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Patric borrows money from Zanele at a simple discount rate of 9,75% per annum. He must pay him R35 000 in 27 months’ time. The amount of money that he receives from Zanele now is
[1] R27 321,88.
[2] R44 835,87.
[3] R28 389,51
[4] R42 678,13.
[5] R28 703,23
Q. 2) Calculate the species richness, evenness and the diversity (use Shannon index) in each area (Community ecology). Compare and contrast both areas
Consider a portfolio made up of two stocks, S1 an S2. The variance of the 1-year returns on the two stocks are denoted s12 and s22.
[a] Assume we construct a portfolio consisting of long positions in the two stocks. Explain why the variance of the 1-year return on the portfolio can’t exceed the larger of s12 and s22.
Suppose we invest $150 in a stock S1:
$100 of our own capital
$50 of borrowed 1-year money (at an interest rate of 3%)
Let R1 denote the 1-year return on S1. Let E[R1] = m.
[b] In terms of s12 what’s the expected value and variance of the 1-year return on our $100 investment?
Question 4
Finally, there is a last consideration:
a) Selling the company: Considering that our plant produces annual cashflows of $240,000 increasing at a 0,5% annual, expected to last for many years, for how much should we value the company today if investors are willing to obtain a profitability of 3%?
Question 3
A potential client has offered the possibility to sign a contract, starting in 6 years, with a duration of 8 years (so it will produce 8 payments), to purchase a specific part that we can produce, but that will require a total reconversion of the whole factory. This contract is signed for annual revenues of $400,000. To do this, we must replace the machinery and the production plant must be reconverted.
a) What is the maximum amount of money we could afford to invest if we want a profitability of at least 4%?
b) If we ask for a loan to be paid back in 5 years in constant equal monthly payments of $30,000, how much will we pay in total for the loan?
Question 2
After these previous calculations, the project still requires a big initial investment, and other options are being considered. We were considering adapting our production line, in order to produce some parts for electric automobiles, this way, and after analyzing the possible market opportunities, we could expect to obtain net revenues of $40,000 per month for at least the next 8 years.
a) What is the maximum that we should invest on this project if we consider a cost of capital of 4%?
b) If we ask for a loan of 2,000,000 at an annual interest rate of 2% compounded semiannually, to be paid in 8 years, how much would you have to pay every semester to cover the loan?
(25%)
A project, that consists of just readjusting some parts to adapt them to assemble to electric cars, would produce net revenues of $200,000 per year, for 10 years. Assuming that these revenues will grow at a constant 1% per year, and are assessed at a cost of capital of 4%:
a) Would it still be profitable if it required an initial investment of $1,500,000?
b) If we take these annual revenues of $200,000 growing at a 1% per year, and we invest them in a bank account that offers an annual rate of 5% for 10 years, how much will we have at the end?
The price S(t) of a share follows the geometric Brownian motion S(t) = Seμt+σW(t). The parameters S and μ are given, but the volatility sigma is not known.
You are asked to compute the implied volatility as an estimate for the parameter σ using the data provided by the market.
What data you may want to use? What is the volatility smile?
The price S(u), 0 u t, of the share is driven by a geometric Brownian motion: S(u) = Seμu+σW(u). A proportional dividend on this share is paid continuously at rate q > 0 and is reinvested in the share. The continuously compounded interest rate is r. Compute the no-arbitrage price of a derivative with expiration time t and payoff function
R(t) = [S(t/3)S(2t/3)S(t)]1/3 .
50 bottles of water were randomly selected from a large collection of bottles in a company's warehouse. The large collection of bottles is referred to as the:
