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 formula for the present value of interest tax shields if the tax shields occur in perpetuity?
You may assume:
- the value of debt (D) is constant through time,
- The cost of debt and the yield on debt are equal and given by ##r_D##.
- the appropriate rate to discount interest tax shields is ##r_D##.
- ##\text{IntExp}=D.r_D##
A project has the following cash flows:
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -400 |
| 1 | 0 |
| 2 | 500 |
The required return on the project is 10%, given as an effective annual rate.
What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time.
You just bought $100,000 worth of inventory from a wholesale supplier. You are given the option of paying within 5 days and receiving a 2% discount, or paying the full price within 60 days.
You actually don't have the cash to pay within 5 days, but you could borrow it from the bank (as an overdraft) at 10% pa, given as an effective annual rate.
In 60 days you will have enough money to pay the full cost without having to borrow from the bank.
What is the implicit interest rate charged by the wholesale supplier, given as an effective annual rate? Also, should you borrow from the bank in 5 days to pay the supplier and receive the discount? Or just pay the full price on the last possible date?
Assume that there are 365 days per year.
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:
Question 449 personal tax on dividends, classical tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Delta buys a future from Alice.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###Question 908 effective rate, return types, gross discrete return, return distribution, price gains and returns over time
For an asset's price to double from say $1 to $2 in one year, what must its gross discrete return (GDR) be? If the price now is ##P_0## and the price in one year is ##P_1## then the gross discrete return over the next year is:
###\text{GDR}_\text{annual} = \dfrac{P_1}{P_0}###