrow 2 \text{ eff annual, real}} = \dfrac{1+r_{0 \rightarrow 2 \text{ eff annual, nominal}}}{1+r_{0 \rightarrow 2 \text{ eff annual, inflation}}}### ###1+0.06 = \dfrac{1+r_{0 \rightarrow 2 \text{ eff annual, nominal}}}{1+0.029951455}### ###\begin{aligned} r_{0 \rightarrow 2 \text{ eff annual, nominal}} &= (1+0.06)(1+0.029951455) -1 \\ &= 0.091748542 \\ \end{aligned}###To find the present value of the $1 million in 2 years that will be lent now,
###\begin{aligned} V_0 &= \dfrac{V_\text{2, nominal}}{(1+r_{0 \rightarrow 2 \text{ eff annual, nominal}})^2} \\ &= \dfrac{1,000,000}{(1+0.091748542)^2} \\ &= 838,986.086 \\ \end{aligned}###The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.
What was CBA's market capitalisation of equity?
The market capitalisation of equity ##(E)## equals the number of shares ##(n)## multiplied by the market share price ##(p)##.
###\begin{aligned} E &= n.p \\ &= 1.62b \times 82.76 \\ &= 134.07b \\ \end{aligned}###The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.
What was MSFT's market capitalisation of equity?
The market capitalisation of equity ##(E)## equals the number of shares ##(n)## multiplied by the market share price ##(p)##.
###\begin{aligned} E &= n.p \\ &= 8.24b \times 47.81 \\ &= 393.95b \\ \end{aligned}###Which of the following statements about book and market equity is NOT correct?
The statement in answer C is untrue. A company's book value of equity is recorded in its balance sheet, also known as the statement of financial position.
Question 461 book and market values, ROE, ROA, market efficiency
One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.
In the year since then, the firm:
- Earned net income of $29m.
- Paid dividends totaling $10m.
- Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.
Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago.
Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance.
###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###
###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###
The required return on assets ##r_V## is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair.
###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###
Similarly for equity and debt.
The statement in answer A is untrue. The book value of equity would have grown from $100m to $119m (=100m + 29m - 10m) due to the addition of earnings and the subtraction of dividends.
The market value equity would be much higher due to the discovery of the valuable new drug which will increase the firm's future earnings and cash flows. This will cause a large increase in the share price, much higher than the $19m increase in book equity.
Notice that book equity is affected by events in the past, while market equity is only affected by what is expected to happen in the future. This is the fundamental difference between book (accounting) values and market (finance) values.
Question 729 book and market values, balance sheet, no explanation
If a firm makes a profit and pays no dividends, which of the firm’s accounts will increase?
No explanation provided.
The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?
Cash is a current asset which is part of net working capital, whether it's in the bank or in notes and coins. The saying emphasizes how business managers need to keep a close eye on their net working capital. They need to make sure they have enough cash to cover their short term liabilities, or else the business will become bankrupt.
The expression 'you have to spend money to make money' relates to which business decision?
The saying 'you have to spend money to make money' alludes to the idea that you have to buy assets to generate income, which relates to the investment decision. Perhaps the saying would be better phrased as 'you have to invest money (in assets) to make money (generate income and capital gains)'.
Question 444 investment decision, corporate financial decision theory
The investment decision primarily affects which part of a business?
The investment decision is about what assets the business should buy. Managers are supposed to buy assets that increase shareholder wealth. Buying undervalued assets is the best way to do this. The business project of buying the undervalued asset and then selling it for a higher price or using it to generate cash flow would be called a positive net present value (NPV) project.
Question 446 working capital decision, corporate financial decision theory
The working capital decision primarily affects which part of a business?
Working capital, also called net working capital (NWC), is the amount of current assets less current liabilities. Working capital decisions seek to manage these accounts to avoid insolvency which is when the business cannot pay its current liabilities when they're due.
Question 445 financing decision, corporate financial decision theory
The financing decision primarily affects which part of a business?
The financing decision is about how to finance the business's assets. If there isn't enough cash to buy assets, more cash must be raised by issuing liabilities such as loans, bills or bonds or by issuing shares.
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
Payout policy is about how much to pay shareholders and in what form, if anything at all.
