Free Essay

Submitted By liudika

Words 905

Pages 4

Words 905

Pages 4

Suppose that the spot price, 6-month forward price, 12-months forward price and 18-months forward price for wheat are 250, 260, 270.4 and 281.216 cents per bushel, respectively.[1] A farmer has a project that involves an immediate expenditure of $20,000 and a further expenditure of $90,000 in six months. The farmer collects two wheat harvests per year, and if this project is implemented, it will increase wheat that is harvested and sold by 20,000 bushels in one year and in 18 months (as compared to his typical harvest). Assume that there is no uncertainty about the harvests (all uncertainty comes from future wheat prices). The continuously compounded risk-free rate is 5% p.a.

a) If the project has no flexibility (a “yes or no” decision), what is the value of the project? Notice that you do not have to use the binomial tree to answer this question. b) Suppose that the wheat price follows a binomial tree process with parameters u=1.1 and d=0.95 (determine y from forward prices and remember to take this variable into account when computing risk-neutral probabilities). Suppose that the farmer can abandon the project in six months and avoid paying the $90,000 cost at that time (in this case, the increase in harvest will be 5,000 bushels per year instead of 20,000). What is the value of this abandonment option? Is this abandonment option a put or a call? What is its strike? Explain. c) Now, assume that there is no option to abandon. Instead, suppose that the project can be delayed for 6 months: the investments can be made in six months and in one year, and the increases in harvests will be observed in 18 months and 2 years. What is the value of this option to delay? d) If the option to abandon and the option to delay are both available, what is the value of the project? Is the value of the portfolio of these two options equal to the sum of their individual values? Explain why.

Problem 2:

Suppose that a company has a project whose value of distributed lognormally with volatility (. The current value of the project is Vt. The project has a constant continuous payout rate (. Suppose the company has an opportunity to increase the size of the project by 20% at cost K1. There is a one-time chance to make the expansion decision T years from now.

a) How much does this type of flexibility add to the company value? Explain.

Suppose the company has a choice between increasing the size of the project by 20% at cost K1 and increasing it by 50% at cost K2 (2K2>5K1). How much does this type of flexibility add to the company value? Explain. (Hint: this is equivalent to having a chooser option with two underlying calls. Show that this chooser option is equivalent to the portfolio consisting of 0.2 units of a European call option written on one unit of the project with strike 5K1 and 0.3 units of a European call option written on one unit of the project with strike [pic]. Then, the prices of these options can be estimated using the BS formula.)

Problem 3:

Suppose that a company is considering replacing each of its existing six widget machines with new machines. The new machines cost $1,000 each and have a five-year life. The management has estimated the expected per-machine cash flows; these flows are defined as the incremental cash flow of replacing a single old machine by a new machine and include the sale of the old machine. The management does not know the exact realization of these annual cash flows, but knows their means. The expected cash flows for each new machine over their lives are: $220, $300, $400, $200 and $150 (these cash flows are uncertain from the firm’s managers’ viewpoint just because the managers have no information about the performance of these machines and there are no other sources of uncertainty).

The financial analyst working on the replacement project has estimated a cost of capital for the project of 12% (the discount rate). a) What is the NPV of this replacement project? b) Suppose that supplier of the new machines gives the following option to the manager in charge of the widget line: replace one machine at cost $2,000 now and get an opportunity to replace the other five machines next year at cost $1000. Assuming that the Black-Scholes formula provides a good approximation, and (=20% (the volatility of the replacement project’s return), rf=6%, what is the value of the project? What is the intuition behind this increase in the project’s value? If you need to make any extra assumptions, state them explicitly.

-----------------------

[1] The forward price of a commodity is given by [pic], where y is the difference between the storage cost and the convenience yield. The variable y corresponds to a (negative of a) dividend yield ( in the case of a dividend-paying stock; however, it is typically positive for commodities. If y is not equal to zero, the expected growth rate of a commodity price under the risk-neutral probability measure is equal to [pic]:

[pic].

Alternatively, [pic] is the growth rate of the “cum-convenience-yield” commodity price [pic].…...

Free Essay

...Binomial Distribution This is a discrete random variable, where the process of obtaining the Binomial distribution is called “Bernoulli “ process. An experiment that often consists of repeated trials, each with two possible outcomes, which could be labeled as “success” or “failure”. This experiment is known as binomial experiment. A binomial experiment is one that possesses the following properties: 1. The experiment consists of n repeated trials. 2. Each trial has only 2 possible outcomes that can be classified as “Success” or “Failure”. 3. The probability of a success and failure , denoted by pand q, remains constant from trial to trial. 4. The repeated, trials are independent. Formula for success in the Bernoulli process. The probability of r success from n trial is : [pic] where; r - the number of success n – the number of trial p – the probability of success from one trial and q – the probability of failure from one trial. q = 1 - p [pic] with mean, [pic] and variance, [pic] It is written as X ~ B(n,p) and read as X is Binomial distribution with parameters n success and the probability of success, p. Example 7.4 One coin is tossed 5 times. If X is random variable for number of heads . Find the probability of getting (a) no heads (b) one head (c) 3 heads (d) at least 3 heads Solution X......

Words: 986 - Pages: 4

Free Essay

...Phase 3 Discussion Board Richard Libeau MATH215-1301B-01 March 4, 2013 Task Type: Discussion Board Deliverable Length: 3 Parts: See Assignment Details Points Possible: 75 Graphs and Trees Task Background: Graphs and trees provide you with ways to visualize data sets, and the opportunity to do analysis on the data (e.g., shortest path). Knowing the structure of a database enables you to choose a proper algorithm for searching for data within a database. Primary Task Response: Within the Discussion Board area, write up to 3 paragraphs that respond to the following questions with your thoughts, ideas, and comments. This will be the foundation for future discussions by your classmates. Be substantive and clear, and use examples to reinforce your ideas. Part I (25 points – distributed as follows) Trees are somewhat less complicated than graphs, which makes things like data searching easier, when a data has the structure of a tree. However, not all data can be represented by a tree. Give an example of a data set that cannot be represented by a tree, but that can be represented by a more general graph. 1) Create, show, and describe your data set. (5 points) V = {Bill, John, Kim, James, Chris, Destiny, Noah, Paul} E = {(Bill, John), (Kim, James), (Chris, Destiny), (Noah, Paul),......

Words: 1054 - Pages: 5

Free Essay

...DISTRIBUSI BINOMIAL Distribusi binomial berasal dari percobaan binomial yaitu suatu proses Bernoulli yang diulang sebanyak n kali dan saling bebas. Distribusi Binomial merupakan distribusi peubah acak diskrit. Secara langsung, percobaan binomial memiliki ciri-ciri sebagai berikut: – – – – percobaan tersebut dilakukan berulang-ulang sebanyak n kali setiap percobaan menghasilkan keluaran yang dapat dikategorikan sebagai gagal dan sukses probabilitas sukses p tetap konstan dari satu percobaan ke percobaan lain percobaan yang berulang adalah saling bebas Ruang sampel A untuk percobaan E yang terdiri dari himpunan tak hingga tetapi masih terhitung dari titik – titik sampel: Jika S = Sukses dan G = Gagal E1 : S (sukses pada percobaan pertama) E2 : GS (gagal pada percobaan pertama dan sukses pada percobaan kedua) E3 : SG (sukses pada percobaan pertama, gagal pada percobaan kedua) E4 : GGS (gagal pada percobaan 1 dan 2, sukses pada percobaan ketiga) E5 : GSG (gagal pada percobaan 1 dan 3, sukses pada percobaan kedua) E6 : SGG (gagal pada percobaan 2 dan 3, sukses pada percobaan pertama) En : SSS ...S GGG...G (sukses sebanyak x kali, gagal sebanyak n – x kali) x n x Jika peluang sukses dinotasikan dengan p maka peluang gagal adalah q = 1 – p. Peubah acak X menyatakan banyaknya sukses dari n percobaan yang saling bebas. Maka peluang X pada masing – masing percobaan E adalah: P(X) p P(X) qp pq P(X) pq 2 2 untuk E1 untuk E2 untuk E3 P(X) q p pq untuk......

Words: 1210 - Pages: 5

Premium Essay

...project. But formal risk analysis and risk management can help you to assess these risks and decide what actions to take to minimize disruptions to your plans. They will also help you to decide whether the strategies you could use to control risk are cost-effective. How to use the tool: Here we define risk as 'the perceived extent of possible loss'. Different people will have different views of the impact of a particular risk – what may be a small risk for one person may destroy the livelihood of someone else. One way of putting figures to risk is to calculate a value for it as: risk = probability of event x cost of event Doing this allows you to compare risks objectively. We use this approach formally in decision making with Decision Trees. To carry out a risk analysis, follow these steps: 1. Identify Threats: The first stage of a risk analysis is to identify threats facing you. Threats may be: * Human - from individuals or organizations, illness, death, etc. * Operational - from disruption to supplies and operations, loss of access to essential assets, failures in distribution, etc. * Reputational - from loss of business partner or employee confidence, or damage to reputation in the market. * Procedural - from failures of accountability, internal systems and controls, organization, fraud, etc. * Project - risks of cost over-runs, jobs taking too long, of insufficient product or service quality, etc. * Financial - from business failure,......

Words: 909 - Pages: 4

Premium Essay

...Decision trees http://www.alchemyformanagers.co.uk/topics/4qpj5es2SiaJVVXn.html Decision trees A decision tree is a visual tool for analysing decisions. In using it, you generate a tree-like graph of decisions and their consequences. In the simplest form of this technique Squares represent decisions Triangles represent end points. Jewish proverb When the graph is completed, you can then add probabilities for each of the individual branches and from the overall probabilities of the end points. If there are two courses of action, you should take the third. Using the technique As a simple example, let’s suppose that I decide that I want to travel from my home to a hotel in town A. So let’s draw the options in a decision tree: We can now add some percentages to reflect either our preferences or an estimate of some factor that we would like to consider (for example cost, estimated likelihood and so on). In this case, I will use personal preferences: I am assuming here that the train station is close to my home. For ‘walk’ I have added 0 per cent because it is a long distance to town A. The bus takes a long time, but it is quite cheap, so I have given it ten per cent. Notice that I have also added end points to ‘walk’ and ‘drive’ as they both get me to my destination. ‘Train’ and ‘bus’ however do not get me to my final destination, so I now extend my decision tree by adding more decision points, options and estimates: We can now see what the final end point......

Words: 720 - Pages: 3

Free Essay

...Read this essay on the Importance of Trees ! Plants are very important for us. They provide us fresh fruits, wood, natural herbs and many things of professional value. They are home to numerous wildlife, bugs and creatures. They provide colour to men and creatures. They prevent famine and cause rain fall. They help in verifying polluting the environment. They provide us fresh air to take in and play essential role in the process of CO2. So, we should increase forestation. Wood is the most effective product that trees provide us with. We use wooden often. Wood is used as petrol and wood. Wood is used to make furnishings. Wood is also used to lay the paths of the railways. Plants are excellent sources of therapeutic natural herbs, ribbons and raw materials for many sectors. We get resins, organic gum area, etc. from the trees. The bamboo sheets bedding is an essential wide range of shrub which develops in large quantity. It is of excellent professional value. It is found everywhere. It is used as building content to make short-term shed. It is an essential resource of protection for the poor and financially sluggish individuals. Bamboo is used to make pads, barrier, bag and various products of the crafts. Bamboo is used as raw content to make paper. Cane is another wide range of shrub which is used in many things. Mats, rules and furnishings are created from the cane. Furniture created of cane is highly creative, wonderful and costly. Lac is one of the most......

Words: 456 - Pages: 2

Premium Essay

...Importance of trees Trees are really important in a human being’s life. Without them we, humans, can’t live. Although trees are important, they aren’t cared about and are used unwisely. Trees need to be saved and people should stop wasting paper and such so that we can save as much trees as we can. Trees have a lot of benefits which we should appreciate and care about. Starting off, trees provide the oxygen that we breathe. Without that oxygen, we won’t be able to live. If trees are the ones keeping us alive, shouldn’t we be thankful and help save them? Trees produce a lot of oxygen to keep us alive. “In one year an acre of mature trees can provide enough oxygen for 18 people” (TreePeople). This means that in one year, a bunch of fully developed trees can produce enough oxygen to keep 18 people alive. Trees help us live, so we should help them too. Second, tees help moderate the earth’s temperature. The shade from trees helps cool the earth’s temperature. (eco kids). Without the shades from the trees the earth would be a burning hell. It would be too hot to go outside. Those shades help maintain the temperature and cool it down. The trees do that by absorbing heat, and producing shade. This, again, is another reason we should be thankful to trees. Last but not least, trees provide us with an enormous amount of food that we need to survive. They provide us with food directly and indirectly. Directly, is when we eat fruits or vegetables. We get the fruits from the tree...

Words: 538 - Pages: 3

Premium Essay

...Internet that said, “Imagine if trees gave off Wi-Fi signals, we would be planting so many trees and we’d probably save the planet too. Too bad they only produce the oxygen we breathe.” It’s sad how true that statement is, we value access to the Internet more than we value the air we breathe every day. Trees are the one thing that help us survive and people view them as trivial objects more and more each day, underestimating the fact that our destruction of them could lead to a destruction of us. The leaves of trees can come in all different shapes and sizes. They form in bunches and give a sense of hair to the tree, adding a way to differentiate one tree from another. With the leaves, trees give us beauty. There’s not a prettier sight than mid-October, when all the tree’s leaves have changed colors and everywhere you turn there are different types of reds, oranges, yellows and more. The foliage is just one of the many reasons why trees are important, they give us natural beauty. They could be described as a painting in nature just without using brushes, paint or canvases. Tree’s trunks come in all different sizes, some thicker than others, giving protection in a way, to us humans and to animals. Since most trunks are big, hunters usually hide in between them when they’re looking for potential game. They wear camouflage to blend in with the trees, usually in patterns of different types of greens, browns and light mustard yellows. Speaking of game, trees also are the home......

Words: 980 - Pages: 4

Free Essay

...Trees Most trees around the world are located in the Russian taiga. It is only fitting since Russia is the largest country by far, although lots of trees around the world are being cut down at an alarming rate so it wouldn't be surprising to see the tree population of Russia go down. Trees are a renewable resource- by the planting of more trees even though it takes a few years for trees to get big we still have plenty of them around. Wood is made of tiny fibers called cellulose and the natural glue that holds them together is called lignin. When wood is turned into paper, heat and chemicals dissolve the lignin and the cellulose fibers come out. Byproducts of this process are used in asphalt, paint, chewing gum, detergents and turpentine. Cellulose is used for more than just paper. It is used for dinnerware including melamine in it, toilet seats, tool handles and cellophane. You can also use it to produce helmets, toothbrushes and electrical outlets. Some other you can make from it is nail polish, rocket fuel and industrial explosives. Wood pulping by-products are used for lots of weird things like cleaning stuff, deodorants, hair spray, and even fake vanilla flavorings! We obtain all the wood by cutting down trees with machines, chainsaws, and sometimes axes! Deforestation is the clearing Earth's forests in a big way, often resulting in damage to the quality of the land. Deforestation has many negative effects on the environment. The biggest impact is a loss of habitat for...

Words: 507 - Pages: 3

Premium Essay

...and bamboos are also trees. Trees tend to be long-lived, some reaching several thousand years old. The tallest known tree, a coast redwood named Hyperion, stands 115.6 m (379 ft) high. Trees have been in existence on the Earth for 370 million years. Trees are not a taxonomic group but include a variety of plant species that have independently evolved a woody trunk and branches as a way to tower above other plants to compete for sunlight. A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically contains woody tissue for strength, and vascular tissue to carry materials from one part of the tree to another. For most trees it is surrounded by a layer of bark which serves as a protective barrier. Below the ground, the roots branch and spread out widely; they serve to anchor the tree and extract moisture and nutrients from the soil. Above ground, the branches divide into smaller branches and shoots. The shoots typically bear leaves, which capture light energy and convert it into sugars by photosynthesis, providing the food for the tree's growth and development. Flowers and fruit may also be present, but some trees, such as conifers, instead have pollen cones and seed cones; others, such as tree ferns, produce spores instead. Trees play a significant role in reducing erosion and moderating the climate. They remove carbon dioxide from the atmosphere and store large quantities of carbon in their tissues. Trees and forests......

Words: 402 - Pages: 2

Free Essay

...Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay Trees Essay......

