What is the Internal Rate of Return (IRR) of the project detailed in the table below?
Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 0 |
| 2 | 121 |
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
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), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
Question 526 real and nominal returns and cash flows, inflation, no explanation
How can a nominal cash flow be precisely converted into a real cash flow?
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.
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
The following is the Dividend Discount Model (DDM) used to price stocks:
###P_0=\dfrac{C_1}{r-g}###
If the assumptions of the DDM hold and the stock is fairly priced, which one of the following statements is NOT correct? The long term expected:
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?
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.
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?
Question 50 DDM, stock pricing, inflation, real and nominal returns and cash flows
Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.
You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.
You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.
Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.
What is the current price of a BHP share?
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.
Question 488 income and capital returns, payout policy, payout ratio, DDM
Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.
BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.
Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.
Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.
All things remaining equal, which of the following statements is NOT correct?
The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.
Every week he is supposed to pay his 1,000 employees $1,000 each. So $1 million is paid to employees every week.
The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever.
Bank interest rates are 10% pa, given as a real effective annual rate. So ##r_\text{eff annual, real} = 0.1## and the real effective weekly rate is therefore ##r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569##
All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.
What is the net present value (NPV) of the boss's decision to pay later?
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).
If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?
Assume that:
- The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
- There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
- The large merged firm's earnings are the sum of the medium firms' earnings.
- The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
- Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.
You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.
Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.
What is the present value of the cost of letting your sister use your current dress for the next 3 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.
You own a nice suit which you wear once per week on nights out. You bought it one year ago for $600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years.
Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5.
What is the present value of the cost of letting your brother use your current suit for the next 4 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new suit when your current one wears out and your brother will not use the new one; your brother will only use your current suit so he will only use it for the next four years; and the price of a new suit never changes.
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 49 inflation, real and nominal returns and cash flows, APR, effective rate
In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.
The inflation rate is currently 2.2% 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 just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.
You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.
At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?
Question 239 income and capital returns, inflation, real and nominal returns and cash flows, interest only loan
A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.
From the bank's point of view, what is the long term expected nominal capital return of the loan asset?
Question 56 income and capital returns, bond pricing, premium par and discount bonds
Which of the following statements about risk free government bonds is NOT correct?
Hint: Total return can be broken into income and capital returns as follows:
###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###
The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.
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?
Which one of the following bonds is trading at par?
Question 207 income and capital returns, bond pricing, coupon rate, no explanation
For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?
Let: ##P_0## be the bond price now,
##F_T## be the bond's face value,
##T## be the bond's maturity in years,
##r_\text{total}## be the bond's total yield,
##r_\text{income}## be the bond's income yield,
##r_\text{capital}## be the bond's capital yield, and
##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.
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?
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 young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.
Ignoring the costs of financial distress, which of the following statements is NOT correct:
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:
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).
Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Scubar Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 200 | |
| COGS | 60 | |
| Depreciation | 20 | |
| Rent expense | 11 | |
| Interest expense | 19 | |
| Taxable Income | 90 | |
| Taxes at 30% | 27 | |
| Net income | 63 | |
| Scubar Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Inventory | 60 | 50 |
| Trade debtors | 19 | 6 |
| Rent paid in advance | 3 | 2 |
| PPE | 420 | 400 |
| Total assets | 502 | 458 |
| Trade creditors | 10 | 8 |
| Bond liabilities | 200 | 190 |
| Contributed equity | 130 | 130 |
| Retained profits | 162 | 130 |
| Total L and OE | 502 | 458 |
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Find the cash flow from assets (CFFA) of the following project.
| One Year Mining Project Data | ||
| Project life | 1 year | |
| Initial investment in building mine and equipment | $9m | |
| Depreciation of mine and equipment over the year | $8m | |
| Kilograms of gold mined at end of year | 1,000 | |
| Sale price per kilogram | $0.05m | |
| Variable cost per kilogram | $0.03m | |
| Before-tax cost of closing mine at end of year | $4m | |
| Tax rate | 30% | |
Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.
Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.
Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.
Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.
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:
A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?
Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###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}###
Question 370 capital budgeting, NPV, interest tax shield, WACC, CFFA
| Project Data | ||
| Project life | 2 yrs | |
| Initial investment in equipment | $600k | |
| Depreciation of equipment per year | $250k | |
| Expected sale price of equipment at end of project | $200k | |
| Revenue per job | $12k | |
| Variable cost per job | $4k | |
| Quantity of jobs per year | 120 | |
| Fixed costs per year, paid at the end of each year | $100k | |
| Interest expense in first year (at t=1) | $16.091k | |
| Interest expense in second year (at t=2) | $9.711k | |
| Tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 6% | |
| Levered cost of equity | 12.5% | |
| Market portfolio return | 10% | |
| Beta of assets | 1.24 | |
| Beta of levered equity | 1.5 | |
| Firm's and project's debt-to-equity ratio | 25% | |
Notes
- The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.
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. Note that interest expense is different in each year.
- Thousands are represented by 'k' (kilo).
- 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 nominal. 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?
Question 69 interest tax shield, capital structure, leverage, WACC
Which statement about risk, required return and capital structure is the most correct?
A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?
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 firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar market risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
Question 337 capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model
A fast-growing firm is suitable for valuation using a multi-stage growth model.
It's nominal unlevered cash flow from assets (##CFFA_U##) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of:
- 12% pa for the next two years (from t=1 to 3),
- 5% over the fourth year (from t=3 to 4), and
- -1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.
Assume that:
- The nominal WACC after tax is 9.5% pa and is not expected to change.
- The nominal WACC before tax is 10% pa and is not expected to change.
- The firm has a target debt-to-equity ratio that it plans to maintain.
- The inflation rate is 3% pa.
- All rates are given as nominal effective annual rates.
What is the levered value of this fast growing firm's assets?
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?
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
- He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
- He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
- Stock markets are weak form and semi-strong form efficient.
- He has no inside information.
- He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
- The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
- The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
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.
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $48.5m | Operating free cash flow |
| ##\text{FFCF or CFFA}## | $50m | Firm free cash flow or cash flow from assets |
| ##g## | 0% pa | Growth rate of OFCF and FFCF |
| ##\text{WACC}_\text{BeforeTax}## | 10% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 9.7% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Cost of debt |
| ##r_\text{EL}## | 11.25% pa | Cost of levered equity |
| ##D/V_L## | 20% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
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.