Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate. Ignore credit risk.
The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r - g } ###
What is ##g##? The value ##g## is the long term expected:
For a price of $13, Carla will sell you a share paying a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
For a price of $1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##100(1+0.05)^1=$105.00##, and the year after it will be ##100(1+0.05)^2=110.25## and so on.
The required return of the stock is 15% pa.
For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.
The required return of the stock is 15% pa.
For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.
The required return of the stock is 10% pa.
For a price of $95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same $10 dividend every year after that forever.
The required return of the stock is 10% pa.
For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.
For a price of $100, Rad will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.
Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?
You own an apartment which you rent out as an investment property.
What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation?
Assume that:
- You just signed a contract to rent the apartment out to a tenant for the next 12 months at $2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment.
- The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year.
So rental payments will increase at the start of the 13th month (t=12) to be $2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.
Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)2), and then they will be constant for the next 12 months until the next year, and so on. - The required return of the apartment is 8.732% pa, given as an effective annual rate.
- Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments.
Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?
Select one of the following answers. Note that D is the value of debt which is constant through time, and ##r_D## is the cost of debt.
Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Candys Corp | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 200 | |
COGS | 50 | |
Operating expense | 10 | |
Depreciation | 20 | |
Interest expense | 10 | |
Income before tax | 110 | |
Tax at 30% | 33 | |
Net income | 77 | |
Candys Corp | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Assets | ||
Current assets | 220 | 180 |
PPE | ||
Cost | 300 | 340 |
Accumul. depr. | 60 | 40 |
Carrying amount | 240 | 300 |
Total assets | 460 | 480 |
Liabilities | ||
Current liabilities | 175 | 190 |
Non-current liabilities | 135 | 130 |
Owners' equity | ||
Retained earnings | 50 | 60 |
Contributed equity | 100 | 100 |
Total L and OE | 460 | 480 |
Note: all figures are given in millions of dollars ($m).
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###
Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Trademark Corp | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 100 | |
COGS | 25 | |
Operating expense | 5 | |
Depreciation | 20 | |
Interest expense | 20 | |
Income before tax | 30 | |
Tax at 30% | 9 | |
Net income | 21 | |
Trademark Corp | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Assets | ||
Current assets | 120 | 80 |
PPE | ||
Cost | 150 | 140 |
Accumul. depr. | 60 | 40 |
Carrying amount | 90 | 100 |
Total assets | 210 | 180 |
Liabilities | ||
Current liabilities | 75 | 65 |
Non-current liabilities | 75 | 55 |
Owners' equity | ||
Retained earnings | 10 | 10 |
Contributed equity | 50 | 50 |
Total L and OE | 210 | 180 |
Note: all figures are given in millions of dollars ($m).
Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
UniBar Corp | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 80 | |
COGS | 40 | |
Operating expense | 15 | |
Depreciation | 10 | |
Interest expense | 5 | |
Income before tax | 10 | |
Tax at 30% | 3 | |
Net income | 7 | |
UniBar Corp | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Assets | ||
Current assets | 120 | 90 |
PPE | ||
Cost | 360 | 320 |
Accumul. depr. | 40 | 30 |
Carrying amount | 320 | 290 |
Total assets | 440 | 380 |
Liabilities | ||
Current liabilities | 110 | 60 |
Non-current liabilities | 190 | 180 |
Owners' equity | ||
Retained earnings | 95 | 95 |
Contributed equity | 45 | 45 |
Total L and OE | 440 | 380 |
Note: all figures are given in millions of dollars ($m).
Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Piano Bar | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 310 | |
COGS | 185 | |
Operating expense | 20 | |
Depreciation | 15 | |
Interest expense | 10 | |
Income before tax | 80 | |
Tax at 30% | 24 | |
Net income | 56 | |
Piano Bar | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Assets | ||
Current assets | 240 | 230 |
PPE | ||
Cost | 420 | 400 |
Accumul. depr. | 50 | 35 |
Carrying amount | 370 | 365 |
Total assets | 610 | 595 |
Liabilities | ||
Current liabilities | 180 | 190 |
Non-current liabilities | 290 | 265 |
Owners' equity | ||
Retained earnings | 90 | 90 |
Contributed equity | 50 | 50 |
Total L and OE | 610 | 595 |
Note: all figures are given in millions of dollars ($m).
A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.
Find World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
World Bar | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 300 | |
COGS | 150 | |
Operating expense | 50 | |
Depreciation | 40 | |
Interest expense | 10 | |
Taxable income | 50 | |
Tax at 30% | 15 | |
Net income | 35 | |
World Bar | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Assets | ||
Current assets | 200 | 230 |
PPE | ||
Cost | 400 | 400 |
Accumul. depr. | 75 | 35 |
Carrying amount | 325 | 365 |
Total assets | 525 | 595 |
Liabilities | ||
Current liabilities | 150 | 205 |
Non-current liabilities | 235 | 250 |
Owners' equity | ||
Retained earnings | 100 | 100 |
Contributed equity | 40 | 40 |
Total L and OE | 525 | 595 |
Note: all figures above and below are given in millions of dollars ($m).
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###
Which point corresponds to the best time to calculate the terminal value?
An old company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###
Which point corresponds to the best time to calculate the terminal value?
A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###
Which point corresponds to the best time to calculate the terminal value?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_{0} = \frac{c_1}{r_{\text{eff}} - g_{\text{eff}}} ###
What is the discount rate '## r_\text{eff} ##' in this equation?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}} ###
What would you call the expression ## C_1/P_0 ##?
Question 31 DDM, perpetuity with growth, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?
The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at ## t=4.5 ## years will be ## 10(1-0.02)^1=9.80 ##, and so on.
A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 0.00 | 1.00 | 1.05 | 1.10 | 1.15 | ... |
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
- the dividend at t=5 will be $1.15(1+0.05),
- the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 0.00 | 1.00 | 1.05 | 1.10 | 1.15 | ... |
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
- the dividend at t=5 will be $1.15(1+0.05),
- the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in three and a half years (t = 3.5)?
The following is the Dividend Discount Model (DDM) used to price stocks:
### P_0 = \frac{d_1}{r-g} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.
Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?
A stock pays semi-annual dividends. It just paid a dividend of $10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.
Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 0.00 | 1.15 | 1.10 | 1.05 | 1.00 | ... |
After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
- the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
- the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 0.00 | 1.15 | 1.10 | 1.05 | 1.00 | ... |
After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
- the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
- the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in four and a half years (t = 4.5)?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_0 = \frac{d_1}{r - g} ###
Which expression is NOT equal to the expected dividend yield?
A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock is 10% pa, given as an effective annual rate.
What is the price of the share now?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}###
Which expression is NOT equal to the expected capital return?
A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock 10% pa, given as an effective annual rate.
What is the price of the share now?
A stock pays annual dividends. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 8 | 8 | 8 | 20 | 8 | ... |
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. Note that the $8 dividend at time zero is about to be paid tonight.
What is the current price of the stock?
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{r-g} ###
Which of the following statements about the Dividend Discount Model is NOT correct?
A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 2 | 2 | 2 | 10 | 3 | ... |
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's total dividends be as large as the country's GDP?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_0= \frac{c_1}{r-g} ###
Which expression is equal to the expected dividend return?
In the dividend discount model:
###P_0 = \dfrac{C_1}{r-g}###
The return ##r## is supposed to be the:
In the dividend discount model:
### P_0= \frac{d_1}{r-g} ###
The pronumeral ##g## is supposed to be the:
A share just paid its semi-annual dividend of $5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective 6 month rate.
Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective annual rate.
What is the price of the share now?
Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.
If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only ##(P_\text{0 one-off})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:
Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.
A stock is expected to pay the following dividends:
Cash Flows of a Stock | ||||||
Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
Dividend ($) | 0 | 6 | 12 | 18 | 20 | ... |
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what is the share price?
Question 210 real estate, inflation, real and nominal returns and cash flows, income and capital returns
Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate.
An old rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Some investors also regard property to be as risky as the stock market, therefore property is thought to have a required total return of 9% pa which is the average total return on the stock market including dividends.
Assume that all returns are effective annual rates and they are nominal (not reduced by inflation). Inflation is expected to be 2% pa.
You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property.
Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance').
How does an accountant calculate the annual interest expense of a fixed-coupon bond that has a liquid secondary market? Select the most correct answer:
Annual interest expense is equal to:
Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.
In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.
If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.
Remember:
### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###
where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.
The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
For a firm with debt, what is the amount of the interest tax shield per year?
Question 121 capital structure, leverage, financial distress, interest tax shield
Fill in the missing words in the following sentence:
All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.
There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets ##(V_L)##? Assume that:
- The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
- The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
- Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
- There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
- The firm operates in a mature industry with zero real growth.
- All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.
Where:
###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}###A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed.
In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.
A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
A company has:
- 50 million shares outstanding.
- The market price of one share is currently $6.
- The risk-free rate is 5% and the market return is 10%.
- Market analysts believe that the company's ordinary shares have a beta of 2.
- The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
- The company's debentures are publicly traded and their market price is equal to 90% of their face value.
- The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.
What is the company's after-tax weighted average cost of capital (WACC)? Assume a classical tax system.
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?
Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.
In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.
If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?
Assume that:
- No income (rent) was received from the house during the short time over which house prices fell.
- Your friend will not declare bankruptcy, he will always pay off his debts.
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?
Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?
A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.
Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.
You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of $40 for a premium of $3.
Which of the following statements best describes your situation?
Which one of the following is NOT usually considered an 'investable' asset for long-term wealth creation?
Question 386 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?
The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.
Locked mobile phones are cheaper than unlocked phones because the locked-in network operator helps create a monopoly by:
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
A credit card offers an interest rate of 18% pa, compounding monthly.
Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as a fully amortising loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month).
Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.
If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?
A European bond paying annual coupons of 6% offers a yield of 10% pa.
Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###
Question 64 inflation, real and nominal returns and cash flows, APR, effective rate
In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.
The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
Calculate the effective annual rates of the following three APR's:
- A credit card offering an interest rate of 18% pa, compounding monthly.
- A bond offering a yield of 6% pa, compounding semi-annually.
- An annual dividend-paying stock offering a return of 10% pa compounding annually.
All answers are given in the same order:
##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##
You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You're trying to save enough money to buy your first car which costs $2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.
How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.
Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.
A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually.
Find the effective monthly rate, effective six month rate, and effective annual rate.
##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
What will be your monthly payments?
You're trying to save enough money for a deposit to buy a house. You want to buy a house worth $400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other $320,000 that you need.
You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change.
How long will it take to save the $80,000 deposit? Round your answer up to the nearest month.
A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of $1,000.
Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price?
Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7).
What is the net present value (NPV) of lending to your friend?
Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is 10% pa, given as an effective annual rate.
A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its price?
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} ##.
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
Question 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
- 1 year zero coupon bond at a yield of 8% pa, and a
- 2 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price?
Question 96 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds paying semi-annual coupons:
- 1 year zero coupon bond at a yield of 8% pa, and a
- 2 year zero coupon bond at a yield of 10% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Question 108 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
- A 1 year zero coupon bond at a yield of 10% pa, and
- A 2 year zero coupon bond at a yield of 8% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?
Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices?
Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).
The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?
A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is $100. What is its price?
Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.
Which of the following statements is true?
A four year bond has a face value of $100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price?
Which one of the following bonds is trading at a discount?
A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.
What is the bond's price?
Which one of the following bonds is trading at par?
A firm wishes to raise $8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
Which one of the following bonds is trading at a premium?
A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue? All numbers are rounded up.
A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price?
In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.
A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?
A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price?
A 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semi-annual. The bond has a face value of $100.
Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price?
Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
- Inflation remains at 5% over the next 2 years.
- Investors demand a constant real bond yield.
- The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##ΔV = ΔD+ΔE##
A company has:
- 140 million shares outstanding.
- The market price of one share is currently $2.
- The company's debentures are publicly traded and their market price is equal to 93% of the face value.
- The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum.
- The risk-free rate is 8.50% and the market return is 13.7%.
- Market analysts estimated that the company's stock has a beta of 0.90.
- The corporate tax rate is 30%.
What is the company's after-tax weighted average cost of capital (WACC) in a classical tax system?
A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.
The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.
The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.
What is the firm's after-tax WACC? Assume a classical tax system.
A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.
Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.
Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer.
The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.
Assume the following:
- Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
- Motorola had a 20% after-tax WACC before it merged with Google.
- Google and Motorola have the same level of gearing.
- Both companies operate in a classical tax system.
You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.
The mobile phone manufacturing project's:
A company has:
- 100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
- 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
- Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.
The corporate tax rate is 30%. All returns and yields are given as effective annual rates.
What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
Project Data | ||
Project life | 1 year | |
Initial investment in equipment | $8m | |
Depreciation of equipment per year | $8m | |
Expected sale price of equipment at end of project | 0 | |
Unit sales per year | 4m | |
Sale price per unit | $10 | |
Variable cost per unit | $5 | |
Fixed costs per year, paid at the end of each year | $2m | |
Interest expense in first year (at t=1) | $0.562m | |
Corporate tax rate | 30% | |
Government treasury bond yield | 5% | |
Bank loan debt yield | 9% | |
Market portfolio return | 10% | |
Covariance of levered equity returns with market | 0.32 | |
Variance of market portfolio returns | 0.16 | |
Firm's and project's debt-to-equity ratio | 50% | |
Notes
- Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
- The project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Question 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
Project Data | ||
Project life | 1 year | |
Initial investment in equipment | $6m | |
Depreciation of equipment per year | $6m | |
Expected sale price of equipment at end of project | 0 | |
Unit sales per year | 9m | |
Sale price per unit | $8 | |
Variable cost per unit | $6 | |
Fixed costs per year, paid at the end of each year | $1m | |
Interest expense in first year (at t=1) | $0.53m | |
Tax rate | 30% | |
Government treasury bond yield | 5% | |
Bank loan debt yield | 6% | |
Market portfolio return | 10% | |
Covariance of levered equity returns with market | 0.08 | |
Variance of market portfolio returns | 0.16 | |
Firm's and project's debt-to-assets ratio | 50% | |
Notes
- Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 2% pa.
- All rates are given as effective annual rates.
- The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
A 90-day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?
Question 147 bill pricing, simple interest rate, no explanation
A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
Question 157 bill pricing, simple interest rate, no explanation
A 90-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 6% pa and there are 365 days in the year. What is its price?
A 60-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
Question 327 bill pricing, simple interest rate, no explanation
On 27/09/13, three month Swiss government bills traded at a yield of -0.2%, given as a simple annual yield. That is, interest rates were negative.
If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?
Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock?
Portfolio Details | ||||||
Stock | Expected return |
Standard deviation |
Correlation | Beta | Dollars invested |
|
A | 0.2 | 0.4 | 0.12 | 0.5 | 40 | |
B | 0.3 | 0.8 | 1.5 | 80 | ||
What is the beta of the above portfolio?
Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?
Question 244 CAPM, SML, NPV, risk
Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:
Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?
A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Sidebar Corp | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 405 | |
COGS | 100 | |
Depreciation | 34 | |
Rent expense | 22 | |
Interest expense | 39 | |
Taxable Income | 210 | |
Taxes at 30% | 63 | |
Net income | 147 | |
Sidebar Corp | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Cash | 0 | 0 |
Inventory | 70 | 50 |
Trade debtors | 11 | 16 |
Rent paid in advance | 4 | 3 |
PPE | 700 | 680 |
Total assets | 785 | 749 |
Trade creditors | 11 | 19 |
Bond liabilities | 400 | 390 |
Contributed equity | 220 | 220 |
Retained profits | 154 | 120 |
Total L and OE | 785 | 749 |
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Ching-A-Lings Corp | ||
Income Statement for | ||
year ending 30th June 2013 | ||
$m | ||
Sales | 100 | |
COGS | 20 | |
Depreciation | 20 | |
Rent expense | 11 | |
Interest expense | 19 | |
Taxable Income | 30 | |
Taxes at 30% | 9 | |
Net income | 21 | |
Ching-A-Lings Corp | ||
Balance Sheet | ||
as at 30th June | 2013 | 2012 |
$m | $m | |
Inventory | 49 | 38 |
Trade debtors | 14 | 2 |
Rent paid in advance | 5 | 5 |
PPE | 400 | 400 |
Total assets | 468 | 445 |
Trade creditors | 4 | 10 |
Bond liabilities | 200 | 190 |
Contributed equity | 145 | 145 |
Retained profits | 119 | 100 |
Total L and OE | 468 | 445 |
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Over the next year, the management of an unlevered company plans to:
- Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
- Pay dividends of $1m.
- Complete a $1.3m share buy-back.
Assume that:
- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Your friend is trying to find the net present value of an investment which:
- Costs $1 million initially (t=0); and
- Pays a single positive cash flow of $1.1 million in one year (t=1).
The investment has a total required return of 10% pa due to its moderate level of undiversifiable risk.
Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.
He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).
He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.
Your friend has listed a few different ways to find the NPV which are written down below.
Method 1: ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##
Method 2: ##-1m + 1.1m - 1m \times 0.1 ##
Method 3: ##-1m + \dfrac{1.1m}{(1+0.1)^1} - 1m \times 0.1 ##
Which of the above calculations give the correct NPV? Select the most correct answer.
A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###
One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).
###\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\###
One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###
One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).
###\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###
Question 413 CFFA, interest tax shield, depreciation tax shield
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).
One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:
###FFCF=NI + Depr - CapEx -ΔNWC + IntExp###
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )###
Another popular method is to use EBITDA rather than net income. EBITDA is defined as:
###EBITDA=Rev - COGS - FC###
One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?
According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?
Which statement(s) are correct?
(i) All stocks that plot on the Security Market Line (SML) are fairly priced.
(ii) All stocks that plot above the Security Market Line (SML) are overpriced.
(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.
Select the most correct response:
A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?
According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?
A fairly priced stock has a beta that is the same as the market portfolio's beta. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the expected return of the stock?
A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.
What is the price of the stock now?
A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 2.5% pa and there are 365 days in the year. What is its price now?
A stock just paid its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.
What is the implied growth rate of the dividend per year?
Two years ago Fred bought a house for $300,000.
Now it's worth $500,000, based on recent similar sales in the area.
Fred's residential property has an expected total return of 8% pa.
He rents his house out for $2,000 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 $23,173.86.
The future value of 12 months of rental payments one year ahead is $25,027.77.
What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?
Three years ago Frederika bought a house for $400,000.
Now it's worth $600,000, based on recent similar sales in the area.
Frederika's residential property has an expected total return of 7% pa.
She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.
The present value of 12 months of rental payments is $29,089.48.
The future value of 12 months of rental payments one year ahead is $31,125.74.
What is the expected annual capital yield of the property?
Question 405 DDM, income and capital returns, no explanation
The perpetuity with growth formula is:
###P_0= \dfrac{C_1}{r-g}###
Which of the following is NOT equal to the total required return (r)?
All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:
Diversification in a portfolio of two assets works best when the correlation between their returns is:
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?
Question 100 market efficiency, technical analysis, joint hypothesis problem
A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?
(I) Weak form market efficiency is broken.
(II) Semi-strong form market efficiency is broken.
(III) Strong form market efficiency is broken.
(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
- The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
- JP Morgan Chase's historical earnings per share (EPS) is $4.37;
- Citi Group's share price is $50.05 and historical EPS is $4.26;
- Wells Fargo's share price is $48.98 and historical EPS is $3.89.
Note: Figures sourced from Google Finance on 24 March 2014.
Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).
- The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
- ICBC 's historical earnings per share (EPS) is RMB 0.74;
- CCB's backward-looking PE ratio is 4.59;
- BOC 's backward-looking PE ratio is 4.78;
- ABC's backward-looking PE ratio is also 4.78;
Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.
A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?
(i) buy call options on live cattle.
(ii) buy put options on live cattle.
(iii) sell call options on live cattle.
Select the most correct response:
Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered
You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market.
You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets?
Select the most correct response:
A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the call option?
A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the call option?
A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the put option?
Question 432 option, option intrinsic value, no explanation
An American style call option with a strike price of ##K## dollars will mature in ##T## years. The underlying asset has a price of ##S## dollars.
What is an expression for the current intrinsic value in dollars from owning (being long) the American style call option? Note that the intrinsic value of an option does not subtract the premium paid to buy the option.
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?
Question 180 equivalent annual cash flow, inflation, real and nominal returns and cash flows
Details of two different types of light bulbs are given below:
- Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
- Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.
The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.
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?
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.
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.
A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). 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} ##.
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}##.
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}##.
A share was bought for $10 (at t=0) and paid its annual dividend of $0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (at t=1).
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{dividend}##.
A share was bought for $4 and paid an dividend of $0.50 one year later (at t=1 year).
Just after the dividend was paid, the share price fell to $3.50 (at t=1 year). What were the total return, capital return and income returns given as effective annual rates? The answer choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ## r_\text{income}##
A 90-day $1 million Bank Accepted Bill (BAB) was bought for $990,000 and sold 30 days later for $996,000 (at t=30 days).
What was the total return, capital return and income return over the 30 days it was held?
Despite the fact that money market instruments such as bills are normally quoted with simple interest rates, please calculate your answers as compound interest rates, specifically, as effective 30-day rates, which is how the below answer choices are listed.
##r_\text{total}##, ##r_\text{capital}##, ## r_\text{income}##
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.
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.
Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.
Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:
- The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
- The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
- The total required return on equity is 6% pa.
- The required return and growth rate are given as effective annual rates.
- Dividend payment dates and ex-dividend dates are at the same time.
- Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
Question 22 NPV, perpetuity with growth, effective rate, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 10% given as an effective annual rate?
The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(1-0.03)^1=87.3 ##, and so on.
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).
You just signed up for a 30 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month).
You want to buy an apartment worth $300,000. You have saved a deposit of $60,000.
The bank has agreed to lend you $240,000 as an interest only mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.
How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:
###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###Assume that:
- Interest rates are expected to be constant over the life of the loan.
- Loans are interest-only and have a life of 30 years.
- Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the start-of-year amount, but it is paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:
- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the end-of-year amount, paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that:
- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
- The fund invests its fees in the same companies as it invests your funds in, but with no fees.
The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.
Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).
You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.
Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car?
On his 20th birthday, a man makes a resolution. He will deposit $30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.
The bank account pays interest at 6% pa compounding monthly, which is not expected to change.
If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows | |
Time (yrs) | Cash flow ($) |
0 | -100 |
1 | 0 |
2 | 121 |
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows | |
Time (yrs) | Cash flow ($) |
0 | -100 |
1 | 11 |
2 | 121 |
The following cash flows are expected:
- 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3).
- 1 payment of $600 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
Question 408 leverage, portfolio beta, portfolio risk, real estate, CAPM
You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.
You estimate that:
- The house has a beta of 1;
- The mortgage loan has a beta of 0.2.
What is the beta of the equity (the $200,000 deposit) that you have in your house?
Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.
The following cash flows are expected:
- 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3 and last at t=12).
- 1 payment of $400 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
A text book publisher is thinking of asking some teachers to write a new textbook at a cost of $100,000, payable now. The book would be written, printed and ready to sell to students in 2 years. It will be ready just before semester begins.
A cash flow of $100 would be made from each book sold, after all costs such as printing and delivery. There are 600 students per semester. Assume that every student buys a new text book. Remember that there are 2 semesters per year and students buy text books at the beginning of the semester.
Assume that text book publishers will sell the books at the same price forever and that the number of students is constant.
If the discount rate is 8% pa, given as an effective annual rate, what is the NPV of the project?
A project's NPV is positive. Select the most correct statement:
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?