Words: 1536 - Pages: 7

Free Essay

...Christmas Trees Christmas trees are an icon around this time of year. It doesn’t fail while driving down the road and there’s a car with a tree strapped on the hood. Christmas trees come in a variety of different shapes, size, and color and yes smell. Before starting a Christmas tree farm, one must figure out what type of trees they want to have, or what variety they want. The most common types of trees that would be found in a person’s tree stand would be Douglas fir, Fraser Fir, Noble Fir, Scotch pine, Eastern White Pine, Virginia Pine, Grand Fir, and Eastern Red Cedar. Douglas fir have soft needles with a dark green in color. The needles can reach to an inch in half. The needles have a sweet fragrance when crushed, most common Christmas tress species. The Fraser Fir have branches that face up, with an excellent scent as well. They have a blue-green color. These trees are easy for shipping. Noble Fir are known for their beauty. They have strong branches to hang ornaments, and are used well for wreaths and garland. Scotch pine have needles that are an inch in length and have a bright green color. The needles will not fall off the tree when dry. It is also a common tree because of the freshness it keeps through the holidays. Eastern White Pine have soft green needles. It has a strong scent, and produces decorative pine cones. Virginia Pine is the most unusual as it can tolerate warmer winter temperatures. The tree is smaller than the other varieties, and is more common......

Words: 1373 - Pages: 6

Free Essay

...cost which makes the production unprofitable 4. High energy cost because of the machines that will produce fiber 5. Continuous cutting of trees which is the major source in producing paper Opportunities of the industry 1. Growth of paper in local consumption because of population growth 2. Cheap price compare to other competing product 3. More cities are complying to total plastic ban in the Philippines which means mostly paper will serve as carrier bag 4. Paper is one of the fastest way used to give information 5. Most paper serves as food container because of its safe composition Threats of the industry 1. There environmental requirements are getting more stringent 2. Increasing competition in other competing materials 3. Innovation of materials in other industry happened while paper retained its traditional uses throughout decades 4. Paper quality is weak that it cannot hold heavy materials 5. The sources of raw material are only limited and may take time to produce Alternative Courses of Action 1. Create own source of wood pulp (through industrial plantation and recycled papers) Advantages * Environmental friendly * Improve country’s wastepaper recovery and recycling rate * Low cost in long term benefits Disadvantages * It takes time to wait for trees to be used in production (5-7 years) * Reforestation would be costly * Costly because another large area of plantation will be needed......

Words: 539 - Pages: 3

Premium Essay

...PART 1 The binomial Test Click Link Below To Buy: http://hwcampus.com/shop/part-1-the-binomial-test/ 1- Insurance companies charge young drivers more for automobile insurance because they tend to have more accidents than older drivers. To make this point an insurance representative first determines that only 16% of licensed drivers are age 20 or younger. Because this age group makes up only 16% of the drivers it is reasonable to predict that they should be involved in only 16% of the accidents. In a random sample of 100 accident reports however the representative finds 31 accidents that involved drivers who were 20 or younger. Is this sample sufficient to show that younger drivers have significantly more accidents then would be expected from the percentage of young drivers? Use a two-tailed test with a significance of .05 2- A researcher would like to determine whether people can really tell the difference between bottled water and tap water. Participants are asked to tasted two unlabeled glasses of water, one bottle and one tap, and identify the one they thought tasted better. Out of 40 people in the sample, 28 picked the bottled water. Was the bottled water selected significantly more often than would be expected by chance? Use a two tailed test with a=.05 A researcher is investigating the relationship between personality and birth order position. A sample of college students is classified into four birth order categories (1st, 2nd, 3rd,4th, or later)...

Words: 473 - Pages: 2

Free Essay

...Chapter 5 Discrete Probability Distributions Learning Objectives 1. Understand the concepts of a random variable and a probability distribution. 2. Be able to distinguish between discrete and continuous random variables. 3. Be able to compute and interpret the expected value, variance, and standard deviation for a discrete random variable. 4. Be able to compute and work with probabilities involving a binomial probability distribution. 5. Be able to compute and work with probabilities involving a Poisson probability distribution. A random variable is a numerical description of the outcome of an experiment. A discrete random variable may assume either a finite number of values or an infinite sequence of values. A continuous random variable may assume any numerical value in an interval or collection of intervals. Discrete Probability Distributions n Random Variables n Discrete Probability Distributions n Expected Value and Variance n Binomial Distribution n Poisson Distribution [pic] A random variable is a numerical description of the outcome of an experiment. A discrete random variable may assume either a finite number of values or an infinite sequence of values. A continuous random variable may assume any numerical value in an interval or collection of intervals. Example: JSL Appliances n Discrete random variable with a finite number ......

Words: 789 - Pages: 4