The firm can distribute cash to shareholders in the form of dividends which are distributed to all, or buy backs (also called repurchases) where shareholders can elect to sell their shares back to the company which then cancels those shares.
Question 443 corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy
Business people make lots of important decisions. Which of the following is the most important long term decision?
The investment decision determines what assets to buy to carry on the business. If managers buy assets that fail to create enough revenue to cover costs then the business will eventually fail.
You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.
Which is the safest investment? Which has the highest expected returns?
If a firm goes bankrupt, investors in different securities get paid back in this order:
- Senior debt
- Mezzanine debt
- Junior debt
- Preferred shares
- Ordinary shares
Ordinary stock holders get paid back last and only if there are any assets remaining, so they have the highest risk and deserve the highest return.
Senior debt gets paid first so it has the lowest risk and deserves the lowest yields (returns are usually called yields for debt).
A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).
On which securities must it pay interest or dividend payments in this terrible financial year?
Coupon and principal payments on debt must be paid or else the firm will be forced to declare bankruptcy.
In most countries, corporate law only allows dividends on preferred stock and common stock to be paid out of retained profits. This prevents firms from issuing shares and simply paying shareholder's money back to them as dividends without actually investing in productive assets and earning any cash or profits, a common feature of Ponzi schemes.
Which business structure or structures have the advantage of limited liability for equity investors?
Corporations have the advantage of limited liability, so equity investors will never lose more than the amount that they have invested in the company. On the other hand, sole traders and partners can be sued and forced to sell their personal assets such as their house and property if the business's assets are insufficient to cover its liabilities.
Therefore sole traders', partners' and corporate shareholders' business equity are at risk. But sole traders' and partners' personal assets are also at risk whereas corporate shareholders' personal assets are safe due to limited liability.
Question 452 limited liability, expected and historical returns
What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?
Let the current share price be ##p_0##, the expected future share price be ##p_1##, the expected future dividend be ##d_1## and the expected return be ##r##. Define the expected return as:
##r=\dfrac{p_1-p_0+d_1}{p_0} ##
The answer choices are stated using inequalities. As an example, the first answer choice "(a) ##0≤p<∞## and ##0≤r< 1##", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.
Due to limited liability, shares in companies will never have a negative price. Therefore the lowest possible share price is zero. The highest possible share price is infinity, there's no limit to how much the shares could be worth. Therefore: ###0≤p<∞###
Returns are a function of price. The highest possible return is also infinite similar to price, but the lowest possible return will occur at the lowest possible future price of zero, so substituting ##p_1 = 0## and ##d_1 = 0## into the return formula: ###\begin{aligned} r &= \dfrac{p_1-p_0+d_1}{p_0} \\ r_\text{min} &= \dfrac{0-p_0+0}{p_0} \\ &= -1 \\ \end{aligned}###
So the lowest possible return is -1 which is -100%. This makes sense since you can't lose more than what you invest into the share. Therefore the bounds of returns are:
##-1≤r<∞##Question 531 bankruptcy or insolvency, capital structure, risk, limited liability
Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.
Darren has negative equity in his business. His business equity is -$7,000 since the business's liabilities of $10,000 are greater than its assets of $3,000. Since the business is a sole tradership rather than a company, Darren is personally liable for the business's debts.
Darren's non-business personal assets of $10,000 less personal liabilities of $6,000 net to $4,000. Therefore Darren's total personal wealth including the business is -$3,000 (=4,000-7,000), so he is most in danger of going bankrupt when the business's liabilities have to be repaid.
Notice that Billy's business also has negative equity of -7,000 (=3,000-10,000) and therefore his company is in danger of going bankrupt when its debts are due. However, since the business is a company, Billy will not be personally liable for those debts. He won't have to pay them, unlike Darren whose business is not a company.
Which one of the following businesses is likely to be a public company in Australia, judging by its name?
Australian public companies have limited liability, therefore the company name is always followed by the word 'Limited' or the abbreviation 'Ltd', such as Bloggs Ltd.
Private companies, also known as Proprietary companies, also have limited liability. To differentiate them from public companies, private companies' names are followed by the words 'Proprietary Limited' or the abbreviation 'Pty Ltd', such as Doe Pty Ltd. Sometimes this is further abbreviated to Doe P/L.