Quantitative Methods For Decision Makers 4th Edition Mik Wisniewski - Solutions

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The prevailing interest rate is 10% per annum for the tenor of 20 years. Suppose a bond pays 7% per annum and the frequency of coupon payment is semiannual. This bond is traded at $74.26 per $100 par value.(a) If $74.26 is invested as a time deposit at the prevailing interest rate of 10% for 20
Annuity is a stream of regular cash flows, either in the form of payment or receipt. Suppose you save an amount c every year, up to n years from time 0. The interest rate is y. Let x := 1 + y.(a) Show that the cash flow of this annuity at maturity amounts to cxxn−1 − 1 x − 1 .(b) Suppose you
The effective annual rate (EAR) is a useful concept to compare the yields of money market securities, which mature in less than a year. Suppose Bank U offers a structured product consisting of two time deposits with equal weight:(A) A 1-year time deposit at 2.68%.(B) A half-year time deposit of
This is the First Illustration in one of the earliest books on financial mathematics by Moore [Moo29]: The Marshall National Bank pays 4% on time deposits. What is the annual interest payment on a time deposit of $250,000?
A futures contract is a standardized forward contract traded through a futures exchange rather than bilaterally over the counter. An index futures is a derivative product for investors trading and hedging in the equity market.Take the Dow Jones Industrial Average (DJIA) index as an example. Being a
The risk-free rate r0 is a key ingredient of the first principle of Quantitative Finance. Consider a frictionless world — absolutely no taxes, transaction costs and so on. In this idealized economy, not only is the risk of default absent, but also the regulatory risk (such as changes in the
The adjective “uncertain” from which “uncertainty” is derived has many different meanings in different contexts. In Quantitative Finance, uncertainty refers to the state of limited knowledge to adequately identify the existing state or a future outcome. Risk is uncertainty qualified by an
Consider the following FX quotes:Bid Ask EUR/USD 1.3501 1.3502 USD/SGD 1.2711 1.2734 EUR/SGD 1.7077 1.7100 A trader has spotted a triangular arbitrage opportunity starting with SGD. The trader who is based in Singapore has S$1,710.(a) How much will the trader make from one round of triangular
A Treasury bond has one year left before maturity. The annual coupon rate is c and the coupon is paid semi-annually. An investor has invested an amount of A for this bond at the price of P.(a) Solve the quadratic polynomial to express the yield to maturity y in terms of P, C = Ac, and A.(b) Since y
An investor buys a Treasury bond at 103% of the par value and holds it to maturity, which is two years later. The coupon rate is 6%.(a) What is the return on this investment for holding the bond to maturity?(b) The current yield is the ratio obtained from dividing the coupon amount by the bond
Show that, for the three averages of Pythagoras, namely, arithmetic meana, geometric mean g, and harmonic mean h, they satisfy the following inequality:h ≤ g ≤ a.That is, T 1x1 + 1 x2 + ··· + 1 xT≤ x1x2 ··· xT 1T ≤1 TT∑i=1 xi.
In addition to the arithmetic and geometric means, another average is called the harmonic mean. These three means were proposed and studied by Pythagoras. The harmonic mean h of T positive real numbers x1, x2,..., xT is defined as h := T 1x1 + 1 x2 + ··· + 1 xT.(a) Compute the arithmetic,
Incorporated in 1974, Temasek is a sovereign wealth fund based in Singapore. Temasek manages a portfolio (asset under management (AUM)) valued at S$223 billion as of March 31, 2014. The 1-year total returns (TR) of this investment company over the years, and for comparison, the 1-year TR on
Given a sample rt, t = 1, 2, . . . , T, of simple returns or total returns over one period, say, a year. The arithmetic mean a is defined as a := 1 TT∑t=1 rt.The geometric mean g is an average return that takes into account the compounding nature of growth. Mathematically, we write T∏t=1(1 +
Total return is simple return with the inclusion of dividends received. In the typical long first and short later setting, let Pt be the selling price and Pt−1 be the buying price one period ago. The total return r˘t is r˘t := Pt + Dt − Pt−1 Pt−1, where Dt is the sum of all dividends
The simple return (2.1) can be rewritten as r := simple return = selling price buying price − 1.The ratio R defined by R := selling price buying price is known as the simple gross return. The natural logarithm of R is called the log return. Often, we are interested to know how long does it take
An investor from the eurozone bought 500 shares of Microsoft a year ago for $38.13 per share. The exchange rate was $1.3591 per euro then. Today, Microsoft is traded at $47.74 and the exchange rate is $1.2460.(a) What is the simple return in dollars?(b) What is the simple return in euros?
Suppose you are a forex trader domiciled in the U.S. and you hold the view that the euro is going to weaken against the Greenback. The exchange rate GBP/USD is nicknamed cable. You decide to short the cable when quotes are 1.5591/92 to obtain $1 million (i.e., sell the pound). When the quotes
Suppose one in 100 actively managed mutual funds in the database is truly based on skill and not luck. Moreover, suppose a statistical test can diagnose the difference between skill and luck. If a fund’s return is due to skill, there is a 99% chance of testing positive. If a fund’s return is
A stock mutual fund’s performance is usually measured relative to a stock index such as the S&P 500 index. For a start, consider simply the difference between the return on the fund and the return on the S&P 500 index over the same period of time. If the difference is positive, the fund is said
Over the same period from 1977 to 1990 when Peter Lynch was in charge of the Magellan Fund, the total return of S&P 500 index had only three negative annual returns. In other words, the whole stock market was in a bull run.(a) A fund manager adopts the follow-the-market approach.Assuming that the
The legendary fund manager Peter Lynch was in charge of an actively managed mutual fund called the Magellan Fund between 1977 and 1990. Over the decade of 1980, the asset under management (AUM) increased phenomenally from $18 million to $13 billion, almost a thousand fold.(a) In these 13 years,
How many combinations are there in picking k unordered outcomes from n possibilities? The answer to this question is known as the binomial coefficient, which is the number of combinations in choosing k items from n items. Denoted by (n k) or nCk, the number of “n choose k” is computed by the
Professor Nouriel Roubini, nicknamed Dr. Doom, is another prominent economist who had forecasted correctly the 2008 financial crisis. On September 7, 2006, to the laughter and scepticism from an audience of economists at the International Monetary Fund, he made a bold prediction that in the coming
An organisation has recently purchased a company car for one of its senior managers at a cost of £25 000 and is trying to determine the most suitable time for replacement. It is estimated that the car will depreciate by £5000 in the first year,£2000 in each of the next two years and £3000 in
A large organisation is considering replacing part of its vehicle fleet with the latest equipment. Although such a decision is expensive, it is felt that the investment will be worthwhile in terms of generating future cost savings in repairs, maintenance and running costs and will also help improve
A local authority is under severe financial pressure and is considering selling some of the land it owns to a building company. The building company is offering to pay£150 000 for the land now or a payment of £40 000 a year for the next five years.(a) If the current interest rate is 8 per cent,
A hospital has decided to replace an important piece of medical equipment at a cost of £30 000. The expected life of the equipment is five years and it will have a resale value of £4000 at this time. The hospital is trying to decide how to finance the purchase. One option is to buy the equipment
A production company is considering purchasing a new piece of equipment for the production process for one of its products. The product itself is due to be withdrawn from the market in five years’ time. The equipment will cost £600 000 and have a scrap value of £5000. Included in this price is
The company you work for is considering acquiring several of the latest generation desktop computers for use in an office. The company expects the equipment to have a useful life of three years. The finance director has asked you to recommend whether the equipment should be purchased outright or
You have the choice of investing a sum of money in four alternative schemes:(a) one which will pay 10 per cent per annum interest compounded daily;(b) one which will pay 10.25 per cent per annum interest compounded monthly;(c) one which will pay 10.5 per cent per annum interest compounded
A utility company is currently reviewing its manpower requirements in the domestic-appliance servicing department. One feature of the servicing work relates to domestic central-heating systems. For an annual fee, a trained engineer will undertake a safety check on a customer’s domestic
You are currently employed by a high street bank and have been asked to investigate the bank’s policy in one particular area of its operations, that relating to small loans to individual customers. The loans in question are usually short-term and requested for financing the purchase of domestic
An investigation is being carried out into a local authority’s housing policy. The local authority has a limited supply of housing which it owns and lets. It receives requests for housing from a number of individuals and families throughout the year. Some of these applications come from those who
Call up the second simulation at the DOS prompt by typing the command:and then pressing the ENTER key. The program should then start up and you can follow the on-screen instructions. Run the simulation for the small unit and the large unit several times and plot the results on a scatter diagram.
Call up the first simulation from the DOS prompt by typing the command:and then pressing the ENTER key. The program should then start up and you can follow the on-screen instructions.(a) Run the simulation using bed options for five, six through to ten beds. Produce your own scatter diagram similar
For a particular project the information in Table 13.17 has been obtained.(a) Construct a network diagram for this project showing EFTs, LFTs and the critical path.(b) The company concerned has indicated that it would like the project completed in no more than 16 days. Determine the additional cost
A firm is making minor alterations to its automated stock-handling system in one of its warehouses. The relevant information relating to this project is shown in Table 13.16.The table shows the activities that must be completed, their expected duration times in weeks, and the activities that must
A project comprises the activities shown in Table 13.15, which also shows the duration of each activity.(a) Construct a network diagram for this project and determine the expected completion time together with the critical path.(b) Determine the probability that the project will take longer than 50
You have been appointed secretary of a student group which has an annual programme of invited speakers from the business world. The group has suffered from a membership decline over the last few years and you are keen to reverse this trend by planning a more ambitious programme of guest speakers.
In the project detailed in Table 13.13, activity labels indicate the major activities to be completed in a project.492 13 PROJECT MANAGEMENT ATM project Normal Crash Preceding duration Normal duration Crash Activity activities (weeks) cost (£s) (weeks) cost (£s)A – 9 900 3 6 300 B – 7
A large banking organisation is installing a network of automated teller machines(ATMs) for use by its customers in a large town. These machines are installed in an exterior wall of the bank and allow customers to withdraw cash from their accounts. A number of major activities that have to be
2 A business organisation is trying to improve staff morale and motivation and has decided to replace the existing staff canteen with a modern cafeteria. The works department has drawn up a detailed list of the various activities that will need to be completed, together with an estimate of how long
Consider the situation of waking up in the morning and going to the kitchen to make yourself a cup of tea or coffee. Identify the various activities you would need to complete for this project and determine the dependencies between each activity.Use this information to construct a network diagram.
A large construction company has recently won the contract for routine inspection and maintenance of the Channel Tunnel linking the UK to France. Obviously, routine maintenance and repair work, unless carefully planned, will have adverse consequences on traffic flows through the tunnel and on
A domestic appliance manufacturer is evaluating its delivery system from the production plant to showrooms around the country. One item used in the transportation of large appliances is a prefabricated polystyrene-foam packing case.These are supplied by an outside contractor and have to be ordered
Following internal reorganisation in a large brewing company, a comprehensive review of stock-control procedures is currently being undertaken. You have been asked to investigate stock control in the context of one of the firm’s products: lowalcohol lager. The company operates a sophisticated
A local authority operates over a large geographical area. The Education Department is responsible for ensuring that stocks of a certain item are kept for distribution to schools through the area on request. In order to try to ensure supplies reach the schools promptly, the department currently
A company requires a particular item from an outside supplier for its production process. Annual demand for the item is 3000 units. Order costs are estimated at £15 and holding costs at 20 per cent of the purchase price of the item, which is £5.50 per unit.(a) Determine the optimum order
Describe the quantitative techniques that are available to assist a manager with stock-control responsibilities in an organisation.
What are the basic decisions that a manager with stock-control responsibility faces and what are the likely objectives of such a manager in this context?
A small electrical repair shop finds it has two main types of work. Customers bring items in for repair: TVs, videos, etc. require major repair; other repairs are classed as minor. At present the shop has more business than it can handle and is trying to prioritise the work it should do. The firm
A small engineering company makes two products for export, A and B. Both products go through a four-stage process: turning, grinding, polishing, finishing.The two products are produced in batches of 100 items and the time taken, in hours, for each batch to go through each stage is shown in Table
For the problem in Exercise 1 assume the firm now wishes to maximise revenue rather than profit.(a) Formulate this problem in terms of determining the revenue-maximising combination of the two products on a weekly basis.(b) Solve the problem graphically.(c) Confirm the solution using simultaneous
A manufacturer is trying to determine the combination of two products, A and B, that should be produced. Each product passes through a three-stage production process: Stages I, II and III. For product A Stage I takes three hours of labour, Stage II four hours and Stage III one hour. For product B
A senior police manager is reviewing manpower allocation of police officers to a number of geographical districts which fall under her responsibility. Data has been collected on a number of variables, as shown in Table 10.20.Crimes The number of reported crimes Officers The number of full-time
A training agency is currently reviewing part of its operations. It runs one particular scheme whereby young people who are unemployed are put through a training course which provides them with a variety of IT skills including word-processing, spreadsheets, database systems, e-mail and the
A large retail organisation has a number of home-furnishing outlets in a particular region, selling products such as carpets, curtains, domestic furniture and fittings.The organisation has been affected badly by the downturn in domestic property sales in the region over the last few years, as it
As manager of a local leisure centre you are investigating the frequency of use of the centre by its members. You hope that by understanding some of the key factors that influence how often members use the centre’s facilities you will be better able to market the centre and attract more members.
The corporate planning department in a large brewing company has been trying to develop a medium-term forecasting model relating to the demand for one of their products: a low-alcohol lager. The method used has been based around multiple regression. The department has collected and analysed data on
A small engineering company has been monitoring its total costs over the last few years on a quarterly basis together with the number of employees and production level. In order to assist the company to evaluate alternative strategic and operational options, the data has been put through a computer
Table 10.15 shows data on two variables for the UK from the Central Statistical Office for the period 1970 to 2003.Cars New registrations of cars shown in thousands as a monthly average.Income Real household disposable income, per head at 2001 prices.(a) What type of causal relationship might you
For the following data calculate the correlation coefficient and plot the data on a scatter diagram. Do you think it measures the strength of the relationship accurately?x 1 2 3 4 5 6 7 y 8.25 7 6.25 6 6.25 7 8.25 2 Return to the variables used in Chapter 9, Exercise 3. In that exercise you were
Investigate sources of published statistics that show a seasonal pattern in publications such as Monthly Digest of Statistics, Economic Trends. For a variable which is published in both unadjusted and seasonally adjusted format, find out the seasonal adjustment method used.
Working with a small group of colleagues, develop a consensus view of private car sales in Western Europe in five years time. In order to do this you will need to:● collect historical data on car sales● collect data on related variables: population trends, income levels, public transport,
A large retail organisation is currently investigating a number of areas of its operations with a view to improving performance in terms of efficiency, sales and profits. The organisation has been monitoring the monthly sales of one its more profitable products for the last few years with a view to
Table 9.20 shows the official seasonally adjusted series for the consumer expenditure categories shown in Table 9.19. Compare these with your own calculations. Comment on any differences.EXERCISES 333 UK household final consumption expenditure, £m at constant prices, seasonally adjusted Food
The following exercises all relate to the development of a suitable time-series decomposition model for the data shown. In each case you should adopt the following procedure:(a) Plot the original data as a time-series graph.(b) Determine whether an additive or multiplicative model would be
Return to the unit sales data used in this chapter. Apply the exponential-smoothing model to this data using values for α of 0.15, 0.2, 0.25 and 0.3. Assess the accuracy of each choice of α and decide which you would use to forecast future values.Consider the two sets of sales data in Table
A public transport organisation has had a reputation for many years of caring little for its customers – the passengers it carries. In particular, the enquiry office has had a particularly poor reputation. New management have decided to try to improve the office’s performance and image, and
A hospital laboratory has the task of screening blood samples of patients and producing a summary report for clinicians. Because of the limitations of equipment, staff training and time, the laboratory manager knows that there is an error rate‘The Role of Training in Total Quality
A large manufacturing firm is concerned about lost production: that is, production capability that was not utilised for a variety of reasons. One of the causes of such lost production has been identified as employees taking time off work because of illness. Last year the firm estimated that around
Return to Exercise 10 in Chapter 4. Test to see whether there is a significant difference between mean customer spend in the two stores. Draft a short report explaining your conclusion in non-technical terms for the store managers.1 To try to illustrate how effective the Ishikawa diagram can be,
In Chapter 1 reference was made to a survey undertaken by the author into the use of quantitative techniques by businesses. One of the questions in the survey asked whether businesses were using such techniques, with responses as either yes or no. The survey was undertaken across three countries
The author has been involved in research into the use of something known as compensation orders in Scottish courts (The Use of the Compensation Order in Scotland, J Hamilton and M Wisniewski, Scottish Office Central Research Unit, 1996). Convicted offenders can be ordered to pay compensation to
An airline operating between London and Aberdeen knows that a large part of its customer base represents business executives. The airline is considering offering a limousine service tofrom the airport to be included in the airline ticket price, which would have to increase as a result. A survey
Recent legislation requires adherence to detailed and complex food-labelling requirements on products sold to consumers. A recent survey examined whether the food labelling on supermarket own-brand products met these requirements.The results were categorised as:● Complete compliance with
An international company routinely rotates its senior managers every five to six years around its activities worldwide. Staff are financially compensated for such moves but with many staff buying a house in their new location, there are concerns about relative house prices. The company has recently
A company employs largely part-time staff, and in the past has found staff turnover to be 23 per cent each year (that is 23 per cent of staff in any one year leave the company). This is felt to be too high, with implications for morale, motivation and costs (since new staff have to be recruited and
The Inland Revenue has introduced a self-assessment system for tax payments whereby citizens themselves calculate the amount of tax to be paid on income each year. Naturally, the Inland Revenue checks such self-assessments, although it does not have the resources to check them all each year. At the
Historically it has taken a local council an average of 18 weeks to reach a decision about planning applications for building development work submitted by construction companies. The companies have complained that decisions are taking too long and delays are costing them money. The chief executive
An organisation is trying to evaluate which of two PC computer systems to standardise on within the organisation. In terms of price, specification and performance there is little to choose between the two models being considered, Model A and Model B. However, the computer services manager is
A local training agency is trying to get government support for its activities –which relate to the provision of industrial and commercial training for the local labour force – on the basis that unemployed workers who are better skilled have a better chance of finding new employment than
A local hospital is trying to assess its performance vis-à-vis national performance.The Department of Health has recently indicated that, nationally, for a particular hospital-based treatment the mean length of stay of patients in hospital was 8.6 days. The local hospital has checked the records
A local authority has a pool of cars available for staff to use on official business.One particular make and model of car, of which the authority has a considerable number, claims to give a miles per gallon (mpg) performance of 52 mpg for simulated out-of-town driving. For a sample of 20 cars the
A small engineering firm manufactures high-precision components for the aeronautical industry. In order to ensure quality, the production equipment has to be regularly maintained. One particular component in the production equipment must be replaced regularly. At present the component is supplied
In the Worked Example in Chapter 5 we had a distribution of a sample of customers’ electricity consumption. Test whether this distribution is Normal.CLTPIT
Several years ago a new chief executive was appointed to a group of firms. On appointment the CE expressed concern about the quality of the senior management in one of the major companies in the group. He felt that this group of managers was by and large out of touch with new technology, new market
Return to Exercise 9 in Chapter 4. The Finance Department in the local authority has estimated that at least 45 people per day on average need to use the local library to justify the cost of keeping it open – costs relate to staff wages, heating, lighting, cost of periodicals and so on. You have
Return to Exercise 8 in Chapter 4. Calculate the mean and standard deviation if you have not already done so. Given that this data is a sample, calculate the 90 per cent, 95 per cent and 99 per cent confidence intervals around the mean.Provide a management interpretation of these in the context of
On the website that accompanies this textbook you will find a small file which can be used to simulate the Central Limit Theorem. The file has been written so that it should work on most PCs.In Windows switch to the drive containing these data files, highlight the file named CLTPIT.EXE and then RUN
Complete the appropriate test to determine whether there is a significant difference in mean profit between the two regions. How do you explain your conclusion given that the difference between the means of the two samples is over £4000?
Return to the Worked Example in this chapter. After conducting market research we have found that the possibility of a customer in the top 5 per cent group switching to a competitor is 0.85 if we do not offer a price discount and 0.15 if we do. Consider how you could use this information to
Return to the example used in the chapter of two machines filling bottles of shampoo. One machine had a mean of 500 ml, SD 10 ml, the other a mean of 750 ml, SD 15 ml. For each machine calculate the lower and upper amounts (in ml) between which:(a) 90 per cent of all output will fall(b) 95 per cent
A firm is involved in manufacturing high-quality electrical equipment. Each item produced costs £6000 and total annual output is 500 items. At the end of the production process each item is individually tested for quality and safety. If the item is defective in any way it is scrapped at a complete
A supermarket sells one particular item in its store on a regular basis. It currently has 750 units of this item in stock and no deliveries are expected until next week.The manager knows that average weekly sales of this item are 625, standard deviation of 55, and that sales are Normally
An enterprising MBA graduate who has been unable to find gainful employment has taken to visiting an office block in town each lunchtime with an array of freshly made sandwiches for sale. The graduate reckons that he has a 90 per cent chance of selling a sandwich to any of the people working in the
An auditor is checking invoices that have been paid to see if they contain any errors. Historically around 7 per cent of all invoices are expected to contain some error. The auditor takes a random batch of ten invoices. Calculate the probability distribution of errors for this batch of ten. What
On average last year a local leisure centre had 230 customers per day, standard deviation 27, and the distribution of customers was found to be Normal.Determine the probability that on any one day the centre has:(a) more than 270 customers(b) less than 210 customers(c) between 225 and 250 customers.
A small firm has recently purchased a new PC system comprising a colour monitor, a CPU, a laser printer and a keyboard. The supplier of the equipment states that the chance of any one of the components developing a fault in the first year is 1 per cent. What is the probability that the firm will

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Quantitative Methods For Decision Makers 4th Edition Mik Wisniewski - Solutions

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