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.
Suppose that the US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year.
Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year.
What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)?
Assume that:
- Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices.
- No taxes, transaction costs, information asymmetry, bid-ask spreads or other market frictions.
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).
Question 213 income and capital returns, bond pricing, premium par and discount bonds
The coupon rate of a fixed annual-coupon bond is constant (always the same).
What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:
###r_\text{total} = r_\text{income} + r_\text{capital}###
###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}###
Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.
Select the most correct statement.
From its date of issue until maturity, the income return of a fixed annual coupon:
Question 215 equivalent annual cash flow, effective rate conversion
You're about to buy a car. These are the cash flows of the two different cars that you can buy:
- You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
- Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.
Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.
Should you buy the or the ?
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
In the 1997 Asian financial crisis many countries' exchange rates depreciated rapidly against the US dollar (USD). The Thai, Indonesian, Malaysian, Korean and Filipino currencies were severely affected. The below graph shows these Asian countries' currencies in USD per one unit of their currency, indexed to 100 in June 1997.
Of the statements below, which is NOT correct? The Asian countries':
The saying "buy low, sell high" suggests that investors should make a:
Which one of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
Question 793 option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing
A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.
| European Options on a Non-dividend Paying Stock | |||
| Description | Symbol | Put Values | Call Values |
| Spot price ($) | ##S_0## | 10 | 10 |
| Strike price ($) | ##K_T## | 12 | 7 |
| Risk free cont. comp. rate (pa) | ##r## | 0.05 | 0.05 |
| Standard deviation of the stock's cont. comp. returns (pa) | ##\sigma## | 0.4 | 0.4 |
| Option maturity (years) | ##T## | 1 | 1 |
| Option price ($) | ##p_0## or ##c_0## | 2.495350486 | 3.601466138 |
| ##N[d_1]## | ##\partial c/\partial S## | 0.888138405 | |
| ##N[d_2]## | ##N[d_2]## | 0.792946442 | |
| ##-N[-d_1]## | ##\partial p/\partial S## | -0.552034778 | |
| ##N[-d_2]## | ##N[-d_2]## | 0.207053558 | |
| Gamma | ##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2## | 0.098885989 | 0.047577422 |
| Theta | ##\Theta = \partial c/\partial T## or ##\partial p/\partial T## | 0.348152078 | 0.672379961 |
Which of the following statements is NOT correct?