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?
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?
Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.
What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?
Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.
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.
Your firm's research scientists can begin an exciting new project at a cost of $10m now, after which there’s a:
- 70% chance that cash flows will be $1m per year forever, starting in 5 years (t=5). This is the A state of the world.
- 20% chance that cash flows will be $3m per year forever, starting in 5 years (t=5). This is the B state of the world.
- 10% chance of a major break through in which case the cash flows will be $20m per year forever starting in 5 years (t=5), or instead, the project can be expanded by investing another $10m (at t=5) which is expected to give cash flows of $60m per year forever, starting at year 9 (t=9). Note that the perpetual cash flows are either the $20m from year 4 onwards, or the $60m from year 9 onwards after the additional $10m year 5 investment, but not both. This is the C state of the world.
The firm's cost of capital is 10% pa.
What's the present value (at t=0) of the option to expand in year 5?
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?
Question 547 PE ratio, Multiples valuation, DDM, income and capital returns, no explanation
A firm pays out all of its earnings as dividends. Because of this, the firm has no real growth in earnings, dividends or stock price since there is no re-investment back into the firm to buy new assets and make higher earnings. The dividend discount model is suitable to value this company.
The firm's revenues and costs are expected to increase by inflation in the foreseeable future. The firm has no debt. It operates in the services industry and has few physical assets so there is negligible depreciation expense and negligible net working capital required.
Which of the following statements about this firm's PE ratio is NOT correct? The PE ratio should:
Note: The inverse of x is 1/x.
An economy has only two investable assets: stocks and cash.
Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.
Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.
The nominal total return of the shares over the next year is expected to be:
A put option written on a risky non-dividend paying stock will mature in one month. As is normal, assume that the option's exercise price is non-zero and positive ##(K>0)## and the stock has limited liability ##(S>0)##.
Which of the following statements is NOT correct? The put option's: