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 |
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.
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.
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 owning (being long) the put option?
The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.
What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
Question 580 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to quadruple (be four times as big, say from $1 to $4) if the price grows by 15% pa?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So ##r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01##, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.
What do you think was the stock's historical return over the last year, given as an effective annual rate?
Question 701 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
A firm wishes to raise $50 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 6 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
Question 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct.
What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever):