Introduction to Corporate Finance

Introduction to Corporate Finance. A practical guide for postgraduate and research students.

Dr Michel Zaki Guirguis 13/04/2015Bournemouth University1

Institute of Business and LawFern BarrowPoole, BH12 5BB, UKTel:0030-210-9841550Mobile:0030-6982044429Email: [email protected]

Biographical notes

I hold a PhD in Finance from Bournemouth University in the U.K. I have worked for several multinational companies including JP Morgan Chase and Interamerican Insurance and Investment Company in Greece. Through seminars, I learned how to manage and select the right mutual funds according to various clients needs. I supported and assisted the team in terms of six-sigma project and accounts reconciliation. Application of six-sigma project in JP Morgan Chase in terms of statistical analysis is important to improve the efficiency of the department. Professor Philip Hardwick and I have published a chapter in a book entitled “International Insurance and Financial Markets: Global Dynamics and Local Contingencies”, edited by Cummins and Venard at Wharton Business School (University of Pennsylvania in the US). I am working on several papers that focus on the Financial Services Sector.

1 I have left from Bournemouth University since 2006. The permanent address of the author’s is, 94, Terpsichoris road, Palaio – Faliro, Post Code: 17562, Athens – Greece.

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Table of contents

Ratio analysis 5

Present and future value 9

Investment appraisal methods and a consultancy report 11

Risk and return 24

Modern portfolio theory, (MPT) 34

Capital asset pricing model, (CAPM) 37

Arbitrage Pricing Theory Model (APT) 40

Managing the weighted average cost and the marginal cost of capital. WACC, MCC 42

The management of working capital 59

Leverage effect 62

Performance measurement 69

Measuring the value of a business 72

Financial derivatives 74

Case study based on capital investment appraisal methods 110

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Project management

Your consultancy report should include:

a) A review of the current position of the business.b) A review of the proposed project.c) Your recommendations as to whether the project should proceed and any general recommendations ( both financial and operational) you feel are pertinent to ensure the long term success of the company.

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EXECUTIVE SUMMARY

This financial report will be an analytical tool for each member of staff at a managerial position. It will include a detailed analysis, and financial interpretation of the results of the existing business and the proposed project.

In order to assess the current flow of the operation, we will use a range of different ratios. They will help us to ensure that the money have been put in a good use.

On the other hand, we will implement different types of appraisal techniques to verify the viability of the proposed project. Detailed explanations will be given in order that the shareholders have a clear picture of the proposed project.

Finally, this report will include recommendations on how to improve financial and operational aspects of the operations and a general overview to ensure the log-term success of the company.

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Ratio analysis

A) THE CURRENT POSITION OF THE BUS INESS

The current position of the business can be verified through ratios analysis. According to this analysis managers, creditors, and investors can receive valuable information about the effectiveness and efficiency of the operations.

Managers by using especially profitability, operating, and asset utilization ratios can maintain a fairly accurate perception of the financial health of their business. Different type of ratio can help them as they are indicator of well goals are being achieved. When actual results can not meet the standard set then ratios indicate where the problem may be.

In more details, we will assess the current position of the business by using a combination of financial statements such as : profitability, asset utilization, liquidity, working capital, and shareholder’s ratios.

Liquidity ratios

1) Current Ratios

1996 1997 £000 £000Current Assets 352 588 ------ = 1.33 times ------ = 1.69 times Current Liabilities 264 348

2) Acid test Ratios 1996 1997 £000 £000Current Assets - Stock 312 538 ------- = 1.18 times ------ = 1.54 times Current Liabilities 264 348

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PROFITABILITY AND ASSET UTILIZATION RATIOS

1) Return on net assets 1996 1997 £000 £000 Profit before interest & tax 320 480 -----= 19.42% ------ = 26.1% Total assets less C. liabilities 1648 1840

2) Gross Profit Margin 1996 1997 £000 £000 Gross profit 1600 2240 ------- = 80% ------- = 80% Sales 2000 2800

3) Net Profit Margin 1996 1997 £000 £000 Profit before interest & tax 320 480 ----- = 16% ------ = 17.14% Sales 2000 2800

4) Net Asset turnover 1996 1997 £000 £000 Sales 2000 2800 ------- = 1.21 times ------- = 1.52 times Total assets less C. liabilities 1648 1840

SHAREHOLDERS RATIO

1) Return on capital employed (Net) 1996 1997 £000 £000Profit after tax 208 312 ----- = 12.62% -----= 17% Shareholder’s Funds 1648 1840

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2) Dividend cover 1996 1997 £000 £000Profit after tax 208 312 ------- = 2.1 times ----- = 2.6 times Dividends 100 120

WORKING CAPITAL RATIOS

1) Stock Turnover 1996 1997 £000 £000Cost of sales 400 560 -------- = 10 times ------- = 11.2 times Stock 40 50

COMMENTS OF THE RATIOS ANALYSIS

According to the above analysis, it is obvious that the business perform well and have a healthy financial statements. We have the following results:

The current ratio, which indicate the ability of the company to cover its current liabilities is high enough. It reflects security and safety for creditors and potential investors that the company has enough assets to cover its long term debt.

The high Acid - Test Ratio, indicate a safe position of the company in the competing marketplace.

The Net Profit Margin shows clearly by comparing the two years that the business generate more profits on sales. Therefore, expenses are controlled efficiently and effectively.

The Net Asset Turnover, indicate the management effectiveness in using the resources of the business such as: fixed assets. The highest asset turnover is a good indicator of the financial health of the business.

The higher amount of stock turnover, indicate that there is sufficient stock to meet customer service requirements. The high return on capital employed and dividend cover, indicate safety of payment of future dividends and ability to cover the additional risk that managers take.

The company has a good high gross profit percentage as most of its products have a low cost of sales.

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Investment Appraisal

Learning Objectives

What is Investment Appraisal?

Time Value of Money

Present Value

Future Value

Net Present Value

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What is Investment Appraisal ?

It is a process which assists mangers to take decisions and evaluate the future success of a project in terms of profitability, suitability, and compatibility with company objectives.

Time Value of Money

The value of money changes with time. Money received today has a different value from money received in the future.

Present Value

For £100 generated in 3 years from today, what is the sum of money invested today if interest rate is 10%.

This is present value (PV): value today of future cash flows.

Solution

1 PV = 100 x ----------- (1+0.10)3

1PV = 100 x ------------ 1.331

PV = 100 x 0.7513 = £75.13

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Future Value

End of year 2? Initial investment = Value: £100 Interest rate: 6%

Future value = Present value x (1+r)n

Solution

Future value = Present value x (1+r)n

Future value = 100 x (1+0.06)2

Future value = 100 x 1.1236 = £112.36

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Net Present Value (NPV)

The Net Present value is an investment appraisal method. It is based on the view that a project will be regarded as successful if the present value of all expected cash inflows is greater than, or equal to the capital invested at the outset. The net present value of a project is equal to the present value of the cash inflows minus the present value of the cash outflows, all discounted at the specified rate.

It is called net present value because, in calculation, the capital invested is deducted from the present value of the discounted cash flows. If the present value of the expected cash flows is greater than the capital invested, then the net present value will be positive. If the present value of expected cash flows is less than the capital invested, then the net present value will be negative. A positive net present value indicates that the project should be accepted, while a negative net present value indicates that it should be rejected.

The NPV decision rule is as follows

1. Where the net present value of he project is positive, accept the project.2. Where the net present value of the project is negative, reject the project.3. Where the net present value of he project is zero, the project is acceptable in

meeting the cost of capital but gives no surplus to its owners.

Example

Calculation of net present value of Project A using a discount factor of 10% and initial cost of investment 120,000

End of year Cash flow (£) Discount factor 10% Present value(£)1 60,000 0.9092 60,000 0.8263 60,000 0.751Present value of cash inflowsLess Investment costNet present value

Solution

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End of year Cash flow (£)

Discount factor 10% Present value(£)

1 60,000 0.9091 54,5462 60,000 0.8264 49,5843 60,000 0.7513 45,078Present value of cash inflows

149,208

Less Investment cost (120,000)Net present value 29,208

NPV is positive so the project is viable. Accept it.

Advantages

Discounted Cash Flow Technique.

The time value of money, and the timing, is taken into account on all the cash flows

Disadvantages

More difficult to calculate

A company is trying to decide between two competing projects. Calculate the net present value of Project A and Project B using a discount factor of 10%. The initial

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cost of investment is £120,000 for Project A and £130,000 for Project B. The following cash flows are as follows:

Year Project A (£) Project B(£)1 50000 400002 60000 600003 70000 800004 80000 90000

Solution

End of year Project A Project B Discount Factor 10%

PV of A PV of B

1 50000 40000 0.9091 45455 363642 60000 60000 0.8264 49584 495843 70000 80000 0.7513 52591 601044 80000 90000 0.6830 54640 61470Present value of cash inflows

202,270 207,522

Less cost of investment

120,000 130,000

Net Present Value

82,270 77,522

Calculate the discounted payback period for project A. Initial Investment 120,000

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Year Project A (£)1 500002 600003 700004 80000

Solution

End of year Project A Discount Factor 10%

PV of A

1 50000 0.9091 454552 60000 0.8264 495843 70000 0.7513 525914 80000 0.6830 54640Present value of cash inflows

202,270

Discounted payback of initial investmentInitial investment 120,000Less year 1,2 95,039Total 24,961

The discounted payback period is between years 2 and 3.

24,961So, discounted payback = 2 years + ----------- = 2.47 years. 52,591

Exercise

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A company is wondering whether to spend £18,000 on an item of equipment, in order to obtain cash flows as follows:

Year £1 6,0002 8,0003 5,0004 1,000

The company requires a return of 10% per annum.

Required

Use the NPV method to assess whether the project is viable.

Exercise

A company would like to invest in a project with an initial investment of 2,000,000 USD. The cost of capital is 10% and the expected cash flows are as follows:

Year 1 : 500,000 USDYear 2 : 1,000,000 USDYear 3 : 2,500,000 USD

Please calculate the NPV?

Solution

Cash flows Discount factor of 10% Present value500,000 0.9091 454,5501,000,000 0.8264 826,4002,500,000 0.7513 1,878,250

3,159,200

The discount factor calculation are as follows:

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The project should be accepted.

Exercise

Please calculate the IRR for a project with initial investment 4,000,000 USD. The required return is 12% and the expected cash flows are as follows:

Year 1: 1,000,000 USDYear 2: 2,000,000 USDYear 3: 2,500,000 USD

Please use Texas instrument calculator BAII Plus

Solution

The first step is to clear the memory by pressing 2ND --------CLR WORK

The second step is to input your cash flows:

CF0 = 4,000,000 Enter

CF1 = 1,000,000 Enter

CF2 = 2,000,000 Enter

CF3 = 2,500,000 Enter IRR CPT

B) A REVIEW OF THE PROPOSED PROJECT

In order to verify if the proposed project will be viable and successful in the long run, we will implement a range of investment appraisal techniques, and a breakeven calculation. They will be the following:

1) The Accounting Rate of Return (ARR)2) The Net Present Value (N.P.V), and the Internal Rate of Return (IRR)3) The profitability Index4) The breakeven calculation

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With the above mentioned methods, we can ensure that the project selected by the organization yield maximum returns with a minimum level of risk. Before we start our analysis, we must calculate the profits, the cashflows, the depreciation, and the initial investment.

Year Sales Variable cost 55% 0f sales

Fixed cost-rising 5% per year

Profit £

1 600,000 330,000 200,000 70,0002 600,000 330,000 210,000 60,0003 800,000 440,000 220,500 139,5004 1,000,000 550,000 231,525 218,4755 1,200,000 660,000 243,102 296,8986 1,500,000 825,000 255,258 419,742

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Depreciation workings £ Fixed assets cost 800,000 Less: Residual Value of fixed assets 200,000 ----------- Total Depreciation 600,000

Annual Depreciation--------------------------- = 100,000 per year 6 Years

The initial investment £Capital Expenditure 800,000Working Capital 75,000Initial Investment 875,000

Cashflows

Year Profits Depreciation Cashflows1 70,000 100,000 170,0002 60,000 100,000 160,0003 139,500 100,000 239,5004 218,475 100,000 318,4745 296,898 100,000 396,8986 419,742 100,000 519,742Total 1,204,615 600,000 1,804,615

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1) ACCOUNTING RATE OF RETURN

Year Project £1 70,0002 60,0003 139,5004 218,4755 296,8986 419,742Total 1,204,615Average Net Profit 1,204,615 ----------------------- = ----------------- = 200769 ( over 6 years) 6 Average profit 200769Average accounting rate of return = ---------------------------- = ---------- Average Book Value 575000

Average accounting rate of return = 35%

2) NET PRESENT VALUE AND INTERNAL RATE OF RETURNYear Cash Flow Discounted @

14%Discounted @ 20%

£ Factor £ Factor £1 170,000 0.877 149090 0.833 1416102 160,000 0.769 123040 0.694 1110403 239,500 0.675 161,663 0.578 1386714 318,475 0.592 188,537 0.482 1535055 396,898 0.519 204,005 0.401 1595536 519,742 0.455 237,002 0.334 174114Total 1,804,615 1063337 878493Residual Value 200,000 0.455 91000 0.334 66800Working Capital 75,000 0.455 34125 0.334 25050Cash Inflows 2,079,615 PV

INFL-0WS

1188737 PV INFLOWS

970618

Less: initial investment

(875,000) 875,000 875,000

Total 1,204,615 NPV 313,737 95,618

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Range of rates 14%--------------6%------------------20%

Range of NPV 313,737-----------218,119-----------95,618

Taking the lower rate as a base ( and using its NPV),313,737----------- X 6% = 8.63%218,119

SO IRR is 14% + 8.63 % = 22.63%

3) DISCOUNTED PAYBACK PERIOD

Year Cash Flow Discounted @ 14% £ Factor £

1 170,000 0.877 1490902 160,000 0.769 1230403 239,500 0.675 161,6634 318,475 0.592 188,5375 396,898 0.519 204,0056 519,742 0.455 237,002Total 1,804,615 1063337Residual Value 200,000 0.455 91000Working Capital 75,000 0.455 34125Cash Inflows 2,079,615 PV

INFL-0WS

1188737

Discounted payback of initial investmentInitial investment 875,000Less year 1,2,3,4,5 826,335Total 48,665

The discounted payback period is between years 5 and 6.

48,665So, discounted payback = 5 years + ----------- = 5.21 years. 237,002

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4) PROFITABILITY INDEX

P.V inflows 1,188,737Profitability Index = ------------------- = -------------- = 1.36 times P.V outflows 875,000

5) BREAKEVEN CALCULATION

Fixed Cost Breakeven = ----------------------------- Contribution Margin Contribution Margin = 100% - 55% = 45%

200,000 Breakeven = ------------- = 444444.4 0.45

COMMENTS OF THE PROPOSED PROJECT

According to the results obtained from the above methods, the proposed project is viable. In more details, the IRR is over the weighted average cost, which is a positive sign. In addition, the NPV is positive, and the profitability index is higher than 1, which mean that the project can generate enough revenues to cover the initial investment.

The accounting rate of return, which shows the profitability of the business, is high enough to create a reasonable profit for the investors and shareholder’s.

However, there are problems that can affect the long-term success of the project and reduce the shareholder’s wealth. Specifically, the long-term discounted payback period is a negative sign, as it means that the project can cover the initial investment after the fifth year. So if managers accept it, they must ensure a very good strategic planning in both financial and operational terms. Otherwise, they have to face a business, operational, and financial risks. This is obvious, as the business will operate in a highly competitive environment.

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RECOMMENDATIONS FOR THE PROPOSED PROJECT AND THE EXISTING BUSINESS

It is a matter of choice of the management whether they can accept the responsibility for such long term investment. In order to succeed they need a good strategic plan and fundamental changes in management style, as I mention below. Otherwise, they have to depend on the revenues of the existing business in order to sustain the proposed project. This is negative, as it can weaken the power of the existing business significantly.

The existing company should change the culture, in order to maximize more revenue. In more details, managers must implement a quality culture, which consider staff and customers as the most valuable assets and resources. The existence of quality culture is essential factor to motivate and improve the performance of the staff to achieve quality of output.

From the operational point of view, shareholders must change the policy of recruitment. Staff and managers must be skilled and qualified with the appropriate knowledge in order to be recruited. Only with this way, they can succeed to increase profits in the long term.

Training and Education must be provided in a consistent way in order to ensure a common language of production throughout the business. The training must also focus on helping managers to identify improvements available in their areas of responsibility.

Company A must change his leadership behaviour by empowering and delegating authority to the managers of each operations. He must be prepared to share some of their powers and responsibilities. This also involves seeking and listening carefully to the views of employees and acting upon their suggestions. Employees must be encouraged to manage and improve their performance within their sphere of responsibility. For example, prices from suppliers can be negotiated from managers of each outlet.

Decentralization of decision-making will be a positive step for both the managers of each outlet. Managers will not have to waste their time by travelling from one unit to the other. In contrast, he can focus to more important aspect of the operations such as: strategic planning, operating risks, and new advancements of the technology.

On the other hand, managers of each outlet will feel more involved and motivated within their work. Participation in decision-making will reinforce them to be more creative and innovative.

Company B must focus not only by reviewing the internal operations but also the external environment and the role of the competition. His strategic plans for the new project must be based on a five years profit & loss account, balance sheet, and cashflows.

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Company B is responsible for the administrative aspect of the business, must avoid any business risk for the new project by using information technology, and the computerized Yield Management systems. In more details, he can verify the marketing opportunities offered by the internet. By using the travelweb, he can find new markets which are rapidly increasing. Only, with this way, he can increase revenues, and gain more profits in the future.

There is not a good flow of information in the existing businesses. Each manager at each outlet is told verbally and informally of their results. Therefore, the style of management becomes more reactive than pro-active. This is negative, as in the future a lot of mistakes and variances will occur.

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Risk and return

Risk is defined in Webster’s Dictionary as “a hazard, a peril, exposure to loss or injury”. On the other hand, according to Charles, (1998), risk is defined, as the chance that the actual return on an investment will be different from the expected return. Thus, risk refers to the chance that some unfavourable event will occur. A situation of risk is said to exist if an individual is willing to base his actions on probability distributions. When considering any security, the investor is always concerned with the return expected on the investment and the risk of the investment, that is, how likely it is that the return expected will be achieved.

In the case of an investor, he/she is taking a risk in the hope of making an appreciable return. The risk of an asset can be analysed in two ways. Firstly, on a stand-alone basis, where the security is considered in isolation, and secondly, on a portfolio basis, where the security is held as one of a number of assets in a portfolio.

On the other hand, the investors before making any investment must take into consideration that different types of securities will have different kinds of risks. The several sources of risk can be classified as: interest rate risk, market risk, inflation risk, business risk, exchange rate risk, financial risk, country risk, and liquidity risk. For example, UK government securities do not suffer the risk of default but are vulnerable to changes in interest rates.

No investment will be made unless the expected rate of return is high enough to compensate the investor for taking extra risks. In general, it is believed that the higher the perceived risk associated with an investment opportunity, the higher should be its expected return to persuade an investor to accept the investment opportunity. Thus, investment risk is related to the probability of earning a return, which is less than the expected return. The greater the probability of low or negative returns, the riskier the investment. In the following part of this chapter the return on a security will be displayed and the methods of measuring risk that are commonly used will be analysed.

The total return of an investment during a time period is calculated from the following equation:

where: r is the return on a financial asset at the end of period 1. P1 is the price of a financial asset at the end of period 1. P0 is the price of a financial asset at the beginning of the period. D1 is the dividend received on the asset at the end of period 1.

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Risk and return exercise

Observations ProbabilityReturn onStock A

Return onStock B

1 50% 13% 19%

2 25% 5% 8%

3 25% 2% 4%

Calculate the following based on the above table:

Expected return on stock A and stock B

Variance and standard deviation of stock’s A and stock’s B

Solution

The expected return on stock A = probability 1 * return 1 + probability 2 * return 2 + probability 3 * return 3

The expected return on stock A = 0.0825 or 8.25%

The same principle applies for the expected return on stock B = probability 1 * return 1 + probability 2 * return 2 + probability 3 * return 3

The expected return on stock B = 0.125 or 12.5%

Observations Probability Return onStock A

Return onStock B

Probability * return A

Probability * return B

1 50% 13% 19% 0.065 0.0952 25% 5% 8% 0.0125 0.023 25% 2% 4% 0.005 0.01

Total 0.0825 0.125Expected

return8.25% 12.5%

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The variance and standard deviation formulas of stock’s A and B are as follows:

The sample variance

Based on the above table we have the following formula:

0.50*(0.13-0.0825)2 + 0.25*(0.05- 0.0825)2 + 0.25*(0.02 – 0.0825)2

The standard deviation is the square root of the result of the variance.

or 4.9%

Based on the above table we have the following formula:

0.50*(0.19-0.125)2 + 0.25*(0.08- 0.125)2 + 0.25*(0.04 – 0.125)2

The standard deviation is the square root of the result of the variance.

or 6.65%

Stock B offers a higher expected return than Stock A. Stock B is riskier since its variance and standard deviation are greater than Stock A. Most investors choose to hold securities as part of a diversified portfolio.

Two-asset portfolio expected return

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ERp = wA* E(RA) + (1 – wA) E(RB)

The expected return on stock A = 8.25%

The expected return on stock B = 12.5%

wA = 0.50

(1 – wA) = 1 – 0.50 = 0.5

ERp = 0.5* 0.0825 + 0.5*0.125 = 0.04125 + 0.0625 = 0.10375 or 10.375%

MEASURES OF PORTFOLIO RISK

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COVARIANCE

CORRELATION COEFFICIENT

VARIANCE

STANDARD DEVIATION

The covariance and the correlation coefficient are two key concepts in a portfolio analysis. Given the significant amount of correlation among security returns, we must

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measure the amount of comovement and incorporate it into any measure of portfolio risk because such co movements affect the portfolio’s variance or standard deviation. Covariance is a measure which combines the variance of a stock’s returns with the tendency of those returns to move up or down at the same time as other stocks move up or down. The following formula gives the covariance (Cov) between stocks A and B:

Covariance = Cov (AB) or AB =

where: AB = the covariance between securities A and B. n is the number of outcomes. Pi is the probability associated at time i. RAi is the rate of return on security A at time i. RBi is the rate of return on security B at time i. E(RA) and E(RB) is the expected rate of return on security A and B.

In the case that the covariance between two stocks is negative then this indicates that the rates of return tend to move in opposite direction. In the case that the covariance between two stocks is positive, it means that these assets tend to move together. In the case that the covariance between two stocks is zero, then there is no relationship between the variables. Thus the variables are independent.

However, because the covariance term is difficult to be interpreted, the correlation coefficient is often used to measure the degree of movement between the two variables. It is a statistical measure of the relative comovements between security returns. However, it denotes only association, not causation. It is a relative measure of association that is bounded by +1.0 and – 1.0, with

I,j = + 1.0 = perfect positive correlation

I,j = -1.0 = perfect negative correlation

I,j = 0.0 = zero correlation

The correlation coefficient standardises the covariance by dividing it by the product of the two standard deviations of returns. The correlation coefficient can be related to the covariance in the following manner:

AB

Correlation coefficient (AB) = AB = ----------- A B

The closer is the value to +1, then the stronger the positive relationship between two securities. The closer the value is to -1, then the stronger the negative relationship.

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The correlation coefficient shows only the extent to which the relationship is positive or negative.

Given the above definition of the correlation coefficient, the covariance can be written as follows:

AB = AB A B

As we will see in the next chapter the covariance and correlation terms play a crucial role in modern portfolio theory.

Example of how to calculate the covariance and the correlation coefficient of a portfolio of two stocks A and B

Please consider the following table:


Return onStock B

1 50% 13% 19%2 25% 5% 8%3 25% 2% 4%

The expected return on stock A = 0.0825

The expected return on stock B = 0.125

or 4.9%

or 6.65%

The covariance is calculated as follows:

The correlation coefficient is as follows:

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The returns are said to be perfectly positively correlated as it is close to +1. The risk of the individual stocks can be eliminated through diversification. The correlation coefficient between most stocks ranges between 0.4 to 0.85

The variance and the standard deviation of a two asset portfolio are calculated as follows:

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The variance of a portfolio of two assets is given by the following formula:

where: is the variance of return on a portfolio consisting of two assets. wA is the value weighted proportion of a portfolio invested in asset A. is the variance of the rate of return on Asset A. wB is the value weighted proportion of a portfolio invested in asset B. is the variance of the rate of return on asset B.

is the standard deviation of return on asset B. is the standard deviation of return on asset A. is the correlation coefficient of returns between asset A and asset B.

Please consider the following table:


Return onStock B

1 50% 13% 19%2 25% 5% 8%3 25% 2% 4%

The expected return on stock A = 0.0825

The expected return on stock B = 0.125

or 4.9%

or 6.65%

The weights of the portfolio are 50 % of stock A and 50% of stock B.

The variance is as follows:

0.5*0.5*0.99*0.049*0.0665

The standard deviation is as follows:

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Exercise

Considering that you are going to have a portfolio with 60% of your money invested on stock A and 40% on stock B calculate the following:

Portfolio expected return ER

Covariance σαβ

Correlation coefficient ραβ

Variance and standard deviation of the two-asset portfolio σρ

Modern portfolio theory

In economics in general, and investment analysis in particular, the standard assumption is that investors are rational. Rational investors prefer certainty to uncertainty. It is easy to say that investors dislike risk, but more precisely, we should say that investors are risk averse, namely that they want to reduce their risk through a diversified balanced portfolio. This leads us to modern portfolio theory, which was developed by Markowitz (1959). According to Markowitz, a good portfolio is more than a long list of good stocks and bonds. It is a way to provide the investor with

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protection and opportunities with respect to a wide range of contingencies. He argued that for any given level of risk, the rational investor would select the maximum expected return, and for any given level of expected return, the rational investor would select the minimum risk. By measuring risk, Markowitz laid down the cornerstones of modern portfolio theory.

Furthermore, according to modern portfolio theory, an investor faces two types of risk, market risk and firm-specific risk. Market risk cannot be eliminated by diversification because it is associated with economic or market factors that systematically affect all or most firms (Weston, Besley and Brigham 1996). These factors can be inflation, recession, high interest rates, etc. and are non-diversifiable.

On the other hand, firm-specific risk is the part of a security’s risk associated with random outcomes generated by events or behaviours specific to the firm, Cuthbertson, (1996). These risks can be caused by factors such as strikes, successful and unsuccessful management, and failure to advertise the product properly. This type of risk, however, can be eliminated through diversification. Thus, an investor cannot avoid market risk because it derives from the uncertainties of the whole economy. In contrast, firm-specific risk, which is related to a particular company or project, can be avoided by investing in several different kinds of shares (Franks and Broyles, 1979, Pilbeam, 1998, Rutterford, 1993)

In addition, an investor can diversify more than half of the total risks that he/she would bear by investing in different shares. Thus, a portfolio of shares can “average out” the firm-specific risks of the different shares. The above is illustrated in figure 1.

Figure 1: Market and firm-specific risk

RiskAs % Unsystematic 40 _ risk or firm- specific risk

35 _

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30 _

20 _ Systematic risk or market risk

10 _

0 / / / / 10 20 30 40 Number of shares

Source : Solnik (1974), pp 48-54

According to Figure 1, Solnik (1974) finds that risk can only be eliminated in a reasonably well diversified portfolio, which is one containing up to 20 stocks. As the number of shares becomes very large the investor cannot diversify anymore the risk and he/she faces the market risk.

Finally, Markowitz (1952) demonstrated that the covariance between securities in a portfolio is the most important element in determining the overall risk of the portfolio. Ceteris paribus, the lower the covariance between the securities in the portfolio, the lower the standard deviation of the portfolio. It is thus important in selecting an asset for diversification purposes to establish the covariance of the asset with all other assets in the portfolio.

Portfolio Theory is concerned with the allocation of an individual’s wealth among the various available assets. Therefore, the selection of a portfolio among those represented by the efficient frontier will depend upon the individual’s utility function. Knowledge of the preference of the investor is normally required before we can choose between portfolios. Portfolio theory, therefore, makes several reasonable assumptions about preferences between risk and return.

If two portfolios have the same standard deviation and different expected returns, the one with the larger expected return is preferred.

If two portfolios have the same expected return and different standard deviations of return, the one with the smaller standard deviation is preferred.

If one portfolio has a smaller standard deviation and a larger expected return than another, it is preferred.

In more detail, the efficient set is represented by the upper left-hand boundary of the points a and c as shown in figure 2.

Figure 2 Markowitz efficient frontier

U3 U2 U1 Utility curvesPortfolio expectedReturn E(rp)

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Efficient Frontier

c

Attainable frontier

E(R1 ) b d

a

s(R1) s(R2) Portfolio standard deviation p

Source: Dobbins & Witt, 1983, p.31

According to Figure 2, the dashed rectangle area represents all attainable portfolios that are all the combinations of risk and expected return which may be achieved with the available securities and different levels of correlation coefficients. For example, consider the portfolios represented by points b and d. Portfolios b and d promise the same expected return E(R1) but the risk associated with b is s(R1), whereas that associated with d is s(R2). Investors therefore prefer portfolios on the efficient frontier rather than interior portfolios given the assumption of risk aversion. Obviously, point a on the frontier represents the portfolio with the least possible risk, while c represents the portfolio with the highest possible rate of return (Dobbins and Witt, 1983, p.31). In other words, the portfolio efficiency frontier consists of those portfolios with the maximum rate of return for a given level of risk, or equivalently those portfolios with the minimum level of risk for a given rate of return (Pilbeam,1998, p.136).

In addition, the investor has to select a portfolio among all those represented by the efficient frontier according to his risk-return preference. According to Figure 2, this is shown by the utility curve. The investor therefore wishes to be on the highest possible indifference curve in order to obtain the maximum possible level of utility and this is given by the point of tangency between an indifference curve and the efficient frontier, that is point b. This point therefore represents the optimal portfolio (Dobbins and Witt, 1983, p.32).

Capital Asset Pricing Model (CAPM)

Shortly after Treynor (1961) began his work on asset pricing, Sharpe set out to determine the relationship between the prices of assets and their risk attributes. Sharpe, Lintner and Mossin (1964) aims to use the theory of portfolio selection to construct a market equilibrium theory of asset prices under conditions of risk.

The CAPM divides equity risk into two components:

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Specific Risk Systematic risk

Investors cannot diversify away about one-third of the total risk of a single security, no matter how many shares he/she holds. This represents the market risk to which all shares are subject. This leads us to the Capital Asset Pricing Model (CAPM), which is basically derived from modern portfolio theory. Its foundation is based upon the fact that the portfolio is diversified, and the only variable that we have to calculate is market volatility. This model is based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return (e.g. the yield on treasury bills) plus a risk premium where risk reflects diversification. The equilibrium relationship between expected return and risk for individual securities is known as the Security Market Line, and can be expressed accordingly:

where is the excess security return defined as , that is excess security

return less one-month risk-free rate return, is the excess market return and is the beta coefficient which measures a stock’s sensitivity to market fluctuations and is given by the following formula:

The CoVari,m is the covariance of returns on security i with those of the market portfolio m. The beta measures the responsiveness of a security’s return to changes in the market. For example, it measures the degree to which a security’s return rises or falls as the market rises or falls. In more detail, a beta of 1 means that the share is as risky as the market portfolio, whereas a beta of 0.5 implies that the share is half as risky as the market. The above security market line equation is illustrated in Figure 3.

Figure 3: Security market line

Expected Overvalued stock Return % A Security market Ra line Rm

Rf = risk free

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Undervalued stock Rb B

Ba 1 Bb Beta

By referring to Figure 3, we can see why the CAPM is often called the equilibrium model of capital markets. If at any given time, there is a financial asset A with the combination of Return Ra and beta Ba, as shown in Figure 3, then this would immediately be recognised as overvalued. There would in theory be an excess demand for asset A and the price of A would increase until the expected return falls back to the capital market line, thus in ‘equilibrium’. The process would work in exactly the opposite direction in the case of an undervalued asset such as B. In this sense, the security market line may be interpreted as an ‘equilibrium concept’, enabling statements to be made as to whether a financial asset is over or under-valued at any given time and how prices should react to eliminate such anomalies.

4 .3.1 Assumptions of the CAPM

All investors are risk averse and aim to maximize their expected utility of wealth and therefore are interested in two features of a security, its expected return and its standard deviation.

All investors have similar assessments of the probability distributions of returns expected from traded securities.

There are no transaction costs entailed in trading securities. All securities are marketable

With regard to investment trusts, it can be said that the first assumption seems reasonably based on the utility function and efficient frontier that we discussed above. Clearly, the next three assumptions are invalid. As we will see in chapter 5 there is a moderate dispersion between the mean and standard deviation by various categories of trusts. In addition, transaction costs are always incurred in trading securities and some categories of investment trusts hold securities that are illiquid. For example, venture and development investment trusts, private equity trusts, emerging market funds, hedge funds, and split capital trusts all hold securities that are illiquid.

CAPM exercises

1. Find the expected return on a stock given that the risk-free rate is 5%, the expected return on the market portfolio is 10%, and the beta of the stock is 1.5.

Solution

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Expected return =

Expected return = 5% + (10% - 5%)* 1.5 = 12.5%

2. Find the beta on a stock given that its expected return is 14%, the risk-free rate is 3%, and the expected return on the market portfolio is 11%.

Solution

Expected return =

Arbitrage Pricing Theory Model (APT)

An alternative model that could potentially overcome the CAPM problems while still retaining the underlying concept was the arbitrage pricing theory (APT) developed by Ross (1976). In more detail, CAPM's basis in mean variance analysis determines that it is optimal for the investor to choose investments on the basis of expected returns, standard deviations or mean-variance analysis. Furthermore CAPM considers a single factor, the market portfolio, to explain security returns, relating them to the security's beta coefficient. CAPM’s failure to explain adequately differences in returns of the

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various assets using the beta terminology led to the development of other asset pricing models.

On the other hand, APT is a more general approach to asset pricing because it allows for the possibility that many factors can be used to explain security returns. The APT can include any number of risk factors that could determine the required return.

The logical development of APT is similar to that of CAPM: that is, that investors should get rewarded for accepting a non-diversifiable risk. Unlike CAPM, APT assumes that returns are generated by a factor model. Furthermore, although CAPM is based on strong assumptions about investors’ preferences, APT makes no such assumptions. APT does not accept the idea that investors look at portfolios in terms of expected returns and standard deviations.

It is based on the law of one price: two identical items cannot sell at different prices in a perfect market. The description of equilibrium is more general than CAPM, implying that pricing can be affected by influences beyond means and variances. The assumption of investors utilizing a mean variance framework is replaced by an assumption of the process generating security returns. APT starts by stating that the returns on any stock are linearly related to a set of k systematic factors without specifying exactly what these are:

where: is excess security return defined as , that is the return on security i less the return of 1 month risk-free rate. are the betas with respect to factors 1,2,…,n are the factors 1,2,….,n

is a random error term or disturbance termThe above equation says that the return on a security is affected separately by all the F factors that systematically affect the return on a security. These factors might include firm specific characteristics such as size, and book-to-market effect. Equation 3 contrasts with equation 1 of the CAPM in that it has several beta coefficients rather than just one. In addition, the CAPM deals with market risk while the arbitrage pricing theory does not have market risk coefficients, the whole point of the model being that market risk is unidentifiable. The proponents of the APT argue that it has several advantages over the CAPM model:

The CAPM requires that the investors’ utility function is based upon expected returns and the standard deviation of systematic risk. The APT does not require standard deviations to be used as a measure of risk.

APT does not require an observed market index .

It does not make assumptions about the empirical distribution of asset returns

It does not make assumptions about individuals' utility functions

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APT can easily be extended to a multi-period framework according to Ross (1976) work

Weighted average cost of capital, WACC and marginal cost of capital, MCC

The assets of a company are financed by either debt or equity. After calculating the cost of capital for equity and debt, then, we combine them in a form of weighted average to calculate the final weighted average cost of capital. The reason of measuring the weighted average cost of capital is to find how much interest the company or the government has to pay for every Euro it borrows. The long-term interest should be compared with the expected return that the government is getting from the European markets. For example, issuing a long-term debt though a government bond should be adjusted regularly and compared with the different types of interest rates and returns available in the market. The marginal cost of capital,

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MCC, is the cost of the last Euro of capital raised. The marginal cost of capital increases as more capital is used.

Factors that affect the cost of capital are the capital structure of the company, the dividend policy, the investment policy, the level of interest rates and the tax rates. It is very important the shareholder’s negotiate the level of interest rate of their debt and the financial risk involved. When the interest rates increase, then, the cost of debt increases and therefore the cost of capital. Shareholder’s should control the level of debt in the balance sheet and replace it with capital. Finally, dividend policy will affect the breakpoint of the debt or equity marginal cost of capital.

Investment projects should only be considered if the expected return is greater than the calculated WACC that will be used by the company or the government to adjust expenses with revenues. In contrast, if the expected return is less than the WACC, then the project should be rejected. Managers of the company to keep a successful corporate strategy should check regularly the interest rates, the liquidity, the foreign exchange and the credit margin. They should diversify their debt assets among different maturities of short, medium and long – term interest rates. High risks are associated with high returns and low risks with low returns.

The formula for WACC is as follows:

Where:

wd : the weight of the debt. rd : cost of debt. rd (1-t): after tax cost of debt. t: tax rate. wp: is the weight of preferred stock. rp : the cost of preferred stock. wce: the weight of equity. rce: cost of equity.

The WACC formula is changed when the weights are not known and instead you are given the market value. The mathematical formula is as follows:

Where:rce: cost of equity.rd : cost of debt.

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rP: cost of preferred stock.E: the market value of the firm’s equity.P: the market value of the firm’s preferred stock.D: the market value of the firm’s debt.V: the total market value of the company.t : Corporate tax rate

Cost of capital is the opportunity cost of capital invested in an enterprise. The capital is divided into debt and equity. The cost of capital is divided into the cost of debt and the cost of equity.

Example of cost of debt

The government has notes payable amounted 8,234,000 Euros with a fixed interest of 4%. The total debt in percentage is around 88% of total debt.

In addition, the capital leases on infrastructure and equipment are estimated of 200,000 Euros at a fixed rate of 5.5%. It is accounted of 12% of total debt.

The corporate tax of rate is 0.35 or 35% .

The total debt is 8,234,000 + 200,000 = 8,434,000 Euros. This is 100% of the debt and it is divided as shown in the above figures.

The pre-tax cost of debt = (0.04 * 0.88) + (0.055 * 0.12) = 0.0352 + 0.0066 = 0.0418

The pre – tax cost of debt = 4.18%

After-tax cost of debt= pre-tax cost of debt *(1- corporate tax rate)

After-tax cost of debt= 0.0418 * (1 - 0.35) = 0.0418* 0.65= 0.02717

Ater-tax cost of debt= 0.02717 or 2.72%

Example of cost of equity

The cost of equity is based on the capital asset pricing model. It is based on the expected return that the shareholders are expecting or the opportunity cost from investing in a company in relation to other stakes in another company. The greater the risk, the greater the expected return. The risk is measured by the beta, which is a measure of market risk.

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The cost of equity is based on the CAPM formula and it is calculated as follows:

If the risk – free rate is 4.3%, the beta is 1.5 and expected market return is 8.23%, then, the expected return of the company is as follows:

Once we have calculated the cost of debt and the cost of equity, then, we can calculate the weighted average cost of capital, WACC.

For example, you have the following information.

Cost of equity = 10.2%

Cost of debt = 2.72%

Total debt = 10 % of total capital

Total equity = 90% of total capital

WACC = (cost of debt x total debt) + ( cost of equity x total equity)

WACC = (0.0272 * 0.10) + ( 0.102* 0.90) = 0.00272 + 0.0918 = 0.09452

WACC = 0.09452 * 100 = 9.452%

Ex ample of WACC calculation

The government is trying to find the optimum WACC that is composed from debt and equity in order to compare it with the expected return that he will get from the European market.

The information is as follows for the expected return.

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Expected return on the European stock market is 12%Risk – free rate of return is 2%Beta 1.4

The information is as follows for the WACC.

rce: cost of equity 13%rd : cost of debt 8%E/V : percentage of financing that is equity 80% D/V : percentage of financing that is debt 20%t : Corporate tax rate 40%

The WACC formula is as follows:

The project is positive and it will create value for the political party as the expected return from the European capital markets, , is greater than the WACC, which is 11.36%.

The company or the political party should also consider their investment based on the country equity premium. The mathematical formula is as follows:

For example, the yield on the 5 year US government bond nominated in Euro is 10% and the 5 year US Treasury bond yield is 7%.

Then, the sovereign yield spread = 0.10 – 0.07 = 0.03.

The

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Exercise

Please consider the capital structure of the following company:

Equity 80,000,000 Euros

Debt 2,000,000 Euros

Preferred stock 500,000 Euros

Total V= 82,500,000 Euros

Other relevant information

The pre-tax cost of debt is 2%

The cost of equity is 5%

The market price of preferred stock is 20 Euro.

Dividend of preferred stock is 1.23

The corporate tax rate is 40%.

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Solution

The mathematical formula for calculating the WACC is as follows:

Where:rce: cost of equity.rd : cost of debt.rP: cost of preferred stock.E: the market value of the firm’s equity.P: the market value of the firm’s preferred stock.D: the market value of the firm’s debt.V: the total market value of the company. V = E + P + D.t : Corporate tax rate

First of all, we calculate the cost of preferred stock.

We substitute the data in the above equation.

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Exercise

Please consider the capital structure of the following company:

Equity 40,000,000 Euros

Debt 3,000,000 Euros

Preferred stock 200,000 Euros

Total V= 43,200,000 Euros

Other relevant information

The pre-tax cost of debt is 3%

The cost of preferred stock is 2%

The corporate tax rate is 40%.

The beta is 0.80

Expected return on the market is 8.2%

The risk – free rate is 1.55%

Solution

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First of all, we calculate the cost of equity.


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Exercise

An operation has divided its capital into debt and equity. The capital structure of the business is as follows:

D0 = Dividend per share 3.00 PoundsMarket price 20.00 PoundsExpected dividend growth rate 2%Beta 0.5Expected return on the share 8% Risk –free rate 1.5%Tax rate 35%

Please calculate the cost of equity using the dividend discount model, DDM.

Solution

The mathematical formula of the dividend discount model is as follows:

Dividend1 = Dividend0 x (1+g) = 3.00 x ( 1+ 0.02) = 4.02

Exercise

An operation has divided its capital into 20% debt and 80% equity. The capital structure of the business is as follows:

Dividend yield 2.30%

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Expected market return 8.00%Risk – free rate 2%Beta 0.7 Tax rate 35% Bond yield to maturity 5%

Please calculate the weighted average cost of capital?

Solution


WACC = wd rd (1-t) + wce rce

Where: wd : the weight of the debt. rd : cost of debt. rd (1-t): after tax cost of debt. t: tax rate. wce: the weight of equity. rce: cost of equity.

WACC = 0.20*0.05*(1-0.35) + 0.80 rCE (1)

We calculate the rce from the asset pricing model.

rce = risk- free rate + (expected market return – risk free rate)* Beta (2)

rce = 0.02 + (0.08 – 0.02) * 0.7 = 0.062 or 6.2%

We substitute the result from equation (2) into (1)

WACC = 0.20*0.05*(1-0.35) + 0.80 * 0.062

WACC = 0.0065 + 0.0496 = 0.0561 or 5.61%

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Exercise

The capital structure of the business is as follows:

Cost of debt before tax 10%Debt weight percentage of capital 20%Cost of preferred stock 15%Preferred stock weight of capital 30%Cost of equity 20% Cost of equity weight of capital 50%

The tax rate is 40%. Please calculate the weighted average cost of capital?

In this case we have preferred stock, thus, the WACC equation will incorporate the preferred stock.

Where:

wd : the weight of the debt. rd : cost of debt. rd (1-t): after tax cost of debt. t: corporate tax rate. wp: is the weight of preferred stock. rp : the cost of preferred stock. wce: the weight of equity. rce: cost of equity.

Solution

WACC= 0.20*0.10*(1-0.40) + (0.30 * 0.15) + (0.20 * 0.50)

WACC = 0.012 + 0.045 + 0.1 = 0.157 or 15.7%

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Exercise

In this exercise, I will show how to calculate weights based on absolute Euro amounts.

For example, if the debt is 10,000 Euro, the preferred stock is 500 Euro and the equity is 20,000 Euro. The total capital structure is 30,500 Euro.

SolutionThe weight of debt is (10,000 / 30,500)*100 = 32.79%

The weight of preferred stock is (500 / 30,500)*100 = 1.64%

The weight of equity is (20,000 / 30,500)*100 = 65.57%

Exercise

Calculate the company new debt break point and its marginal cost of capital, (MCC). The company would like to increase its capital by an amount of 80,000,000 Euro.

The capital structure of the company is as follows:

Amount of new debt: 10,000,000 EurosDebt percentage : 50%Equity percentage: 50%After – tax cost of debt: 2%Cost of equity: 7%

Solution

The new debt breakpoint is as follows:

10,000,000 / 0.50 = 20 million Euros.

The marginal cost of capital by including the new capital that is issued is as follows:

80,000,000 * 0.50 = 40 million Euros. New debt80,000,000 * 0.50 = 40 million Euros. New equity

MCC = (0.50 * 0.02) + (0.50 * 0.07) = 0.01 + 0.035 = 0.045 or 4.5%

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Exercise that includes in the WACC calculation a flotation cost


Debt weight is 30%Equity weight is 70%The cost of debt is 7%The market price of the share is 15 EuroExpected dividend is 3 EuroDividend growth rate is 4%Flotation cost is 3%Corporate tax is 40%

Calculate the cost of equity and the WACC.

Solution

rce =

Where: rce is the cost of equity. Div1 is the next year expected dividend. P is the market price of the share. f is the flotation cost per share. g div is the annual growth rate of the dividend.


Where:

wd : the weight of the debt.

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rd : cost of debt. rd (1-t): after tax cost of debt. t: tax rate. wp: is the weight of preferred stock. rp : the cost of preferred stock. wce: the weight of equity. rce: cost of equity.

Exercise


The debt to equity ratio is 1:1.The total amount of equity and debt is 10,000,000 Euros.The corporate tax rate is 40%Beta is 1.20Expected return on the market index 10%Risk – free rate 4%Cost of pre-tax debt 5,5%Expected dividend on the share 1.2%

Calculate the weighted average cost of capital, WACC.

Solution

The total amount of equity and debt is 10,000,000 Euros. This means that 5,000,000 Euros is debt and 5,000,000 Euros is equity.



First of all, we calculate the cost of equity.

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WACC exercise

Company M is a member of the London Stock Exchange with 4,000,000 common shares outstanding. The closing price of M stock yesterday was 3 pounds per share. The company long-term liabilities are as follows:

Long-term loan of 3,500,000 pounds at a fixed rate of 4.2%. 8.3%

Mortgage of 10,000,000 pounds at a floating rate of 3%.

Yield to maturity on 3-year Treasury bonds at 4.2%

Marginal tax rate at 40% Risk of M stock 1.4 The London stock exchanges expected return at 6.1% Re: cost of equity 11% Rd : cost of debt 7% E/V : percentage of financing that is equity 70% D/V : percentage of financing that is debt 30%

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Calculate the cost of capital, WACC, and the expected return for M.

[Hint: There is irrelevant information, please use only the information that you need according to the mathematical formulas.] Thanks for your time and patience.

The management of working capital

Managing the working capital of the business is very important step that will prevent the shareholders from bankruptcy. It is very important to control short and long – term cash in relation to short and long – term liabilities. Strategic objectives are achieved by having enough cash to pay the creditors and the suppliers. Therefore, it is essential to maintain a successful strategy based on the following components:

Working capital and measurement tools Managing debtors Managing creditors Inventory control

Working capital and measurement tools

Working capital is defined as the result of current assets less current liabilities. Surplus occurs when current assets are greater than current liabilities. In contrast, deficit occurs when current liabilities are greater than current assets. It is wise to keep a positive working capital by having enough assets to cover current liabilities. The formula is as follows:

Working capital = current assets – current liabilities

Uncertainty in terms of future sales and bad debts create difficulty in forecasting the working capital in different time periods. Seasonality in sales and low level of profit create different levels of difficulty to maintain a positive working capital and cash flows. Business risk should be monitored in advance before setting up a business. Otherwise, the shareholders will face financial and business risks that they are not able to monitor successfully. In other words, if there is no sufficient cash to cover short- term payments, then, the shareholders will have to liquidate the business and exit from the market. They should balance their decisions with the opportunity cost of lost interest of the initial investment. For example, suppose that we have two persons that they want to increase their capital. They have two choices. The first option is to invest the available cash in short-term deposits and earn an interest of 2%. The other option is to start a business and earn an interest of 1.5% on the profit. They have to balance the financial and business risks before taking a final decision. Other factors that affect the working capital are the size of the company, growth rates, interest rates, the competition, the macroeconomic situation and new technologies.

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In addition, it is very important to understand the cash operating cycle to reconcile the cash received from sales in relation to the cash paid to suppliers.

The cash cycle is as follows:

Days that raw materials kept in stockDays required to produce goodsDays that finished goods kept in stockDays required from debtors to pay for the goods purchased

- Days required to pay suppliers=Ending cash

The successful operation will keep enough stock to cover its clients and to provide the required service. The key idea is to control the time span between getting cash from debtors and paying the suppliers. In addition, the operation should keep low the expenses and make sure that the debtors will pay back the money. In case that the operation has bad debts, it should keep enough reserves to cover short – term liabilities.

Working capital is also calculated through different types of ratios such as the current ratio and the acid test ratio. The current ratio measures the relation between assets and liabilities. A safe benchmark will be to keep a ratio of 2 to 1. The business should keep twice assets in relation to liabilities. The acid test ratio measures the relation between liquid assets and liabilities. Liquid assets are cash received from debtors and current cash. The benchmark will be again to keep a great amount of liquid assets in relation to liabilities.

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Managing debtors

The management of debtors is very important as they form the basis to receive cash and pay back the creditors. The costs that are associated with debtors are various such as administrative costs, opportunity costs of lost interest and increased number of bad debts. To resolve the problem of bad debts a successful credit policy should be adopted. There should be a sales ledger that records the invoices and the length that it takes for the debtors to pay back the company.

Suppose that a company takes 20 days to pay its accounts payable and the following data are available:

Cost of goods sold, (COGS) 8,000 EuroInventory 1,000 EuroAccounts receivable 3,000 EuroCredit sales 10,000 Euro

Managing creditors

It is important to pay on time creditors to keep a healthy and successful relationship. Creditors will offer the product and service on time in a sustainable or discount price level that is negotiated with the management of the company. Checking the monthly outstanding invoices in the accounting department is of paramount importance for prompt payment. Debtors and creditors management is a two – way relationship that should be monitored for the success of the business in relation to cash management.

Number of days of payables =

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For example, a company has 20,000 Euro of accounts payable. The cost of sales is 5,000 Euro. How long it takes to pay the suppliers?

Number of days of payables = = 1460 Euro.

Calculate the cost of trade credit if the discount price that is negotiated with the management of the company is 2% and the number of days beyond the discount period is 20. The mathematical formula is as follows:

*100

Trade credit cost =

This is very important calculation as it shows the number of days beyond the discount period when the company pays its creditors for its purchases and stocks.

Inventory control

Inventory is defined in terms of raw materials, work in progress and finished goods. Lack of inventory management would cause to the business to loose money and bankrupt in some cases. Inventory is associated with various costs such as staffing, insurance costs, storage space and lost opportunity interest in different investment products. Just in time is very important concept to align your stock control with the needs of the clients. Thus, this strategy will reduce delays in services and increase the flexibility to attract more customers.

For example, if the inventory is 4000 Euros and the cost of goods sold, COGS is 70000 Euros. The number of days of inventory is as follows:

Suppose that a company takes 20 days to pay its accounts payable and the following data are available:

Cost of goods sold, (COGS) 8,000 EuroInventory 1,000 EuroAccounts receivable 3,000 Euro

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Another formula to calculate the number of days of inventory is as follows:

Number of days of inventory = net operating cycle + number of days of payables – number of days of receivables.

Please consider the following data:

Number of days of receivables: 30Net operating cycle: 40Number of days of payables: 20

Number of days of inventory = 40 + 20 – 30 = 30 days.

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Leverage effect

The relationship between fixed and variable costs is very important to determine the amount of leverage that the company will use. Leverage is determined by the profit changes due to changes in sales. The proportion of costs in the capital structure of a company determines the level of leverage that the company will use. For example, when sales increase a leveraged company will have a substantial increase in its profit. In contrast, when sales decrease a leveraged company will have a substantial decrease in its profit. Companies with a large amount of fixed assets in relation to the unit of production will experience a higher leverage. The formula for calculating profit is as follows:

Profit = revenues – total costs

The managers and shareholders of each company should monitor the proportion of fixed and variable costs to determine if it is worth to use additional debt to finance the capital of the company. Business risk should be monitored to decrease the volatility of expenses turnover. Operating expenses leverage could affect negatively the cost structure of the company. As operating expenses leverage increase, it results in direct increase of operating risk and liquidation in some cases. For example, if the degree of operating leverage is 2 and the changes in sales are 3%, then, the company will expect and increase of earnings before interest and tax, EBIT of 6%. The mathematical formula is as follows:

Earnings before interest and tax, EBIT = operating leverage * % changes in sales

On the other hand, managers will also consider the financial risk inherent in the capital structure of the firm. Managers are interested in the proportion of debt in relation to capital. The mathematical formula of the financial leverage is as follows:

When shareholders require increased return on equity, it means an increase in financial leverage.

For example, if the changes in net income are 3,000 Euro and the changes in operating income are 7,000 Euro. Then, the financial leverage will be as follows:

The financial leverage is = 3,000 / 7,000 = 0.43 (to 2d.p.).

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Exercise

A company is showing the following financial information for the current year.

Financial leverage 1.23Operating leverage 1.40Net Income 300,000 EuroGrowth in unit sales 10%

Calculate the growth of earnings before interest and tax?

Solution

Total leverage = financial leverage * operating leverageTotal leverage – 1.23 * 1.40 = 1.722

Total leverage = % changes in net income / % changes in sales

1.722 = % changes in net income / 0.10

% changes in net income = 1.722 * 0.10 = 0.1722.

Earnings growth = net income * (1 + % change in net income)

Earnings growth = 300,000 * ( 1 + 0.1722) = 351,660 Euro.

Exercise

A company is showing the following financial information nominated in Euro for two years.

Year 1 Year 2Earnings before interest and tax, EBIT 10,000 20,000Earnings per share, EPS 2.14 3.12

Calculate the financial leverage of the company?

Solution

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Finally, breakeven analysis is used to find the level where units produced equals units sold. The mathematical formula is as follows:

For example, if the fixed costs are 2,000 Euro, the price per unit is 10 Euro and the variable cost is 5 Euro, then, the breakeven point is calculated as follows:

Exercise

A company sells products at a market price of 2.15 Euro per unit. Variable costs are 1.34 Euro and fixed costs are 20,000 Euro. Annual interest expenses are 10,000 Euro. How many products the company should sell to breakeven?

Solution

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Exercise

A company sells products at a market price of 10 Euro per unit. Variable costs are 8 Euro and fixed costs are 10,000 Euro. Annual interest expenses are 5,000 Euro. How many products the company should sell to breakeven?

Solution

Let’s take an example to understand the concept of leverage in numerical terms. A company produces 5,000 luxury items and sell them at a market price of 4,000 Euro. Variable costs are 2,500 Euro and fixed costs are 1,000 Euro. The after-tax cost of debt is 800 Euro. Calculate the leverage?

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Performance measurement

Performance measurement is very important as it helps the shareholders through different ratios to measure the financial position of the company. There are different types of ratios. Liquidity ratios are current and quick asset ratios. Profitability and operating ratios are return on asset, gross profit margin and net profit margin. Gearing ratios are divided into debt to equity ratio and number of times interest earned. There are different shareholder investment ratios such as return on shareholders, earnings per share, price earnings ratio, dividend yield and dividend covers. Under asset utilization ratios, we have the net asset turnover, debtor collection period, stockholding period and creditor payment period.

It is used to measure the effectiveness of use of total assets in relation to the net profit.

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It is used to calculate the gross profit in relation to the sales.

It is used to calculate the net profit in relation to the sales revenue.

Net profit margin =

It is used to measure the effectiveness of the operation in using its assets.

Net asset turnover =

It is used to measure the number of days that the stock is in the warehouse before it is used for selling purposes.

It is used to show the period that trade debtors take to pay back the operation.

It is used to show us the period that the operation takes to pay back the creditors.

It is used to show how effective is the operation using the working capital. It shows the relationship between short-term assets and short-term liabilities.

Liquid assets are cash, accounts receivable and short-term investment or marketable securities. This ratio is used to show the relationship between cash and debtors and short-term liabilities. In other words, it is used to show if the operation has enough short-term assets to cover its short-term liabilities.

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This is a very important ratio as it shows the financing of the operation related to debt. Shareholders should pay particular attention as interest rates are changing constantly. The project should be mostly financed by equity.

This ratio measures the number of times interest is earned to be able to pay any outstanding debt.

It is an important ratio that facilitates the shareholders to assess the performance of the business. If the return on equity is high, then, shareholders will buy more shares to increase the dividend cover through a regular income. In addition, they could achieve capital growth in a bullish market.

This ratio measures the performance of the business by taking into consideration the profit that is generated from the shares in issue. The shareholders are interested in this ratio as it is related to the profit in relation to the market capitalization of the business.

This ratio is also important for the shareholders. It shows how long it will take that the earnings per share will cover the current market price of the share.

This is an important ratio for the investors as it shows the return that he/she get each year from the dividend that she/he received.

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Measuring the value of a business

It is very important that the shareholders measure the value of their business for future investment. Business valuation is an important measure in case that the shareholders seek short-term liquidity to finance their debt. The most common measures that are used are as follows:

Dividend yield. Price earnings ratio. Net asset value.

Dividend yield

Shareholders are interesting in estimating the monetary value of their equity invested in a business in terms of regular dividend that is paid each year.

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For example, if the dividend paid is 2.50 and the current market price is 11.35, then, the dividend yield will be as follows:

Price earnings ratio

If the current market price is 5.23 and the earnings per share are 0.35, then, the price earnings ratio is as follows:

The higher is the figure, the better is for the business. It is affected by the economic and political conditions. The type and size of the industry and the market that it operates affect the price earnings ratio. The profits and the gearing are also important factors.

Net asset value

NAV of a closed-end fund or investment trust, usually expressed on a per share basis, is the value of all its assets, less its liabilities, divided by the number of shares.

When the share price is below the net asset value, it is trading at a discount. Share prices above the net asset value are at a premium. If the closed-end fund is trading at £9.50 and its net asset value is £10, then it is trading at a 5% discount.

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Financial Derivatives

Definition and purpose of the derivatives contracts

Options, swaps, futures and forward contracts are the most typical types of derivatives. But what is a derivative? It is a security whose pricing structure is derived from a main asset such as stocks, commodities, bonds, currencies, interest rates and market indexes. The valuation of a derivative product is determined by changes of the main asset. They are risky products and due to the leverage effect they provide high positive or negative returns. They are mainly used for two reasons. Firstly, they are used to hedge or reduce risk. Secondly, they are used to speculate based on the stock exchange momentum and macroeconomic factors of each country. High volatility in the stock markets that is created from economic crisis, debt problems, bankruptcy and low liquidity has forced the practitioners to design options, swaps and futures contracts.

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Types, users and the purpose of the derivatives contracts

The derivatives that we will explain, illustrate and show with examples are the forward future contracts, the standardized future contracts, options and swaps. Options are a special type of financial asset that gives the holder the right but not the obligation to buy or sell an underlying security at a predetermined price. Options are of two types: put options and call options. A call options gives the right but not the obligation to buy, and a put option the right to sell at a specific price within a certain time period. American options give the right to the investors to exercise it before as well as on the expiry date. In contrast, European options give the right to exercise it only on the expiry date. The advantage of buying an option is that the initial outlay is smaller in comparison with buying a large number of shares. Furthermore, the downside risk is limited to a certain amount. In contrast, if the share price falls by a significant amount, then the investor’s could loose a large amount of his capital. Finally, the percentage positive return is greater due to the leverage effect.

The forward future contract involves two parties that agree to settle a monetary transactions or a commodity at a specific date in the future at a price that was agreed when the contract was signed. For example, we can have a currency or a commodity forward contract. Financial futures started to be traded in the United States on the Chicago Mercantile Exchange, (CME) and in the United Kingdom in the London Financial Futures Exchange, (LIFFE). Then, the futures contract started to be traded in the rest of Europe such as Germany, Italy, France and Greece. The standardized future contracts are preferred as they are traded through an exchange. The risk of default is controlled as it is monitored through margin deposits of the buyers or sellers. For example, stock index futures give the opportunity to the investors to buy a limited number of shares of the targeted index instead to be exposed to a large number of portfolios of shares. In other words, he/she is buying a small amount and through leverage they get the opportunity to increase their wealth. To achieve a positive return, they should buy the future contract when the stock index is very low or after a significant correction to guarantee a positive return. It is wise to keep a large portfolio in cash and wait the right moment to penetrate the market by taking a long or short position. During the fluctuations of the share prices, arbitrageurs are taking advantage from the mismatch of futures prices and share prices to gain profit. For example, arbitrageurs could take advantage to keep a short or long position of short or long-term future interest rates contracts. By following the decisions of the monetary policy of the Bank of England or the US Federal Open Market Committee, (FOMC), in the US, they are able to decide their investment decisions in terms of buying or selling the contracts.

Characteristic of an option contract and trading strategies

An option contract involves two parties, the writer who sells the option and the holder who purchases it. In addition, the price in the contract is called the exercise price or strike price, and the date in the contract is known as the maturity or expiry date. For example, according to financial times, we will have the following example:

------------------Calls--------------Puts-------------- Option Aug Nov Feb Aug Nov Feb

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____________________________________________

Tesco 200 111/2 18 24 8 13 16

2011/2 217 41/

2 11 161/2 18 221/

2 25 1/2

1.1 Share Exercise or strike price price Maturity or expiry date

Option premium

The options that we will examine for our investors are European style, namely that they cannot be exercised except on their expiry date. The drawback is that they are less flexible but the benefit is their lower costs.Specifically, we will examine four options of Tesco Plc from the Financial Times, (FT), with different exercise price, and the possible position that the investor can undertake. Then, we will formulate the appropriate strategy for the investor. Tesco Plc is a supermarket located in the United Kingdom. In more detail, he/she can choose among four options positions according to his/her estimation about the market. These can be the following:a. A long position in a call option (buy a call)b. A short position in a call option (write a call)c. A long position in a put option (buy a put)d. A short position in a put option (sell a put)

Furthermore, according to the data obtained from FT, we will have the following combinations: Exercise Price Premium Buy a call at November 153 14

Write a call at August 183 13.5

Buy a put at February 167 13

Write a put at November 200 13

Premium

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1.1.1.1.1 C

Write a call

13.5 Profit 13 Write a put

0 / / / 167 180 196.5 Share price Loss - 13 Buy a put -14 Buy a call

Source: author’s illustration.

