Ba1 Slides 2017_final.pdf

Session

0

Introduction to BA1

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Syllabus outline!

• 

Macroeconomic and Institutional Context of Business – 25%!

• 

Microeconomic and Organisational Context of Business – 30%!

• 

Informational Context of Business – 20%!

• 

Financial Context of Business – 25%!

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Exam Format! • 

2 hour time limit!

• 

60 objective test questions in a range of styles:! • 

Multiple choice, drag and drop, number entry, hot spot, multiple response (will say how many correct answers)!

• 

Must be sat at a CBA centre: instant result!

• 

You choose when to do it: ! • 

Ideally: leave 1 week after the end of the course, but not more than 3 weeks!

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Session structure! 1 Microeconomic and organisational context I: the goals and decisions of organisations 2 Microeconomic and organisational context I: the market system! 3 Financial context of business I 4 Macroeconomic and institutional context I: the domestic economy 5 Macroeconomic and institutional context I: the international economy! 6 Financial context of business I: international aspects 7 Financial context of business III: discounting and investment appraisal 8 Informational context of business I: summarising and analysing data 9 Informational context of business II: index numbers! 10 Informational context of business III: inter-relationships between variables 11 Informational context of business IV: forecasting www.ultimateaccess.net

Session

1

Microeconomic and Organisational Context I: The Goals and Decisions of Organisations

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The Business Organisation! Views of Profit! Profit Maximisation!

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Not For Profit (NFP)!

Not for Profit Organisations! NFP’s will not follow the principles of shareholder wealth maximisation. Instead their goals will be set by their key stakeholders. These key stakeholders are determined by two criteria: •  the stakeholders interest, and •  the stakeholders influence.

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Types of Organisation!

Control! Public! www.ultimateaccess.net

Private!

Shareholder Wealth! Profit oriented businesses are believed to have shareholder wealth maximisation as a key organisational goal. This goal can be assessed in two ways:!

• 

the returns provided to shareholders!

• 

the value of the shareholders’ shares in the organisation!

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Shareholder Interest! • 

Shares – Funds that are raised for the business activity by dividing up ownership of the company into equal parts!

• 

Shareholder – Someone who owns the shares in the company!

• 

Equity – The ownership interest of the shareholder in the which represents his ownership of profits, losses and assets of the company. This is proportional to the number of shares held!

• 

Dividend – Profits paid out to the shareholders!

• 

Stock Exchange – The place where shares in quoted companies are bought and sold!

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Shareholder Returns! •  The returns to a business owner can be considered either as happening: –  In a single instance in time (short run) and could be measured by: •  Return on capital employed •  Earnings per share –  Over a period of time (long run) •  This would involve consideration of the time value of money (more on this later in the syllabus)

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Short Term Measures! •  Return on Capital Employed –  Measured as:

ROCE =

Profit before interest and tax [EBIT] Capital employed

× 100

•  Profit can be measured in different ways. •  Capital employed can be measured differently.

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Short Term Measures! •  Earnings per share measures the profit available to shareholders expressed per share –  To calculate two steps may need to be made: Number of shares in issue = Earnings per share (EPS)

=

Issued share capital Nominal value of a share Earnings after interest and tax Number of shares in issue

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Long Term Measures! The key to measuring long term success will be to ensure that returns to shareholders are at least equal to the cost of acquiring the capital required to produce a long term flow of earnings. This “cost of capital” is then used to value the future income from any investment. See later session on ‘Discounting and Investment Appraisal’

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Long Term Measures! Share Values An investment in shares is no different than any other investment. With shares, the future income will be in the form of dividends from the company and the net present value of these dividends should represent the value of the share. Also, any change in future dividends should impact on the value of these shares.

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Stakeholders! Interest and Influence! Internal!

Connected!

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External!

Risk & Return! Before deciding whether to buy, hold or sell shares in a firm the investor will consider whether the returns from the firm are adequate to compensate them for the risks of investing in the firm. The minimum rate of return that is acceptable to shareholders is called the required rate.! Systematic risk is the risk associated with investing in any equities in a particular section of the market. For example shares in pharmaceutical industries may have greater systematic risks than shares in bakeries. ! Unsystematic risk (or specific risk) is the risk associated with investing in a particular firm. For example a firm’s shares may have high unsystematic risk due to the firm’s high dependence on the sales of a single line of product!

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Risk Return Curve!

Time value of money! Risk Free Rate! Rate of inflation! www.ultimateaccess.net

Corporate Governance! Profit seeking companies should be run for the benefit of shareholders. But it is directors who make decisions and manage the company so there is a threat that they will follow their own goals rather than the goals of the organisation. Therefore some principles of good corporate governance have been created for companies and summarised into a “Combined Code”

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Key Principles! •  separation of CEO and Chairman’s roles •  the board to have equal numbers of executive and non-executive directors •  transparency, openness and fairness •  reflect the interests of all stakeholders •  a fully accountable board •  remuneration committee •  nomination committee for directors •  hold an AGM

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Transaction Costs! •  Production costs vs transaction costs •  Transaction costs of outsourcing •  Variables that impact on transaction costs

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Session

2

Microeconomic and Organisational Context II: The Market System www.ultimateaccess.net

Session

2

Microeconomic and Organisational Context I: Measuring Returns to the Shareholder

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Influences on Prices! Demand: The plans of consumers

Supply: The plans of producers

Price www.ultimateaccess.net

Influences on Prices! Demand: The plans of consumers

Supply: The plans of producers

Price www.ultimateaccess.net

Consumer Behaviour and Demand! • 

Construction of a demand curve.! Price

P2 P1 D Q2

Q1 Contraction

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Quantity

Conditions of Demand! • 

Income!

• 

Tastes and preferences!

• 

Prices of other goods!

• 

• 

Substitutes!

• 

Complements !

Population!

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Shift in a demand curve! Price Shift due to a change in one of the conditions of demand P1

D1 Q1

increase

Q2

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D2 Quantity

Elasticity of Demand! • 

Elasticity measures responsiveness of one variable to changes in another variable in percentage terms.!

• 

The sign indicates the direction of the relationship!

• 

The number indicates the strength of the relationship!

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Price Elasticity of Demand! • 

This is measured as:!

Percentage change in quantity demanded! Percentage change in price! ! • 

Calculated using either the non-average arc method or the average arc method! ! www.ultimateaccess.net

Price Elasticity of Demand! Meanings of elasticity values: PED

Meaning

<1

Relatively inelastic

If price changes by 10%, then quantity changes by less than 10%

=1

Unit elastic Relatively elastic

If price changes by 10%, then quantity changes by exactly 10%

>1

If price changes by 10%, then quantity changes by more than 10%

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Position on the demand curve! • 

Elasticity varies along the length of straight line demand curves as shown:! PED = infinity = perfectly elastic

Price Elastic section

Midpoint PED = 1 = unit elastic Inelastic section

PED = 0 = perfectly inelastic

Quantity www.ultimateaccess.net

Determinants of PED! • 

Income!

• 

Availability and closeness of substitutes!

• 

Necessities!

• 

Habit!

• 

Time!

• 

Definition of market!

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Supply and Market! • 

Construction of a supply curve.! Price S1 P2 P1

Q1

extension

Q2

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Quantity

Conditions of Supply! • 

Costs of production change!

• 

Technological change!

• 

Import prices change!

• 

Indirect taxes!

• 

Number of firms!

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Shift in a supply curve! Price S1

S2

Shift due to a change in one of the conditions of supply

P1

Q1

Q2 increase

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Quantity

Elasticity of Supply! • 

This is measured as:!

Percentage change in quantity supplied! Percentage change in price! ! • 

Calculated using either the non-average arc method or the average arc method! ! www.ultimateaccess.net

Supply Elasticity! • 

Elasticity of straight line supply curves:!

• 

Any supply curve cutting the quantity axis, regardless of slope, is relatively inelastic.!

• 

Any supply curve cutting the price axis, regardless of slope, is relatively elastic.!

• 

Any supply curve passing through the origin, regardless of slope, is unit elastic.! www.ultimateaccess.net

Determinants of Price Elasticity of Supply! • 

Time!

• 

Factors of production!

• 

Stocks!

• 

Number of firms in the industry!

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The Price Mechanism! • 

Equilibrium price determination:! S1

Price Excess supply P1

Equilibrium point where demand = supply

P2

D1 Qd

Q2

Qs

Quantity

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An example:! Price Demand Supply

Equilibrium: Demand = Supply quantity

30p

1000

200

40p

800

400

50p

600

600

60p

400

800

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Changes to the equilibrium! From the initial demand and supply curves and equilibrium position:! – Decide from the information whether the question involves a change in the conditions of demand or supply (shift)! – Determine whether to shift curve to right or left! – Put in new demand or supply curve! – Identify the new equilibrium!

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Effect of a change in demand conditions! S1

Price P2

New equilibrium point where new demand = supply

P1

D2 D1 Q1

Q2

Quantity

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Effect of a change in supply conditions! S1

Price

S2

P1 New equilibrium point where demand = new supply

P2 D1 Q1

Q2

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Quantity

Market failure! The inability of a market to allocate resources in a way that maximises utility!

•  Public

goods!

•  Externalities! •  Merit

goods!

•  Demerit

goods!

•  Competition

policy and fair trading regulations!

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Interferences in market prices! •  Governments

will sometimes interfere with the equilibrium position when they feel this is necessary. An example of this are the minimum wage rule.!

•  This

can lead to excess supply (i.e. unemployment) which the government then have to deal with (through paying unemployment benefits).! •  Minimum •  Maximum

prices! prices!

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Economies and diseconomies of scale! •  Internal

economies of scale:!

– technical! – financial! – trading! •  External

economies of scale!

•  Diseconomies

of scale!

– technical! – trading! – managerial! www.ultimateaccess.net

Session

3

Financial Context of Business I

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Financial Markets! •  money

markets!

•  capital

markets!

•  foreign

exchange markets!

•  commodity

markets!

•  derivatives

markets!

•  insurance

markets !

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Financial intermediaries! Channelling funds between lenders and borrowers can be achieved by:! • 

•  • 

direct contact: unlikely due to the mismatch between the two parties involved! through a financial market! through financial intermediaries: these provide assets and liabilities to meet the needs of borrowers and lenders ! www.ultimateaccess.net

Financial Intermediaries!

• 

Risk reduction!

• 

Aggregation!

• 

Maturity transformation!

• 

Financial intermediation!

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Liquidity surpluses and deficits! Businesses! • 

Receipts!

• 

Payments!

• 

Lack of synchronisation!

Government! • 

Receipts!

• 

Payments!

• 

Lack of synchronisation! www.ultimateaccess.net

Financial products! Considerations:! • 

Yield / cost!

• 

Risk!

• 

The amounts involved / divisibility!

• 

Time period!

• 

Liquidity!

• 

Transaction costs!

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Capital and money markets! Capital markets – maturities > 1 year! Money markets – maturities < 1 year! ! Products:! • 

Ordinary shares / equity!

• 

Bonds!

• 

Certificates of deposit (CD)!

• 

Credit agreements!

• 

Mortgages!

• 

Bills of exchange!

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Yields on financial products! •  Returns/Yields:!

– Coupon rate or bill rate: nominal published rate! – Interest Yield, running yield or flat yield = !

Annual interest or coupon

×

100

Market price of the security •  This

means that yields rise when the market price of the security falls.!

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Relationship with interest rates!

The market value of debt/bonds/gilts normally moves inversely to any movement in interest rates. So if interest rates were to fall, the value of debt should rise.!

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The Central Bank & Interest Rates! •  Interest

rates in a free market economy will be determined by the demand and supply of money (just like any other economy).!

•  However

because interest rates effect other parts of the economy (such as inflation, the housing market, the value of bonds and shares), the central bank often control the supply and demand for money in order to control interest rates.!

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Banks! Main activities:!

• 

safeguarding money!

• 

transferring money!

• 

lending money!

• 

facilitating trade!

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Credit creation! BANK £100 £

Loans £90 Loans £81

Dep £90 Dep £81

Vault £10 £9 £8.10

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Spends £81

Spends £90

Merchant banks! Main activities:! • 

deal in larger amounts!

• 

advise companies in money management!

• 

negotiate bills of exchange!

• 

underwrite new share issues!

• 

supervise company takeovers!

• 

guarantee commercial bills!

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Non-bank financial intermediaries! • 

Building societies!

• 

Investment and unit trusts!

• 

Pension funds!

• 

Insurance companies!

• 

Finance companies! www.ultimateaccess.net

The Central Bank! Roles:!

• 

banker to the banks!

• 

banker to the government!

• 

supervision of the banking system!

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Session

4

Macroeconomic and Institutional Context I: The Domestic Economy www.ultimateaccess.net

Macroeconomics and Government Policy Goals! Government policies! • 

Economic growth!

• 

Manage inflation!

• 

Manage unemployment!

• 

Manage the balance of payments!

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The Circular Flow Model!

In order for government economic policy to be effective, it is not just important to have the figures for national income, but to also understand the factors and processes which determine it’s level and growth.!

These are analysed using the framework of the circular flow model of income.!

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Simple circular flow model! This assumes:!

• 

Closed economy: no exports or imports!

• 

No government!

• 

No savings or investment!

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Simple circular flow model! Income

Expenditure Households

Consumption Expenditure

Land Labour Capital Enterprise

Output of goods and services or real income

Firms

Income

Expenditure

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Rent Wages Interest Profit

A more complex model! This adds the following assumptions:! • 

household may save, and financial institutions can use these savings for investment!

• 

governments tax incomes, and use these taxes for public expenditure!

• 

international trade occurs!

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Abbreviations! Ø 

Y national income!

Ø 

C consumption!

Ø 

S savings!

Ø 

Iinvestment!

Ø 

T

Ø 

G government expenditure!

Ø 

X exports!

Ø 

M imports!

taxation!

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Incorporating withdrawals and injections! Savings & hoarding

Financial Institutions

Outflow on B of P

Income tax & NIC

Households

Inflow on the B of P

Overseas Sector

Consumption Expenditure Specific taxes & VAT

Government

Overseas Sector

Overseas Sector

Wages & salaries Financial Institutions

Government

Contracts

Exports

Imports

Government

investment

Taxes

Firms Government

Savings

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Overseas Sector

Government

Financial Institutions

Withdrawals and injections! Withdrawals [W] are not passed on as expenditure and reduce the level of income! • 

Savings [S]!

• 

Taxation [T]!

• 

Import expenditure [M]!

Injections [J] is spending which is additional to the circular flow and increase the level of income! • 

Investment [I]!

• 

Government expenditure [G]!

• 

Export expenditure [X]!

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Equilibrium! Inflow = Outflow Expenditure [E] = Income [Y] E ≡ C+J Fact Fact Y ≡ C+W

Fact Fact

C+J = C+W J = W J≡I+G+X W≡S+T+M I+G+X = S+T+M

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1

2

3

Consumption! • 

Average propensity to consume (APC):! • 

• 

Proportion of income that is spent given by:! • 

Consumption/income!

• 

APC = C/Y!

Marginal propensity to consume (MPC):! • 

Proportion of any extra income that is spent given by:! • Additional • 

consumption out of/additional income!

MPC = ∆C/ ∆ Y!

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Savings! The level of savings depends on:! • 

income!

• 

interest rates!

• 

inflation!

• 

credit!

• 

contractual savings (e.g. pensions)!

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Investment! This is affected by:!

• 

expectations about future profits!

• 

the present value of those future profits!

• 

the accelerator!

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The multiplier! •  Disturbances

to equilibrium can arise because of increases or decreases in injections! •  Any

change in an expenditure results in income changing by smaller and smaller steps towards a new final equilibrium level! •  The

total eventual change in income is given by:!

•  ΔY

= Δ Exp × 1/(1 – MPC)!

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The Trade Cycle! Aggregate demand! • 

is made up of all components of expenditure in the economy!

• 

is inversely related to prices!

• 

shifts if a component changes through the multiplier effect!

Aggregate supply! • 

is the collective result of production decisions!

• 

is positively related to price levels!

• 

is limited by the availability of resources!

• 

can only shift in the long run! www.ultimateaccess.net

The Trade Cycle!

Boom!

Recession!

Recovery!

Stagflation!

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Government Economic Policy! •  Fiscal

policy!

•  Supply

side policy!

•  Monetary

policy!

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Fiscal Policy! This involves changing:! • 

• 

taxation! • 

raises revenue!

• 

changes markets!

• 

influences aggregate monetary demand!

• 

finances public goods!

• 

changes the distribution of income and wealth!

government spending! www.ultimateaccess.net

Supply Side Policy! This is aimed at increasing aggregate supply by:!

• 

reducing social security payments!

• 

providing more labour training!

• 

reducing the power of trade unions!

• 

deregulation and privatisation!

• 

switching from direct to indirect taxes!

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Monetary policy! In effect, this means managing the interest rate. For example a rise in interest rates should result in:! •  a

fall in spending!

•  a

fall in investment!

•  a

fall in asset values!

•  foreign •  a

funds attracted to the country!

rise in exchange rates!

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Managing interest rate risk! Avoid the effects of a drop in interest rates for monetary deposits and a rise in interest rates for borrowings! Forward rate agreement (FRA)!

- locks company into target interest rate! - hedges against both adverse and favourable interest rate movements! Interest rate guarantee (IRG)! - 

allows company to take advantage of favourable interest rate movements whilst still protecting against downside movements!

Interest rate futures!

Tradable versions of forward rate agreements – standardised values and dates! www.ultimateaccess.net

Unemployment! • 

Demand deficiency! • 

consumer expenditure!

• 

business investment!

• 

exports!

• 

government expenditure!

• 

Structural change!

• 

Supply side problems!

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Effects of unemployment! • 

Under-utilisation of resources!

• 

Labour lose skills!

• 

Increased costs to the government!

• 

Social problems!

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Inflation! Causes of inflation:!

• 

demand-pull inflation!

• 

cost-push inflation!

• 

expectations effect!

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Session

5

Macroeconomic and Institutional Context II: The International Economy www.ultimateaccess.net

International Trade! Reasons countries trade:! •  To obtain goods they cannot produce! •  To obtain goods more cheaply from other countries! Advantages to trade! •  More output for same amount of inputs! •  Increased productivity from repetition! •  Economies of scale! •  Greater consumer choice!

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Protectionism! Reasons for restrictions on trade:! • 

to protect employment!

• 

to help infant industries!

• 

to prevent unfair competition!

• 

to protect the balance of payments!

• 

to raise revenue!

• 

to maintain security!

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Protectionism! Arguments against protectionism:! • 

inefficiency is encouraged!

• 

resources are misallocated!

• 

the cost of living is raised!

• 

retaliation may occur!

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Protectionism! Methods of protection:! • 

tariffs!

• 

quotas!

• 

hidden restrictions!

• 

subsidies!

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Trade agreements! • 

Bi-lateral vs multi-lateral!

• 

Free trade areas!

• 

Customs unions!

• 

Single markets!

• 

Economic unions!

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World Trade Organisation! The major functions are:!

• 

administer trade agreements!

• 

aid trade negotiations!

• 

handle trade disputes!

• 

monitor national trade policies!

• 

provide assistance to developing countries!

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Balance of Payments! This is a record in account form of all the transactions arising between the residents of one country and the inhabitants of the rest of the world for a specified time period.! ! It is made up of two accounts:! • 

the current account!

• 

the capital and financial account!

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The Current Account! Typical Current Account!

Value of physical exports Value of physical imports

£400,000 £20,000 (£800,000) (£30,000) (£10,000) (£400,000)

Balance of trade Services Rent interest profits & dividends Invisible trade balance Current account balance

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£3,000 £1,000 £4,000 (£6,000)

Capital Financial Account! Capital & Financial Account!

Capital Account This includes transfers of capital and acquisition/disposal of non-produced assets

+£300,000 £1,000 £0

£1,000 £300,000

Balance Financial Account UK Overseas investment Overseas investment in the UK Reserve assets

( (£40,000) £40,000) £35,000 £35,000 £9,000

Balance Net movement in external assets/liabilities

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£100,000 £4,000 £400,000 £5,000

Reconciliation! Current account balance

(£400,000) (£6,000)

Balance on capital and financial accounts

£5,000 £400,000

Errors and omissions

£1,000 £0

Reconciliation

£0£0

If the balance on the capital and financial accounts had been £8,000:

Current account balance

(£6,000)

Balance on capital and financial accounts

£275,000 £8,000

Errors and omissions

(£2,000)

Reconciliation

£0

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Deficit Solutions! • 

Expenditure switching strategies:! • 

Import controls and regulations!

• 

Export subsidies and advertising!

• 

Devaluation !

•  Expenditure

reducing strategies (deflation):!

• 

Contractionary monetary policy!

• 

Contractionary fiscal policy! www.ultimateaccess.net

Globalisation! IMF Definition involves:! •  the growing interdependence of countries worldwide ! •  increasing volume and variety of cross-border transactions in goods and services! •  free international capital flows ! •  more rapid and widespread diffusion of technology!

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Globalisation! Other aspects would involve:! •  the reduction of trade barriers! •  homogenisation of tastes! •  firms selling the same product all markets! •  greater harmonisation of laws! •  dilution of traditional cultures!

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Globalisation! Consequences of globalisation:! • 

Industrial relocation!

• 

Emergence of growth markets!

• 

Increased competition!

• 

Cross-national business alliances and mergers!

• 

Increasing economic divisions!

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Globalisation! Factors driving globalisation:! • 

Improved communications!

• 

Political realignments!

• 

Growth of global industries and institutions!

• 

Cost differentials!

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External analysis of the macro environment! PESTEL analysis:! • 

Political!

• 

Economic!

• 

Social!

• 

Technological!

• 

Ecological / environmental!

• 

Legal! www.ultimateaccess.net

Session

6

Financial Context of Business II: International Aspects www.ultimateaccess.net

Foreign Exchange! • 

An exchange rate is the price of one currency in terms of another currency!

• 

Currency is traded on international exchanges!

• 

One view of determination of the rate is basic demand and supply analysis!

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Exchange rates: determinants of demand! • 

Exports of goods!

• 

Exports of services (invisibles)!

• 

Demand for capital purposes!

• 

• 

Direct capital inflows!

• 

Portfolio investment from abroad!

• 

Short term capital inflows (bank deposits)! • 

Interest rates!

• 

Speculation!

• 

Medium of exchange (some currencies)!

Demand by the authorities!

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Exchange rates: determinants of supply! • 

Imports of goods!

• 

Imports of services (invisibles)!

• 

Supply for capital purposes!

• 

• 

Direct capital outflows!

• 

Portfolio investment abroad!

• 

Short term capital outflows (bank deposits)! • 

Interest rates!

• 

Speculation!

Supply by the authorities! www.ultimateaccess.net

Floating Exchange Rate! S

P P1 D1 D2 Q1

Q2

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Foreign exchange risks! • 

Transaction risk!

- mitigated with forward exchange contracts, futures and options! • 

Economic risk!

• 

Translation risk!

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Session

7

Financial Context of Business III: Discounting and Investment Appraisal www.ultimateaccess.net

The time value of money! Shareholders would prefer to get their returns sooner rather than later, and income in the future will have a lower value than the same income today. So when evaluating future income we need to “discount” (reduce) it’s value to get an equivalent current value. This is achieved using the cost of capital.

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The time value of money! Three reasons: Potential for earning interest / cost of finance Impact of inflation Effect of risk

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Simple interest! Interest is paid or received on the principal only! !

Interest = P × r × n! ! !

Future Value = P + (P × r × n)! ! ! P = amount invested! r = interest rate per annum as a decimal! n = number of years! ! www.ultimateaccess.net

Illustration of simple interest! £1,000 is invested for 5 years. The sum earns 10% simple interest each year. How much will accumulate by the end of the fifth year?! ! Answer! Future value at the end of year 5 ! = P + (P × r × n)! = £1,000 + (£1,000 × 0.1 × 5)! = £1,500!

! www.ultimateaccess.net

Compound interest! Interest is paid or received on the principal plus any accumulated interest! ! Formula is given

!

• 

S = value after n years !

• 

X = amount invested!

• 

r = annual rate of interest (as a decimal)!

• 

n = number of years!

S = X (1 + r)n!

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Illustration of compound interest!

£1,000 is invested in an account for 5 years. The compound interest rate is 10% per annum. Find the value of the account (to the nearest pound) after 5 years and calculate the interest earned.!

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Illustration of compound interest! £1,000 is invested in an account for 5 years. The compound interest rate is 10% per annum. Find the value of the account (to the nearest pound) after 5 years and calculate the interest earned.! Answer! Value after 5 years, S = X (1 + r)n! = £1,000 (1 + 0.1)5! = £1,611! Interest = £1,611 - £1,000 = £611!

! www.ultimateaccess.net

Illustration of compound interest! The formula should be used in the exam but it may help to look at the calculation in this way:! ! Year 1: £1,000 + 10% interest = £1,000 × 1.1 = £1,100! Year 2: £1,100 + 10% interest = £1,100 × 1.1 = £1,210! Year 3: £1,210 + 10% interest = £1,210 × 1.1 = £1,331! Year 4: £1,331 + 10% interest = £1,331 × 1.1 = £1,464! Year 5: £1,464 + 10% interest = £1,464 × 1.1 = £1,611!

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Equivalent annual interest rates!

• 

As mentioned, compound interest is often paid or received more than once a year!

• 

It is useful to convert this period rate to an annual rate of interest!

• 

This is called the equivalent annual interest rate or the annual percentage rate (APR)!

Annual percentage rate = (1 + r) n -1! r = period interest rate (as a decimal)! n = the number of compounding periods in a year ! www.ultimateaccess.net

Illustration of equivalent annual interest rates! An account charges compound interest of 1% per month. Calculate the equivalent annual rate. ! ! Answer! APR = (1.01)12 – 1= 0.1268 or 12.68%! ! Some financing companies can be economic with the truth when describing their products. The APR is usually the best indicator of the true cost.!

! www.ultimateaccess.net

Terminal values!

• 

When evaluating investments, may wish to calculate the terminal value at the end of the investment for the cash flows!

• 

Compound each cash flow over the life of the investment using the interest rate!

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Illustration of terminal values! An investment of $3,000 is made initially and then $1,800 at the end of the first, second and third years and finally $600 at the end of the fourth year.! If interest is paid annually at 6.5%, calculate the terminal value at the end of the fifth year.!

Answer! $3,000 × 1.0655 = $4,110.26! $1,800 × (1.0654 + 1.0653 + 1.0652) = $6,531.55! $600 × 1.065 = $639! Total = $11,280.81!

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Sinking funds! • 

These have equal sums paid into them each period, e.g. a regular savings account!

• 

Use the formula to calculate the amount at the end of the investment period!

! !

S = A (Rn – 1)! (R – 1)! ! S = amount at the end of investment period! A = Equal sum! R = 1 + interest rate (as a decimal)! n = number of periods! www.ultimateaccess.net

Illustration of sinking funds! Suppose I pay £1000 a year into an account for 3 years at an interest rate of 10% with all payments made at the end of each year. How much will the fund accumulate to?! Answer! Value after 3 years, S = A(Rn - 1)! (R – 1)! = £1,000 (1.13 – 1)! (1.1 – 1)! = £3,310!

! www.ultimateaccess.net

Illustration of sinking funds! How would the answer differ if the funds were paid in at the start of each year?! Answer! In the previous illustration we said that if the payments were made at the end of each year we would have £3,310 by the end of year 3! ! However, if the payments are made at the start of each year they will attract an extra year’s interest and the final sum will be £3,310 × 1.1 = £3,641!

! www.ultimateaccess.net

Discounting! • 

When we looked at compound interest we said that the future value after n periods,! S = X (1 + r)n!

• 

However, we may know the future value, S, but need to calculate the present value, X Rearranging the equation we get:! S = future sum! n = number of periods! r = cost of capital/ discount rate as a decimal (we called this the interest rate previously)!

Present value, X = S (1 + r)n!

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!

Illustration of discounting!

Find the present value of £25,000 receivable in 6 years’ time, if the interest rate is 10% pa.! (Calculate your answer to the nearest £)!

!

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Illustration of discounting! Find the present value of £25,000 receivable in 6 years’ time, if the interest rate is 10% pa.! (Calculate your answer to the nearest £)! Answer! Present value, X =

S! (1 + r)n!

! = £25,000! 1.16! = £14,112! www.ultimateaccess.net

Discounting the quick way! • 

We already know that present value, X =

!

S n!

(1 + r) • 

Or we could rewrite this to give

X=S×

1! (1 + r)n!

• 

This is called the discount factor and can be found in our mathematical tables!

• 

This gives an alternative and quick method of calculating the present value !

!

!

Present value, X = S × Discount Factor (from tables)!

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Illustration of discounting using tables!

Use the present value table to find the present value of £25,000 receivable in 6 years’ time, if the interest rate is 10% pa.! !

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Illustration of discounting using tables! Use the present value table to find the present value of £25,000 receivable in 6 years’ time, if the interest rate is 10% pa.! ! Answer! Present value, X = S × Discount factor 6 years at 10%! = £25,000 × 0.564! = £14,100! Note: in part 1 of the illustration our answer was £14,112. This is a rounding difference only!

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Net present value (NPV)! The NPV method is used to appraise investments and involves discounting.!

• 

! NPV = present value of all the cash inflows minus the present value of all the cash outflows.!

• 

If the NPV is positive we accept the project. !

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Illustration of NPV!

A company is considering investing £100,000 in a project, which is forecast to yield the following net cash flows:! Year

1

2

3

4

5!

Net cash flow (£000) 40 35 32 25 19! ! Calculate the net present value of this project if the firm has a cost of capital of 10%!

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Illustration of NPV! Answer! • 

Project has a positive NPV of £18,176: accept!

!

Time!

Cash Flow £000!

Discount Factor 10%!

Present Value £000!

!

0!

(100)!

1!

(100)!

1!

40!

0.909!

36.36!

2!

35!

0.826!

28.91!

3!

32!

0.751!

24.032!

4!

25!

0.683!

17.075!

5!

19!

0.621!

11.799! 18.176!

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Annuities! ! • 

Questions may require us to calculate the present value of a constant amount!

! • 

An annuity is a constant amount paid or received for a number of periods !

!

!

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Illustration of annuities!

Suppose I expect to receive £1,000 per annum for 3 years, starting in one year’s time, and want to calculate the present value using a discount rate of 5%.! Answer! There are actually three methods available:! !

!

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Illustration of annuities! Method 1! • 

One approach would be to discount each cash flow separately and sum the results:!

• 

Present value, X = S × Discount factor! Present value for year 1 amount = £1,000 × 0.952 = £952! Present value for year 2 amount = £1,000 × 0.907 = £907! Present value for year 3 amount = £1,000 × 0.864 = £864! 2.723

• 

The present value of £2,723 is correct but this is a time consuming method, particularly if the annuity continues for a long period!

! www.ultimateaccess.net

!

£2,723!

Illustration of annuities! Method 2! • 

This is a quicker method than method 1. Rather than discounting each cash flow individually we can discount the annuity using a cumulative present value.!

• 

This is the sum of all of the individual discount factors and can be found from the tables.!

Present value of an annuity = annuity × cumulative present value factor! !

• 

Using tables this = £1,000 × 2.723 (as seen in method 1)! = £2,723 (method 1 gave the same answer)!

!

! www.ultimateaccess.net

Illustration of annuities! Method 3! • 

The cumulative present value factor may not be available from the tables. ! They are only available for whole numbers from 1% to 20%!

• 

The calculation is the same as in method 2 but we will need to calculate the cumulative present value factor.! Present value of an annuity = annuity × cumulative present value factor!

• 

The cumulative present value factor is calculated using the formula:! 1⎡ 1 ⎤ 1 − r ⎢⎣ (1! + r )n ⎥⎦

(given)

⎤ 1 ⎡ 1 1 − 0.05 ⎢⎣ (1 + 0.05)3 ⎥⎦

PV = £1,000 × !

= £2,723 (as before)

!

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Perpetuities!

! A perpetuity is an annuity that continues forever.! !

Present value of a perpetuity = perpetuity × 1/r! ! ! r = cost of capital/ discount rate! ! ! www.ultimateaccess.net

Illustration of a perpetuity!

Jo is looking to purchase a perpetuity that guarantees a payment of £10,000 per annum. What is a fair price for the perpetuity, assuming a discount rate of 3% per annum? (Round the answer to the nearest £)! ! !

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Illustration of a perpetuity! Jo is looking to purchase a perpetuity that guarantees a payment of £10,000 per annum. What is a fair price for the perpetuity, assuming a discount rate of 3% per annum? (Round the answer to the nearest £)! ! Answer! Present value of the perpetuity = £10,000 × 1/0.03! = £333,333! !

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Internal rate of return (IRR)! ! • 

IRR is another method of appraising investments and involves discounting!

! The IRR is the discount rate at which NPV is zero! ! • 

Accept the project if the IRR is more than the company’s cost of capital!

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Internal rate of return (IRR)! NPV £

Positive NPV

! !

IRR

Cost of Capital % Company cost of capital

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Internal rate of return (IRR)! Estimate of IRR! • 

The process on the previous slide is too time consuming. An estimated IRR is calculated using a three step approach:!

• 

Step 1: Take a small discount rate r1 and calculate the NPV (NPV1 )!

• 

Step 2: Take another discount rate r2 and calculate the NPV (NPV2 )!

• 

Step 3: Use the formula to calculate the IRR!

⎡ ⎤ NPV1 (r2 − r1 )⎥ IRR = r1 + ⎢ NPV1 − NPV2 ⎣ ⎦ (learn)! www.ultimateaccess.net

Illustration of IRR! A project involves investing £140,000, and will produce the following year-end cash flows:! Year

1

2

3

4!

Net cash flow (£000) 60 50 45 30! ! Discount the project at 10% and at 15%, then calculate the internal rate of return of the project!

! www.ultimateaccess.net

Illustration of IRR! Answer! Step 1: Calculate the NPV at 10% (r1)! Year !

Cash Flow (£)!

Discount Factor 10%!

Present Value (£)!

!

0!

(140,000)!

1!

(140,000)!

1!

60,000!

0.909!

54,540!

2!

50,000!

0.826!

41,300!

3!

45,000!

0.751!

33,795!

4!

30,000!

0.683!

20,490!

!

!

!

10,125!

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Illustration of IRR! Answer! Step 2: Calculate the NPV at 15% (r2)! Year !

Cash Flow (£)!

Discount Factor 15%!

Present Value (£)!

!

0!

(140,000)!

1!

(140,000)!

1!

60,000!

0.870!

52,200!

2!

50,000!

0.756!

37,800!

3!

45,000!

0.658!

29,610!

4!

30,000!

0.572!

17,160!

!

!

!

(3,230)!

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Illustration of IRR! Step 3: Calculate the IRR! !

⎡ ⎤ NPV1 (r2 − r1 )⎥ IRR = r1 + ⎢ ⎣ NPV1 − NPV2 ⎦ ! !

! IRR = 10 +

10,125

× (15 -10)!

(10,125 + 3,230)! ! = 13.79%! ! ! www.ultimateaccess.net

Session

8

Informational Context of Business I: Summarising and Analysing Data www.ultimateaccess.net

Information! Data vs information! Characteristics of good information:! • 

A!

• 

C!

• 

C!

• 

U!

• 

R!

• 

A!

• 

T!

• 

E!

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Bar charts! • 

Height of the bar is proportional to the frequency!

• 

There are three types of bar chart:! (a) Simple ! (b) Multiple! (c) Compound!

• 

The data on the continent of origin of a class of students will be used to construct each type of bar chart. !

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Illustration of simple bar chart! ! !

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Illustration of multiple bar chart!

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Illustration of compound bar chart!

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Scatter diagrams! • 

Visual way of determining if there might be a relationship between two variables!

• 

If the variables are related, they are said to be correlated!

• 

Stronger correlation shows as more obvious relationship on the scatter diagram!

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Illustration of scatter diagram!

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Types of correlation! !

! !

!

x x

!

!

x

x x

!

x

!

x

!

x

!

x

x

!

! ! ! !

Perfect positive correlation!

r = +1!

Perfect negative correlation!

r = - 1!

! www.ultimateaccess.net

Types of correlation! ! ! !

x

!

x

!

x

!

x

! x

!

x

!

! x

x

x

!

x

! ! !

! High positive correlation!

High negative correlation!

(r is close to +1)!

(r is close to -1)!

! www.ultimateaccess.net

! ! Types of correlation ! !

! ! x

!

x

x

! !

x

!

!

x x

x x

x

x

x

x

x

!

x x

! ! !

r = 0!

!

!

No correlation!

!

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Histograms! • 

Graph of frequency distribution!

• 

Exam tip: AREA of each bar is proportional to the frequency!

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Illustration of a histogram! 12

10

8

6

4

2

10

20

30

40

50

60

70

80

Weight (kg)

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90

100

110

120

130

140

150

Ogives! • 

Graph of the cumulative frequency distribution.!

• 

More useful for continuous data since the intermediate values of x mean something!

• 

Step 1: Plot the cumulative frequency on the y axis against the UPPER end of each class interval on the x axis!

• 

Step 2: Join the points together to form the ogive!

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Illustration of an ogive! • 

The following cumulative frequency distribution relates to the weight of some sand bags:!

Weight of bag

Number of bags

Cumulative frequency!

(kg)! > 10 ≤ 20

1

1!

> 20 ≤ 30

6

1 + 6 = 7!

> 30 ≤ 40

8

7 + 8 = 15!

> 40 ≤ 50

10

15 + 10 = 25!

> 50 ≤ 70

10

25 + 10 = 35!

> 70 ≤ 90

6

35 + 6 = 41!

> 90 ≤ 120

6

41 + 6 = 47!

> 120 ≤ 150

3

47 + 3 = 50!

50!

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Illustration of an ogive!

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Session

9

Informational Context of Business II: Index Numbers www.ultimateaccess.net

Simple index numbers! •  • 

All index numbers show the percentage changes over time! value in any given year × 100 ! value in base year!

• 

The most common type of indices are price indices. They compare the price in one year to the price in another year, called the base year !

• 

The index in the base year = 100!

!

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Example of a simple price index! Turn the following prices into an index series with 2003 as the base year! Year Price

2003

2004

2005

2006

2007

2008!

£56

£62

£67

£72

£76

£84!

! Answer! Index 100

110.7

119.6 128.6 135.7 150.0!

! Sample working 2004: (62 ÷ 56) × 100 = 110.7! Sample interpretation In 2004 the price was 10.7%

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higher than in 2003.!

Changing the base year! • 

Over time a base year may become less meaningful!

• 

Exam tip: To change to a new base year divide all index numbers by the index number of the new base year and multiply by 100!

Example of changing the base year! Re-base the index calculated in the previous worked example to the Year 2006 !

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Changing the base year! Answer! Year

2003

2004

2005

2006

2007

2008!

Price

£56

£62

£67

£72

£76

£84!

Index if 2003 is base year:! 100

110.7 119.6

128.6 135.7 150.0!

Index if 2006 is base year:! 77.8

86.1

93.0

100

105.5 116.6!

Sample working 2003: (100 ÷ 128.6) × 100 = 77.8! Sample interpretation The price in 2003 was 77.8% of the price in the year 2006.!

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Combining series of index numbers! • 

If an index has been re-based it can be difficult to make comparisons to earlier years which were measured using the old index!

• 

Splicing the series together solves this problem!

• 

Involves redefining the base year of an index in a particular year and then restating the index values in previous years so that comparisons can be made!

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Illustration of combining indices! • 

The price index below changed its base to 1983 after many years with base 1970. Recalculate it as a single series with base 1983. By how much have prices risen from 1981 to 1985?!

Year

Price index !

(1970 = 100)! 1981

271!

1982

277!

1983

280!

!

(1983 =100)! 1984

104!

1985

107! www.ultimateaccess.net

Illustration of combining indices! Answer! Year

Price index

Single index

(1970 = 100)! 1981

271

= 271/280 × 100 = 97!

1982

277

= 277/280 × 100 = 99!

1983

280

100!

!

(1983 =100)! 1984

104

104!

1985

107

107! www.ultimateaccess.net

Illustration of combining indices! • 

Now that we have a single series spanning both 1981 and 1985, we can compare the two:! 100 × (107/97) = 110!

• 

So prices have risen by 10 per cent from 1981 to 1985!

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Relative price indices! • 

When several items are being considered it is important to recognise the importance of the different items within the group. Hence a weighting is usually attached to each item. In the examination the weightings will always be given.!

• 

Relative price index = ∑(w x (P1 /P0) × 100 (given)! ∑w! P1 = price in current year! P0 = price in base year! w = weight: either base or current year weight!

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Illustration on relative price indices! Item

Price (2007)

Price (2008)

Weighting!

Milk

40p per pint

45p per pint

10!

Meat

£6.50 per kg

£6.00 per kg

7!

Caviar

£12.40 per jar £14.00 per jar

1!

! • 

Calculate a weighted relative price index for the data above and interpret your answer.!

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Illustration on relative price indices! Answer! P1/P0

W

P1/P0 x W!

Milk

45/40 = 1.125

10

11.250!

Meat

6.00/6.50 = 0.923

7

6.461!

Caviar

14.00/12.40 = 1.129

1

1.129!

18

• 

18.84!

Weighted relative price index = 18.84/18 × 100! = 104.7!

• 

The average price rise of the three items has been 4.7%!

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Choice of weighting! Advantages of base year weights! • 

Weightings can be used for several periods!

• 

Comparisons can be made between several periods!

! Advantage of current year weights! • 

Weights remain up to date and reflect current trends and fashions!

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Quantity indices! • 

Calculated in a similar way to the price indices but changing quantities are measured instead of price!

• 

Formula for a weighted relative quantity index! = ∑(w x (Q1/Q0)) × 100

(given)!

∑w! where Q1 = the current year quantity! and Q0 = the base year quantity!

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Illustration on quantity indices! A company manufactures two products, A and B. The sales figures over the past three years have been as follows:! Year

A Sales (000s)

B! Sales (000s)!

2006

386

533!

2007

397

542!

2008

404

550!

22

19!

Weighting

Using 2006 as a base, compute a weighted relative quantity index for 2007 and 2008, and interpret their values.!

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Illustration of quantity indices! Answer! 2006 to 2007! Q1/Q0

W

Q1/Q0 x W!

A

397/386 = 1.028

22

22.616 !

B

542/533 = 1.017

19

19.323!

41

41.939!

• 

Weighted relative price index = 41.939/41 × 100 = 102.29!

• 

The sales rose by an average of 2.29% from 2006 to 2007!

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Illustration of quantity indices! 2006 to 2008! Q1/Q0

W

Q1/Q0 x W!

A

404/386 = 1.047

22 23.034 !

B

550/533 = 1.032

19

19.608!

41

42.642!

• 

Weighted relative price index = 42.642/41 × 100 = 104.00!

• 

The sales rose by an average of 4.00% from 2006 to 2008!

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Session 10 Informational Context of Business III: Inter-relationships Between Variables

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Big data! Helps companies make more informed business decisions by! • 

expanding their knowledge of customers!

• 

giving them a deeper understanding of how their customers behave!

• 

analysing customer behaviour to make marketing activities more likely to work!

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Correlation! • 

Correlation establishes the strength of the relationship between variables that are related to each other!

• 

There are three different calculations:! (a) Pearson’s correlation coefficient! (b) Coefficient of determination! (c) Spearman’s rank correlation coefficient!

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Pearson’s correlation coefficient, r! ! r=

n∑xy - ∑x∑y

(given)!

! 2

2

2

2

√(n∑x – (∑x) )(n∑y - (∑y) )!

• 

r = +1 denotes perfect positive linear correlation !

• 

r = -1 denotes perfect negative linear correlation!

• 

r = 0 denotes no linear correlation !

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Illustration of Pearson’s correlation coefficient! A new machine has been purchased and management are keen to explore the link between output and cost. Output and cost figures for the last four months are as follows:!

Output (000s)!

3!

4!

5!

6!

Cost (£000s)!

6!

7!

7!

10!

Calculate the correlation coefficient between these two sets of data!

! www.ultimateaccess.net

Illustration of Pearson’s correlation coefficient! Answer! r=

n∑xy - ∑x∑y! 2

2

2

2

√(n∑x – (∑x) )(n∑y - (∑y) )! =

4(141) − (18)(30)! √ (4 x 86) − (18)2(4 x 234 − (30)2)!

=

24! √(20)(36)

x!

y!

xy!

x2!

y2!

3!

6!

18!

9!

36!

4!

7!

28!

16!

49!

5!

7!

35!

25!

49!

6!

10!

60!

36!

100!

∑x = 18!

∑y = 30!

∑xy = 141!

∑x2 = 86!

∑y2 =234!

= + 0.89!

! www.ultimateaccess.net

Coefficient of determination, r2! ! • 

Coefficient of determination is calculated by squaring the correlation coefficient i.e. r2!

• 

It measures the proportion of changes in y that can be explained by changes in x !

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Illustration of coefficient of determination! Using the information in the previous illustration calculate, and comment on, the coefficient of determination ! Answer! From the previous illustration, r = 0.89! Therefore, the coefficient of determination, ! r2 = 0.892 = 0.7921! ! This means that 79.21% of the change in cost relating to the machine can be explained by a change in machine output!

! www.ultimateaccess.net

Spurious correlation!

• 

A high correlation coefficient does not always mean there is always a cause and effect relationship between the data. This is known as spurious correlation!

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Rank correlation: Spearman’s coefficient! • 

Used when a distribution is given in terms of rank, rather than actual values!

R = 1 -

2 !

6 ∑ d 2

n(n - 1 ) (given)!

d = the difference in ranks ! n = the sample size!

• 

The rank correlation coefficient can be interpreted in the same way as the ordinary correlation!

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Illustration of Spearman’s rank coefficient! As part of its recruitment procedures, a company awards applicants ratings from A (excellent) to E (unsatisfactory) for their interview performance and marks out of 100 for a written test. The results for five interviewees are as follows:!

!

Calculate the rank correlation coefficient for this data and comment on its value! Interviewee!

Interview grade!

Test score!

One!

A!

60!

Two !

B!

61!

Three!

A!

50!

Four!

C!

72!

Five!

D!

70!

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Illustration of Spearman’s rank coefficient! Answer! Note: Interviewees one and three share the best interview grade. They therefore share the ranks 1 and 2 giving them 1.5 each! Interviewee!

Rank of interview grade!

Rank of test score!

d!

d2!

One !

1.5!

4!

2.5!

6.25!

Two!

3!

3!

0!

0!

Three!

1.5!

5!

3.5!

12.25!

Four!

4!

1!

3!

9!

Five!

5!

2!

3!

9! ∑= 36.50!

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Illustration of Spearman’s rank coefficient! R=1 -

2

6 ∑ d

!

2

n(n - 1 )! = 1 – (6 x 36.50)! 5(25-1)! = −0.825! ! • 

There is a strong negative correlation between the interview grade and the test score!

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Regression! • 

Expresses the relationship between two sets of data using the equation of a straight line, ! y = a + bx!

• 

Can be used for forecasting!

• 

There are two possible methods ! Method 1: Draw a scatter diagram and estimate the line of best fit (not directly examinable but it is useful to understand this method)! Method 2: Use least squares regression analysis (exam)!

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Regression using scatter diagram! • 

A scatter graph is drawn showing the sales achieved (£000’s) for different levels of advertising spend (£000)!

• 

A straight line of best fit is then drawn:!

!

Independent variable = advertising spend (£000)!

Y=a + bx! !

Dependent variable = sales (£000)!

!

Intercept on y axis!

• 

Gradient!

This straight line can then be used to forecast the sales for any given level of advertising spend.!

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Regression using least squares method! • 

Finds the line of best fit computationally by minimising the sum of the squares of the distances between the data and the line.!

! • 

i.e. rather than drawing a graph this method uses formulae to calculate the values of ‘a’ and ‘b’ in the equation of a straight line, y = a + bx!

! • 

We can then forecast the value of ‘y’ (e.g. sales)for any given value of ‘x’ (e.g. advertising spend)!

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Regression using least squares method!

Formulae: (both given)! ! b = n∑xy - ∑x ∑y 2

!

2

n∑x - (∑x) ! ! a = y - bx!

n = number of pairs of data in the sample! y and x = mean (average) of y and mean (average) of x! www.ultimateaccess.net

Regression using least squares method! Interpolation and extrapolation! • 

As mentioned, the regression equation can be used for predicting the value of y for a given value of x!

• 

if x is within the range of the original the prediction is known as interpolation !

• 

if x is outside the range of our original data the prediction is known as extrapolation!

• 

in general interpolation is much safer than extrapolation !

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Regression using least squares method! Limitations of linear regression analysis! • 

Assumes a linear relationship between the variables!

• 

Only measures the relationship between two variables!

• 

Only interpolated forecasts tend to be reliable!

• 

Assumes historical behaviour of the data continues into the foreseeable future!

!

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Illustration of least squares method!

!

!

Using the data given below, establish the least squares regression line! Advertising Expenditure (£000)!

Sales (£000)!

10!

62!

14!

75!

6!

53!

9!

48!

3!

28!

12!

70!

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Illustration of least squares method! Answer!

!

!

!

Calculation of b: begin by setting up

a table!

Advertising £000 = x!

Sales £000 = y!

xy!

x2!

10!

62!

620!

100!

14!

75!

1,050!

196!

6!

53!

318!

36!

9!

48!

432!

81!

3!

28!

84!

9!

12!

70!

840!

144!

∑x = 54!

∑y = 336!

∑xy = 3,344!

∑x2 = 566!

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Illustration of least squares method! b = n∑xy - ∑x ∑y 2

n∑x

!

2

- (∑x) !

= 6(3,344) – (54)(336)! 6(566) – (54)2! = 1,920! 480! = 4.0! ! Calculation of a! a = y - bx = 336 - 4 54 = 56 - 36 6

= 20!

6!

!

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Illustration of least squares method! Least squares regression line: y = a + bx! y = 20 + 4x! The result should be more precise than method 1! ! Illustration 2: Using the line for forecasting! Using the regression line ‘y = 20 + 4x’ obtained above, predict the average daily sales of a supermarket if the monthly advertising expenditure is:! (i) £11,000, and! (ii) £100,000! In each case, comment on the level of accuracy!

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Illustration of least squares method! Answer! (i) y = 20 + 4(11) =64, i.e. £64,000! Prediction found by interpolation and some reliance may be placed on this prediction! ! (ii) y = 20 + 4(100) =420, i.e. £420,000! Prediction found by extrapolation, which is dangerous, and may not be placed on this prediction!

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Session 11 Informational Context of Business IV: Forecasting www.ultimateaccess.net

Time series analysis! • 

A time series is a series of figures recorded over time!

• 

Time series analysis is a tool to help forecast the future, particularly sales!

• 

The basic idea is to analyse the past to identify a pattern, of say sales, which can then be used to forecast the future!