This graph is an illustration of the different strategies that are available to the investors. The break-even point is the sum of the strike price plus the premium for the call strategies. In contrast, the difference of the strike price from the premium is used to calculate the put strategies. The investor by buying a call option takes an unlimited reward for limited risk, which is related solely to the loss of the premium he has paid. On the other hand, by writing an uncovered call, he takes a limited reward for unlimited risk. Particularly, in naked option writing, he takes a massive amount of risk, which can lead to financial disaster if he makes an incorrect decision about the future share price movement. For example, an upward price movement due to news of a takeover bid will really destroy financially the investor’s, (Brian J, 1989. P. 111). In contrast, the writing of a covered call option is extremely conservative strategy, and is less risky than buying shares themselves. This hedging strategy can used to insure against a fall in share price, thereby reducing the downside exposure. It can also used to improve the overall return on an investment (Brian J, 1989. P. 112).

A detailed and practical example of buying and selling call options

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An investor wants to buy a call option of 100 shares of stock XYZ, which has a market price of 250 pence or 2.50. The strike or exercise price in August is 270 pence or 2.70 and the option premium is 10 pence per share or 0.10. The maximum amount that the call option investor could loose is 0.10 x 100 = 10 pounds. On the other hand, he or she has unlimited upside gains as the general index and the company sector index is rising. If after three months the market price is below the strike price of 270, then, the investor will not exercise the option and he/she will loose the premium paid, which is 10 pounds. On the other hand, the writer of the call option makes a profit of 10 pounds. For example, if the investors made a wrong prediction and the share price drops to 240 pence, then, the mathematical formula to calculate the portfolio value of a long call is as follows:

(Ending share price – strike price) x number of shares = (2.40 – 2.70) x 100 = -30 pounds.

Let’s assume that the share price increases to 280, then the investor is breaking-even. He or she is not recording any loss or profit as the price is equal to the option premium paid. The share price has to increase above the level of 280 in order that the call option investor starts to record a profit. Let’s say that the share price reached the level of 350. Thus, the mathematical formula for calculating the portfolio value of a long call option is as follows:

(Ending share price – strike price) x number of shares = (3.50 – 2.70) x 100 = 80 pounds.

Share price: 350 Strike price: 270 Option premium: 10 pence

Profit /losson call options

Investor short call option 10 Unlimited Limited profit profit Break-even (strike price + premium) 0 240 280 350

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Limited Share price loss Unlimited loss -10 Investor long call option


It is very important to mention that you should buy a call option when the stock market index and the company sector index is very very low and you expect an aggressive strong bull movement according to the political and macro - economic variables of the country that the stock is traded. These are safe rules that you should respect to safeguard your capital and eliminate the psychological disorders. An excellent question will be what I mean by very very low. The question is very obvious and logical. You should be expert especially in technical and fundamental analysis before to start to trade in the derivatives market. An excellent start for technical analysis is to subscribe to Bloomberg Financial data and start to look to the stock index charts and apply different indicators. The most common indicators that are used in the industry are the Bollinger bands and the relative strength index 30% -70%. The Bollinger bands consist of three lines. The upper band or line, which is above the moving average and shows the maximum that a price could reaches. It is a simple average. If you want, you can use an exponential moving average manually in Excel. Usually, when the price reaches the upper band, you should short your investment. The middle line displays a moving average of 20 days. The lower band or line, which is below the moving average shows signal of buying or going long. On the other hand, the relative strength index shows overvalued and undervalued shares. When the RSI is close to 70% you should start to sell and when it is close to 30% you should start to buy. Please pay particular attention that the indicators alone could be misleading if they are not combined with the general trend of the price of the stock index market. The level of the prices of the stock index market should be very very low.

Let’s say that you want to invest in a call index option in the stock exchange of India and specifically in the S&P BSE Sensex index. If you check the current index price of the index through Bloomberg technical analysis, you will find that the index price in 03/03/2014 is 20946.65 and in 25/03/2009, it was 9667.90. The website of the index is as follows:

www.bloomberg.com/quote/SENSEX:IND/chart

Question

Which S&P BSE Sensex index price you will select to buy the call index option?

Answer

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http://www.bloomberg.com/quote/SENSEX:IND/chart

You have to check carefully the technical analysis of the index for the last 5 years and to spot the very very low and very very high prices. In this case, the best price to buy the call index option is the 9667.90. In contrast, the index price of 20946.65 is the highest price and everyone is starting to sell and guarantee his/her profit.

You should have experience of the trends in terms of bulls, increase of stock market indexes, and bears, decrease of stock market indexes in the different stock markets. The experience should be around 5 to 8 years. The purpose is to have a map of the very very low prices. It is not advisable to gamble or to play blindly as you will definitely loose your capital. The final purpose of money is to cover your financial needs and help the beggars, the Christian Orthodox Church, the poors, and the prostitutes.

Another excellent question is who is going to cover the losses of the opposite party. Losses create unfairness and enlarge the gap between the better – off and worse – off. This is not desirable objective as it conflicts the principles of the Greek Christian Orthodox religion. The purpose is that the individual has a peaceful, holy and without sins morning and afternoon day. We don’t want that the money start to create conflict with the religious principles. As we have said everyone will buy or sell in the highest or lowest point. Thus, the transactions will be limited ONLY to the correct prices. Nobody will be willing to buy in the wrong prices and record losses and psychological disorders. Don’t focus on the quantity of transactions but on the quality and large gains that will create a peaceful condition to both sides. Please focus on long-term gains and sustained excellent health of the investor and not on the short-term looses or small gains that will be eroded from transaction costs and other taxes.

The regulation of the derivative market will have to be amended to cover this weakness. A suggestion will be to create an anonymous account that does not belong to anybody. The parties involved in this account will be the government, the central bank, the Supreme Court and the Orthodox Christian Church. The purpose of including different parties is to eliminate money laundering for illegal activities that are not integrated with the Orthodox Christian approach. The other reason is to eliminate the gap between the very rich and the very poor. This account will be reconciled continuously with cash to offset the losses. It will act as clearing the losses of the opposite party. Thus, we make sure that nobody get hurt financially and get despair with nasty consequences concerning his health, job or marriage. Medium to huge losses in the derivative market will result that the individual get disappointed; loose his/ her faith to the Holy Trinity and to the Virgin Mary and suicide in extreme cases. Thus, the regulatory committee of the derivative market should work closely with the government and the Supreme Court to safeguard the soul and the spiritual integrity of the individual. The money should serve the life of the individual and not the opposite. The building blocks of the Greek Orthodox religion are to protect and safeguard the soul of the individual. Finance should act as a servant and not to create despair, losses, blame, anger, greed, and criminal actions. A detailed and practical example of buying and selling put options

An investor wants to buy a put option of 100 shares of stock XYZ, which has a market price of 230 pence or 2.30. The strike or exercise price in August is 210 pence or 2.10 and the option premium is 20 pence per share or 0.20. The maximum amount

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that the put option investor could loose and the total cost of the portfolio is 0.20 x 100 = 20 Pounds. This is the opposite strategy from buying and selling call options. If after three months the market price is below the strike price of 210, then, the investor will exercise the put option and he/she will record a profit. The price should be below 210 to record a profit as you should subtract the premium paid. The breakeven point is calculated as the difference of the strike price from the premium. In this case, it is 210 – 20 = 190. On the other hand, the writer that shorted a put option makes a loss. For example, if the share price drops to 180 pence, then, the mathematical formula to calculate the portolio value of a long put option is as follows:

(Strike price - ending share price)x number of shares = (2.10 -1.80) x 100 = 30 pounds.

Share price: 230 Strike price: 210 Option premium: 20 pence

Profit /losson put options

20 Investor short put option Profit limited Profit unlimited Break-even (strike + premium) 0 180 230 250 Loss Loss Share price unlimited limited

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Investor long put option -20


You should buy a put option when the stock market index and the company sector index is very very high and you expect an aggressive strong bear movement or tremendous drop of indexes and share prices according to the political and macro - economic variables of the country that the stock is traded. This is safe rule that you should respect to safeguard your capital and eliminate the psychological disorders. If you violate the investment rules, then, be prepared to enter in serious financial troubles with uncertain outcomes. Violations of investment rules will create conflict with the management group of the investment bank and the clients. Please pay particular attention to this point because the customer will blame you and you will have to resign from the company. If the losses are large you could be sentenced to prison or face serious legal charges associated with large compensations. This is why the advice should be crystal clear and represent the best interest of the client.

Let’s say that you want to invest in a put index option in the stock exchange of India and specifically in the S&P BSE Sensex index. If you check the current index price of the index through Bloomberg technical analysis, you will find that the index price in 03/03/2014 is 20946.65 and in 25/03/2009, it was 9667.90. The website of the index is as follows:

www.bloomberg.com/quote/SENSEX:IND/chart

Question

Which S&P BSE Sensex index price you will select to buy the put index option?

Answer

You have to check carefully the technical analysis of the index for the last 5 years and the spot the very very low and very very high prices. In this case, the best price to buy the put index option is the 20946.65. Although, you should be careful because the index could continue to rise for few months from speculator and still loose a substantial amount of your capital. You should have reliable information that a bear market has begun and the investment bank is expecting a tremendous fall in the prices. There are regular meetings in the bank with analyst and investment brokers.Please always remember that a dissatisfied customer with losses in his/her portfolio will close his/her account and withdraw from the bank. Nobody wants to loose his/her initial capital especially if he/she has mortgage debts, insurance, car expenses and high bills to pay for electricity, water and council taxes. So, please be practical and try to put yourself in the situation of the potential investor. In other words, trade as the money is your money.

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http://www.bloomberg.com/quote/SENSEX:IND/chart

Be prepared to trade if the share price is within a trading zone level or levels of resistance for a long period of time. At the same time, check a variety of macro indicators. For example, an economic indicator related to reduction of unemployment or manufacturing indices such as PMI manufacturing index. Make sure that they display significant positive changes from the previous period. Thus, if you have a trading zone for a long period of time and positive macro indicators, you should expect an aggressive positive bull market. Please check carefully the economic calendar agenda provided from Bloomberg markets. I strongly recommend that you register and familiarize yourself with their professional financial platform.

For example,

Source: author’s illustration

To be more protective in your trading check the political and economic situation of other countries and make sure that they will not affect negatively your portfolio. For example, if the call option of the stock that you buy is traded in other stock exchanges in other countries, then, a negative sentiment will affect negatively your investment and vice-versa. Please show particular attention to different aspects of your investment horizon and choices to avoid small, medium or large losses. The client always wants to increase his/her capital.

In addition, please make sure that the share price of the derivative product is close o its minimum or maximum value in relation to the stock index and the macro environment. Do not rely heavily in chart patterns such as triangle, rectangle, head – shoulders and double and triple tops and bottoms. Never start to trade if there is financial crisis and the price direction of the investment products is not clear. You will definitely loose a large part of your capital. Never trade in the wrong prices that are far away from the mean and the standard deviation is high. In other words, if the deviation from the expected returns is substantial, then, avoid trading and giving investment suggestion to the client. You are going to confuse him/her and the probability of monetary loss is quite high.

An excellent question will be what I mean by very very high. The question is very obvious and logical. Before to start to trade in the derivatives market, you should be expert especially in technical and fundamental analysis. An excellent start for technical analysis is to subscribe to Bloomberg Financial data and start to look to the stock index charts and apply different indicators. The most common indicators that are used in the industry are the Bollinger bands and the relative strength index 30% -70%. The Bollinger bands consist of three lines. The upper band or line, which is above the moving average, shows the maximum that a price could reach. It is a simple

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average. If you want you can use an exponential moving average manually in Excel. Usually, when the price reaches this band, you should short your investment. The middle line displays a moving average of 20 days. The lower band or line, which is below the moving average shows signal of buying or going long. On the other hand, the relative strength index shows overvalued and undervalued shares. When the RSI is close to 70% you should start to sell and when it is close to 30% you should start to buy. Please pay particular attention that the indicators alone could be misleading if they are not combined with the general trend of the price of the stock index market in relation to the fundamental analysis. Fundamental analysis is related to the financial position of the share of the company. For example, if you will get involved in equity derivatives, you will have to check the financial statement of the company in terms of balance sheet, income statement or profit and loss account and cash flow before to invest in the underlying product. It is very important to check short-term, medium-term, long-term liabilities, accounts payable and interest expenses or payments before starting to trade in credit derivatives. For example, if the company has a lot of debts in relation to short and long-term assets, then, the company is going to face liquidity and solvency problem. In this case, do not trade! Please pay particular attention to the cost of issuing, servicing the finance and the share premium. The share premium represents the difference between the nominal value or the initial public offering or the initial price that the share started to be traded and the current market price. Thus,

Share premium = Initial share price - current market price.

You should start to trade in a long or buying position when the current market price is very very close to the initial share price. You should start to sell or opening a short position or buy a put option when the current market price is very very away from the initial share price. Never and never, start to trade in median prices as you could get trapped in a mixed picture of a bear and a bull market and finally record losses or small gains. A sudden drop in the share price creates down valuation of the company and creates merger, acquisition and takeover bids opportunities. Thus, you should check very carefully the retained earnings which are past profits that will be used from the company for future investments. They are an important source of funding. Let’s explain an example of shares authorized and issued and how they affect the retained profits.

A company in Europe has issued 5,000,000 Euros and the current market price is 120 cents or 1.20. The authorized shares are 8,000,000 Euros and the retained profits are 2,000,000 Euros. The capital value of the company is

Capital value = 5,000,000 x 1.20 = 6,000,000 Euros

The company decides to make a rights issue on a 1 for 3 shares at a price of 105 cents when the market price is 120 cents. A discount of 12.5% has been shown which is calculated as (105 – 120) / 120 *100 = 12.5 %. If additional 2,000,000 shares are issued, then the cash is raised as follows:

2,000,000 x 1.05 = 2,100,000 Euros.

The new share price is calculated as follows:

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The value of the rights will be calculated as the difference 116 – 105 = 11 cents per share. The changes in the balance sheet will be as follows:

Shareholder’s Equity

Share capital Authorized Issued Ordinary shares of 1 Euro each 8,000,000 7,000,000

ReservesShare premium account 100,000 Retained profit 2,000,000 2,100,000Total 9,100,000

Thus, the conclusion is NEVER buy an equity option if a right issue will take place for the share price as the price will drop and the client will loose money. It is also important to measure the value of the business before to make any investment. The most common measures that are used are gross dividend yield, current market price, and price/earnings ratio. In addition, check carefully the cash flows from investing and financing activities. Is there an increase in cash in the statement of cash flows that will be used in the subsequent years? On the other hand, please have a look to the profit and loss account. Check carefully that the revenues are exceeding the expenses and that you get a positive net income. In other words, the company is recording a gain and not a loss. Check the fixed and variables costs and make sure that they are covered from the sales that the company is doing. Don’t take blind risk that could destroy the capital of the client. Please pay particular attention to this point. Check the number of times interest earned to cover interest expenses from potential loans. Check the profit margin, the current ratio, the acid test ratio and the account receivable turnover, the earning per share and the dividends that are paid annually.

The mathematical formulas are as follows:

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In the workshop, I will include practical examples from the account of companies listed in the stock exchange.

I have also included a table that shows the main accounts that you have to check very carefully in the balance sheet.

Balance SheetFixed assetsFixed assets at net book valueFurniture and buildingsCurrent assets Liabilities (current liabilities less than

a year)Cash and short term securities Account payablePrepayments Bank overdraftAccount receivable / Debtors CreditorsOther current assets Short-term debtShareholder’s equityShare capital Long-term liabilities (more than a

year)Retained earnings Long-term debt


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ExampleAnother example to consider is a company that will have to pay a flotation cost of 3% per share. The offering price is 50.00 Euro. The company is planning to raise 50,000,000 Euros. Please calculate the number of shares and the cash that will be paid for this project.

Solution

The offering price after deducting the flotation cost is as follows:

50 * (1-0.03) = 48.5 Euros

The new shares that will be issued are 50,000,000 / 48.5 = 1,030,927.84

The cash that will be paid is 1,030,927.84 * 0.03 * 50 = 1,546,391.76 Euros.

Please read very carefully Basel I, II, III white paper for risk and strategic exposure in relation to the capital that should be maintained in the shareholder’s equity. Check very carefully the spreads in credit derivatives in relation to the borrowing costs.

You should have experience of the trends in terms of bulls, increase of stock market indexes, and bears, decrease of stock market indexes in the different stock markets. The experience should be around 5 to 8 years. The purpose is to have a map of the very very high prices. It is not advisable to gamble or to play blindly as you will definitely loose your capital. The final purpose of money is to cover your financial needs and help the beggars, the Christian Orthodox Church, the poors, and the prostitutes.

Another excellent question is who is going to cover the losses of the opposite party. Losses create unfairness and enlarge the gap between the better – off and worse – off. This is not desirable objective as it conflicts the principles of the Greek Christian Orthodox religion. The purpose is that the individual has a peaceful, holy and without sins morning and afternoon day. We don’t want that the money start to create conflict with the religious principles. As we have said everyone will buy or sell in the highest or lowest point. The regulation of the derivative market will be amended to cover this weakness. Thus, there will an anonymous account that does not belong to anybody. This account will belong to the government and the central bank. It will be reconciled continuously with cash to offset the losses. It will act as clearing the losses of the opposite party. Thus, we make sure that nobody get hurt financially and get despair. Medium to huge losses in the derivative market will result that the individual get disappointed; loose his/ her faith to the Holy Trinity and to the Virgin Mary and suicide in extreme cases. Thus, the regulatory committee of the derivative market should work closely with the government and the Supreme Court to safeguard the soul and the spiritual integrity of the individual. Finance should act as a servant and not to create despair, losses, blame, anger, greed, and criminal actions.

Definition of Forward and Futures Contracts

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Forward and futures contracts have similarities in terms that they involve two parties to exchange a commodity, a currency or a bond at a specified price in the future. The costs of carry that characterize these contracts are insurance, storage and interest costs. A standardized future contract is traded based on a specified amount at a fixed future date and at a fixed price. In contrast, in the forward contract the two parties negotiate the amount that will be traded. Futures contracts are exchanged on a stock exchange. Forward contracts are done between the parties and they are over - the -counter contracts. The fact that there is a clearing house that regulate the settlements through a margin call make the standardized futures contract more safe by eliminating the credit risk of default. In contrast, forward contracts, as they are over – the - counter are not regulated by a clearing house of the futures exchange and the parties could experience large losses. The only advantage of over- the- counter contracts are that the involved parties could negotiate the quantity, the price and the expiration date. The biggest problem is the risk of default, the lack of liquidity and buying or selling in the wrong price. Standardized futures contract provide liquidity to the parties involved, as they can be sold to another party at any time of the contract until maturity. In contrast, forward contracts could not be sold to a third party, which makes them to lack liquidity. To sum up, the standardized futures contract are regulated, offer high liquidity, correct pricing and low credit risk. The forward contracts offer less pricing transparency, low liquidity, higher credit risk and they are traded over- the- counter. The characteristic of a future contract is the underlying, the standardized unit multiplied by the index points, the initial margin, the settlement method, the minimum price move, the minimum tick value and the time period expressed in months. For example, if you buy the Financial Times, (FT), and check a future contract for the FTSE - 100 Index, you will see a standardized value of 25 Pounds multiplied by the index point. Other characteristics of the index future contract is the time period expressed in months, open interest, the closing price for each trading day, the high, the low, the previous value and the settlement price. Settlement price refers to the closing price of the contract. Open interest refers to the total number of contracts in terms of buying or selling positions. For example, if you bought the index at 3050 and you expected a bull market that reaches the value of 3150, then, the 100 points increase are multiplied by the standardized value of 25. If the initial principal of investment is 5,000 Pounds, the mathematical formula for the gains will be as follows:

5,000 x 100 x 25 = 12,500,000 Pounds

Another example of the name of index futures that are traded in Australia or ASX exchange is as follows:

ASX SPI 200 index futures.

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S&P / ASX 200 VIX futures. S&P / ASX 200 Resource index futures. S&P /ASX 200 Financials – x – A- REIT index futures.

Example of pricing a forward contract

A forward contract of 6 month has a market price of 52 Pounds when the spot price of the underlying commodity is 49 Pounds. There are no costs of carry and the discount rate is 7 percent. Calculate the value of the forward contract and the potential arbitrage profit or loss?

Solution

The current price of the forward contract (F0) should be equal to the value of the underlying commodity, (S0) at the discount rate r. Thus, the equation is as follows:

The current value of the forward contract is 50.715 Pounds. The market price is 52 Pounds. It is overvalued and the arbitrageurs experience a loss of -1.825 Pounds. He/she should sell the expensive one and buy the cheaper one.

To solve problems with forward rate agreements, (FRA), which are forward contract with an interest rate as underlying, you should draw a timeline schedule.

Example

An investment bank buys a 4 x 6 FRA from a building society in the UK for 4.0% by paying 2 million Pounds. 80 days latter, LIBOR is 5%. Who will receive the FRA payment and for how much?

Solution

The mathematical formula for Forward Rate Agreement, (FRA) is as follows:

The timeline schedule is as follows:

t = 0 4months 6 months

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= ………. Please complete

the calculation.

Helpful hint: If the FRA payment is positive, then, the building society is the payer and the investment bank receives the FRA payment.

If the FRA payment is negative, then the investment bank is the payer and the building society receives the FRA payment.

Definition of swaps

Explanation of a swap contract

The aim of this section is to illustrate the various components that constitute a credit default swap, CDS. But what is a credit derivative? It is a financial instrument the value of which is derived from an underlying market value incorporating the credit risk of a bond or a loan. They are used to hedge, to speculate on the spreads through arbitrage. The premium that is incorporated in the default swap, DS, is known as the credit derivative swap spread. Let’s assume a credit default swap based on a long-term US corporate bond. The US corporate bond is knows as a reference obligation in the contract. The principal for this contract is $500,000,000, the swap premium is 80 basis points or 0.80/100 = 0.008 and the bond matures in 5 years. The payments are annually. The buyer will pay the seller $500,000,000 x 0.80% = $4,000,000 each year. The credit risk increases as the ranking and the market price of the bond or loan decrease. If there is a credit event, then an immediate settlement of cash will take place to recover the loss. The seller will pay back to the buyer the difference of the net amount of the principal and the current market value. To minimize the interest and the credit risk of the contract the credit default swap is linked to an interest rate swap or an option. The integration of a interest rate swap with an option is known as swaptions.

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The purpose of this instrument is to transfer or hedge credit risk. As they are over- the- counter instrument (OTC), they are more tailored to meet specific needs of the counterparties. Thus, there is significant difference with exchange traded derivative products such as standardized futures and options. A standardized swap contract involves the exchange of principals, regular coupon payments and return back of the principal in addition to the last interest payment at the expiration of the swap agreement. The most common contracts are plain vanilla interest rate, commodity or foreign exchange swaps. The one party is paying a floating inters rate in dollars and the other receive a fixed rate in a foreign currency. At the end of the swap agreement the two parties must return the initial principal in addition to the last coupon payments.

The swap market has no government regulation, there is no clearinghouse and the swap dealer has to price the swap transactions and manage the potential risks that will arise. The problem of potential default is the most crucial, especially, when one party do not know the creditworthiness of the other party. It involves one party making fixed payments while the counterparty makes variable payments. The purpose of the swap agreement is to protect the spreads and the profit margins of both parties from significant fluctuations in the FOREX and Treasury bill interest rates.

I will examine a simple swap agreement between a US manufacturing company that wants to expand its operation in Germany and an investment bank. The swap covers a 10 years period and consists of annual cash flow payments. The company has issued a US bond and pays a fixed rate of 8% to the bank. On the other hand, the bank agrees to pay a floating rate of LIBOR + 2% to the company. The notional principal is 5 million Euro or 5,000,000 Euro. The LIBOR is 10%. The Company prefers to have issued a Euro bond to cover the working capital in Euro in Germany for the new factory. The purpose of the swap is to facilitate such agreement with low borrowing cost. The company has to pay a fixed interest rate in dollars at 8% every 6 months and the bank has to pay a floating interest in Euro at LIBOR + 2% for the new branch in Germany. The payments will take place every 6 months and the currency exchange rate is EURO/USD = 1.35. The converted amount of €5,000,000 x 1.35 = 6,750,000 dollars.

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Example of semiannually swaps interest payments between an investment bank and an insurance company

The investment bank borrows 20,000,000 Pounds from the insurance company at a fixed rate of 7% for 3 years. The insurance company borrows from the investment bank 10,000,000 Euros at a fixed rate of 5% for 3 years. Calculate the interest payments for the three years, if we assume semiannual payments? If the payments were done annually, then, the mathematical formula will include the principal x by the interest rate x days/360.

€10,000,000

Company

Investment Bank

6,750,000 x 0.08 / 2 = 270,000 Dollars

€ 5,000,000 x 0.12 / 2 =300,000 Euro

10 years

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Investment bank Insurance company

£ 20,000,000

The investment bank pays the insurance company: £20,000,000 x 0.05/2 = 500,000 Pounds.