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Time series analysis components! • 

Trend (T): this is a general movement of the time series over a long period of time!

• 

Seasonal variation (SV): a recurring pattern, due to repetitive events, over a shorter but fixed time period!

• 

Cyclical variation (C): recurring patterns over a long time period, not generally fixed in nature!

• 

Random variation or residual value (R): unpredictable variations due to random or chance events!

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Time series analysis models! • 

Calculation questions tend to focus on the trend and seasonal variation only. These can be combined together in two ways to give the actual results, i.e. the time series:! (a) Additive model: TS = T + SV ! (b) Multiplicative model: TS = T × SV !

• 

It will be clear as to which one should be used!

• 

Some questions also ask for the calculation of the residual (R). In this case, the two equations above should be extended to include R!

! ! www.ultimateaccess.net

Illustration of residual calculation! • 

The multiplicative model for a time series shows that at a certain time the actual, trend and seasonal variations are 555, 463 and 1.16. Find the residual at this point. (Round your answer to four decimal places).!

! Answer! • 

In the multiplicative model TS = T × SV x R!

• 

Therefore, R = TS/ (T × SV)! = 555/ (463 × 1.16) ! = 1.0334 (to four decimal places)! !

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Seasonal variations! • 

For the additive model the seasonal variations will be given as a positive or negative number. The total of the seasonal variations will be zero!

• 

For the multiplicative model the seasonal variations will be given as a percentage or a decimal. The total of the seasonal variations will be four. !

• 

If this is not the case, any difference should be spread evenly across the seasonal variations!

!

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Illustration of seasonal variations! Using the multiplicative model the seasonal variations are found to be ! 1.04, 1.15, 0.91 and 0.95. ! They are subsequently adjusted so that their total = 4. What is the new value of the average currently valued at 1.04?! !

!

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Illustration of seasonal variations! Using the multiplicative model the seasonal variations are found to be ! 1.04, 1.15, 0.91 and 0.95. ! They are subsequently adjusted so that their total = 4. What is the new value of the average currently valued at 1.04?! ! Answer! Total = 1.04 + 1.15 + 0.91 + 0.95 = 4.05, ! hence we adjust by subtracting 0.05/4 = 0.0125 from each average. ! The adjusted first average = 1.04 – 0.0125 = 1.0275!

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!

Forecasting with time series! ! ! method 1: using least squares regression! • 

Step 1: The forecasted trend can be calculated using least squares regression (as seen in previous session). This is appropriate if there is a linear trend!

• 

Step 2: Using the appropriate time series model, i.e. additive or multiplicative, an adjustment can be made to the trend for the seasonal variation and the time series can be calculated! (Ignore the residual, R, unless stated otherwise!

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Illustration using least squares analysis!

• 

Least squares regression was used to calculate the straight line of best fit, y= a + bx, for sales against time.!

• 

This was found to be y = 13.7 + 1.5x, where y is equal to the sales value and x is the quarter!

• 

What are the forecast sales for quarter 14 if:! (a) The seasonal variation is +2.4 for this quarter! (b) The seasonal variation is +10% or +0.1 for this

!

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quarter!

Illustration using least squares analysis! Step 1! • 

Using the least squares regression line the trend, T, can be calculated for quarter 14! y = 13.7 + 1.5x! y = 13.7 + (1.5 × 14)! y = 34.7 This is the forecasted sales trend (T)!

Step 2! • 

An adjustment can be made to the trend to reflect the seasonal variation and the sales can be forecast for quarter 14!

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Illustration using least squares analysis! (a) 

If the seasonal variation is given as a number (positive or negative) we must use the additive model:! Forecast sales for Q14 (TS) = T + SV! = 34.7 + 2.4! = 37.1!

(b) If the seasonal variation is given as a percentage or decimal we must use the multiplicative model:! Forecast sales for Q14 (TS) = T × SV! = 34.7 × 1.1! = 38.17! www.ultimateaccess.net

Forecasting with time series! method 2: using moving averages ! • 

Step 1: The forecasted trend can be calculated using moving averages. This is appropriate if there is no linear trend!

• 

Step 2: Using the appropriate time series model, i.e. additive or multiplicative, an adjustment can be made to the trend for the seasonal variation and the time series can be calculated (as for method 1)! (Ignore the residual, R, unless stated otherwise)!

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Illustration using moving averages! Sales for article B (‘000units)! Q1!

Q2!

Q3!

Q4!

2006!

24.8!

36.3!

38.1!

47.5!

2007!

31.2!

42.0!

43.4!

55.9!

2008!

40.0!

48.8!

54.0!

69.1!

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Illustration using moving averages! Year!

Qtr!

Sales (Y)!

4 point moving total!

8 point moving total!

2006!

1!

24.8!

-!

-!

2!

36.3!

-!

-!

3!

38.1!

146.7!

299.8!

37.4750!

4!

47.5!

153.1!

311.9!

38.9875!

1!

31.2!

158.8!

322.9!

40.3625!

2!

42.0!

164.1!

336.6!

42.0750!

3!

43.4!

172.5!

353.8!

44.2250!

4!

55.9!

181.3!

369.4!

46.1750!

1!

40.0!

188.1!

386.8!

48.3500!

2!

48.8!

198.7!

410.6!

51.3250!

3!

54.0!

211.9!

438.5!

54.8125!

4!

69.1!

226.6!

-!

! ! 2007!

2008!

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4 point moving average (T)!

Seasonal adjustment! • 

If the seasonal variations (SV) are already known, then it is possible to deseasonalise the actual results (TS) to identify the trend (T)! Multiplicative model! Based upon: Actual (TS) = Trend × SV ! Trend = Actual ÷ SV! Additive model! Based upon: Actual (TS) = Trend + SV! Trend = Actual – SV!

!

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Illustration of seasonal adjustment! Unemployment numbers actually recorded in a town for the second quarter of 20X8 were 2,400. The seasonal variation for this quarter is 0.95. Using the multiplicative model for seasonal adjustment, calculate the seasonallyadjusted figure (in whole numbers) for the quarter! !

!

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Illustration of seasonal adjustment! Unemployment numbers actually recorded in a town for the second quarter of 20X8 were 2,400. The seasonal variation for this quarter is 0.95. Using the multiplicative model for seasonal adjustment, calculate the seasonallyadjusted figure (in whole numbers) for the quarter! ! Answer! Seasonally adjusted figure, trend = Actual ÷ SV! = 2,400 ÷ 0.95! = 2,526!

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Revision!

• 

Read your course notes. !

• 

Make short notes, and attempt all the Test your Understanding exercises!

• 

Visit the cimaglobal website to check on any recent articles that may be relevant!

!

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On the assessment day!

• 

Make sure that you are thoroughly familiar with the software before the exam starts !

• 

Work out your answer first!

• 

Write down all the question numbers on a piece of paper and use a key to identify questions!

• 

Do all • 

the easy questions first. !

Flag questions you have not answered and return to them later !

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On the assessment day! • 

• 

Remember: you have not answered until you press ‘submit’ ! • 

your answer can always be changed later by hitting ‘clear’, changing the answer and then again pressing ‘submit’!

• 

Answers only become final when you finish the exam!

You will be given a five minute warning before the end of the exam! • 

• 

Make sure before you finish the exam that you have submitted answers to all questions: guessing if necessary. !

Panic is likely to be your worst enemy. You don’t need to know everything: just enough to pass!! • GOOD www.ultimateaccess.net

LUCK!!