The insurance company pays the investment bank: €10,000,000 x 0.05/2 =250,000 Euros.

£500,000Investment bank Insurance company

€ 250,000

At the end of the third year, the two parties exchange the principal amounts in addition to the final interest payments.

£20,500,000Investment bank Insurance company

€ 10,250,000

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Interest rate swap

Interest rate swaps are very popular agreements between two parties in the debt or fixed-income department of the investment banks. The fixed income department of Bank A pays a fixed rate of 5.5% upon the principal of 50,000,000 Pounds. In contrast, Bank B pays a floating or reference rate of LIBOR accounted to 7.2%. The payment frequency is every 6 months for 2 years.

Fixed payment : £50,000,000 x 0.055/2 = £1,375,000Bank A Bank B Floating payment: £50,000,000 x 0.072/2 = £1,800,000

Suppose in the second year that the LIBOR has increased by 12 basis points or 0.0012. Then, the floating payment will change and the calculation will be as follows:

Second year floating payment for Bank B = 50,000,000 x 0.0732 / 2 = 1,830,000 Pounds.

Bank A will continue to pay the same fixed amount, namely, £50,000,000 x 0.055/2 = £1,375,000.

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We can illustrate in a diagram the cash flows for an interest rate swap for the period of two years.

Floating rate payments

1,800,000 1,800,000 1,830,000

Years

0 0.5 1 1.5 2.0 1,375,000 1,375,000 1,375,000 Fixed rate payments

Stock index swap

Let’s assume a stock index swap based on the IBEX 35 index between two parties that want to eliminate the risk of exposing their portfolios in stocks. The first party A is an investment bank and the second party B is the debt department of an insurance company. The term of the contract is for 4 years. The investment bank pays a total annual return of 8% upon the IBEX 35 index. In contrast the debt department of the insurance company pays a floating LIBOR or reference rate of 3.2%. The principal of this exchange is 100,000,000 USD and the payment is every 6 months.

First year or year 1

Fixed payment : $100,000,000 x 0.08/2 = $4,000,000 Party A

Floating payment: $100,000,000 x 0.032/2 = $ 1,600,000 PartyB

Please complete the calculation for the remaining years by assuming that the total return of the IBEX 35 index is 10% for the second year. At the same year, the LIBOR has increased by 7 basis points. Similarly, we assume that the fourth year the total

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return of the index is -8% and the floating rate of the LIBOR has increased 13 basis points.

Exercise

Calculate the interest payment that Party A will pay to Party B by taking the difference of the fixed and floating Euribor rate. The fixed rate is 5.50%. The floating Euribor rate is 2.56% and it is increased by 20 basis points or 0.002. The principal is 300,000 USD and the payments are due in 3 months or 90 days.

The mathematical formula is as follows;

Interest payment of Party A = principal x [(fixed rate – (floating rate + increases of basis points)] x (days / 360)

Please complete the calculation.

Exercise

Two parties are entering in a 3 year currency swap agreement. Party A will pay a fixed rate of 3.0% on $8,000,000 and party B will pay a floating rate of 4.2% on 5,000,000 CAD or Canadian dollars. The payments will be half a year and will be calculated based on days. Thus, 30 days multiplied by 6 months = 180 days.

The mathematical formulas are as follows:

Interest payment of party A = principal x fixed rate x (days/360)

Interest payment of party B = principal x floating rate x (days/360)

Please add in the third year the final interest payment to the initial principal to close the swap agreement.

Please complete the calculations.

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Example of calculating the quarterly fixed rate and the fixed rate in annual terms of an equity swap

An investor wants to calculate the six months fixed payments in Pounds and the annual fixed rate in percentage terms of a six months equity swap. The initial principal is 10 million Pounds. The annualized LIBOR spot rates are R90 days = 0.020 and R180 days = 0.027.

Solution

The mathematical equation of a six months fixed rate of a swap is as follows:

Please complete the calculation

The six months rate payment is the calculated amount multiplied by the initial principal

Please complete the calculation

The annual fixed rate on the six months equity swap is the fixed rate of a swap six months period multiplied by 180/90

Please complete the calculationRisk Management

Credit Risk

Credit risk is an essential component in the derivatives market and in major investment and retail banks to safeguard their liquidity and to price correctly the credit transactions. It is very common that investors buy a derivative contract, makes the wrong prediction concerning the movement of the market and finally owes money to the bank or to another party. The drop of the value of the contract increases the possibility of default as nobody wants to buy or sell it. In addition, changes and increases in credit spread is an alarming sign of downgrades in quality and future

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default. As an example, we can mention two investment banks that are buying a forward contract based on foreign currency EUR/USD for future use in 30 days. Let’s assume that JPMorgan enter in a foreign exchange rate transaction with Goldman Sachs. JPMorgan buy $500,000,000 in exchange for Euro from Goldman Sachs in a future date of 30 days for a specified price of EUR/USD 1.35. The reason of using a specified price is to mitigate the risk from appreciation or depreciation of the exchange rate. At expiration of the contract, JPMorgan will pay to Goldman Sachs 370,370,370.4 Euro. The amount is calculated as $500,000,000 / 1.35 = 370,370,370.4 Euro.

Let’s explain two scenario of appreciation or depreciation of the exchange rate to illustrate the credit risk and the subsequent profit or loss. Let’s assume that during the 30 days, the dollar appreciates against the Euro. The exchange rate becomes EUR/USD = 1.10. The principal exchanged will worth 454,545,454.5 Euro. The amount is calculated as $500,000,000 / 1.10 = 454,545,454.5 Euro. The difference of 454,545,454.5 – 370,370,370.4 = 84,175,084.1 Euro represents a profit for JPMorgan and a loss for Goldman Sachs. The opposite will apply in case of depreciation of the exchange rate. The purpose in this case of using a forward contract is to lock your buying or selling agreement and hedge the credit risk against a sudden rise or fall of the prices. It could be in the currency exchange market, in the equity market, in the derivatives or the commodity market. Forward rate agreements are applied on currencies, interest rates, and commodities. The profit or loss is realized by the agreed and realized difference in price changes. The problem with forward rate agreement is that one party gain and the other loose. In this case, the gap between the better – off and the worse – off increases. Inequality arises between the parties and each one would like to lock a profitable position at the expense of the other party. A solution to this problem to eliminate such unfairness and credit risk is to follow the Greek Christian Orthodox approach based on limited needs and buying or selling in the range of prices that are not far away from the mean or mean reverting. In this case, the difference will not be large and significant.

Exercise

Let’s assume that during the 30 days, the dollar depreciates against the Euro. The exchange rate becomes EUR/USD = 1.45. Calculate the value of the exchanged principal in Euro and determine which side is recording a profit or loss.

Market Risk

An investor faces two types of risk, market risk and firm-specific risk. So on the one hand, there is market risk, which is the part of a security’s risk that cannot be eliminated by diversification because it is associated with economic or market factors (Weston, Besley & Brigham 1996). These factors can be inflation, recession, high interest rates, etc. and are non-diversiable.

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Market and Firm-specific risk

RiskAs % Unsystematic 40 _ risk or firm- specific risk

35 _

30 _

20 _ Systematic ------------------------------ risk or market risk

10 _

0 / / / / 10 20 30 40 Number of shares

Source : the diagram is from Solnik (1974).

According to the graph, Solnik (1974), find that risk could not be reduced below 35% of the average risk. In addition, risk can only be eliminated in a reasonably well-diversified portfolio, which is one containing up to 20 stocks ( Copland & Weston, 1992). Moreover, elimination of the portfolio risk and the overall performance will depend on the (correlation coefficient) between the stocks. When = -1(perfectly negative correlated), all the risk can be diversified away. When = +1(perfectly positively correlated) diversification is ineffective. For example, by taking Sainsbuy, Tesco and Barclays data, we can draw the following conclusions:

Tesco * Sainsbury

Tesco, Sainsbury = ---------------------- = 0.597

Tesco * Sainsbury

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Tesco* Barclays

Tesco,Barclays = ------------------------- = - 0.379

Tesco * Barclays

Thus, it is obvious that Tesco and Barclays (different sector) offer better diversification than Tesco and Sainsbury (same sector).

The Capital Asset Pricing Model (CAPM), which is basically derived from the Modern Portfolio Theory. Its foundation is based upon the fact that the portfolio is diversified, and the only variable that we have to calculate is market volatility. The equilibrium relationship between expected return and risk for individual securities are known as Security Market Line, and can be expressed accordingly:

E(r)i = Rf +(Rm - Rf) (54)

Where E(r)i is the expected return of the security, Rf is the risk-free borrowing/lending rate, Rm is the expected return on the market portfolio and is the Beta coefficient which measures a stock’s sensitivity to market fluctuations and is given by the following formula:

(55)

By examining 60 monthly observations for 5 years, we get the following Beta:

Tesco = 0.79 Sainsbury = 0.45 Barclays = 1.31

What that mean? In more detail, a beta of 1 means that the share is as risky as the beta of the market portfolio, whereas a beta of 0.5 is half as risky as the market. In addition, a beta of 2 is twice risky as the market. Furthermore, stocks, with 1 help to stabilize portfolios and are referred to as defensive securities. While stocks with 1 increase the volatility of a portfolio and will earn above the market rate of return, and are known as aggressive securities ( Pilbeam, 1998,p.156). Thus, it is better for the investor to keep a combination of stocks with different beta in his portfolio in order to reduce and balance the market risk.

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After analyzing the beta (risk), we will calculate the security market line in order to get the return.

E(r)i = Rf +(Rm - Rf) Where

tesco = 0.79 sainsbury = 0.45 barclays = 1.31 RF = 6%. Rm= 11.42% Consequently, Er Tesco = 6% + ( 11.42% - 6%) * 0.79 = 10.28% Er Sainsbury = 6% + ( 11.42% - 6%) * 0.45 = 8.43%

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Er Barclays = 6% + ( 11.42% - 6%) * 1.31 = 13.1% By plotting all the above results on the security market line, we will have the following Figure:

Figure 1 shows the security market line of three stocks.

Required RateOf return (%)

Undervalued stock C

Er Barcl = 13.1% Security market line

Relatively Risky stock. Risk premium 7.1%

Ret market 11.42% B Er Tesco= 10.28% A Er Sainsb= 8.43% Safe stock

RF = 6% Risk premium Safe stock 2.43% risk premium 3.79%

/ / / /

0.45 0.79 1.0 1.31 Risk According to Figure 1, the shares are the underlying assets and the derivatives product is based on how the shares are moving in the stock market. Due to leverage effect, the returns that are offered from the derivatives instrument are higher than the risk free rate and the return of the shares in the stock exchange. The security market line tells us if a stock or portfolio is properly priced. Tesco plc and Barclays bank are undervalued stocks. That means that investors will rush to buy them including their derivative products. Therefore, their demand will push up its price. As this happens the prospective return will start to drop.

Operational Risk

Operational risk is related to the internal management of an investment bank. Thus, it could be the persons working in the bank, the processes and the technology. In addition, it could be the risk of making mistakes with the monetary transactions or theft. This is why six sigma methodologies are very important, as it covers this type of risk. The yellow belt candidate has a basic knowledge of the Six Sigma in terms of DMAIC. It participates as a team member on a project. He / she perform daily activities such as, data entry and provide assistance in achieving the organization’s overall objectives. They are responsible for planning small level projects in terms of PDCA (Plan, Do, Check, Act). The Green belt works in six sigma projects by

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applying the DMAIC approach in detail. His /her task is to deploy six sigma techniques and to lead small-scale improvement projects by applying DMAIC. He has a partially understanding of DMAIC. Select the right statistical tools and significantly increase profitability. The black belt, (BB), got a thorough knowledge of six sigma philosophies and principles. He / she is a team leadership, understand team dynamics and assigns their team members with roles and responsibilities. They have a complete understanding of DMAIC approach. He/she focuses to oversee and execute the project. He/she is responsible for specific projects. The savings are expected to be around $100,000 - $250,000. Advanced statistics, coaching successful project teams, group organizational assessment, and customer cantered business are the major tasks. The master black belt, (MBB), identify projects and functions for six sigma. He/she has advance understanding of statistics application, and project management experience. He/ she is highly proficient in using six sigma methodology. The Six Sigma Champion (SSC), is a senior or middle level executive who is responsible to choose and sponsor specific projects. He / she ensure the availability of resources. The projects are aligned with the structure and culture of the business. He/she is responsible to remove roadblocks and facilitate employee adaptation and eliminate resistance to change. He/she works closely with the MBB to achieve change management. The speed of project deployment is the responsibility of the Champion. He /she acts as practitioners, mentors, guides and facilitators. They are responsible for transformational leadership style from top to bottom.

Delta – neutral hedge

Delta – neutral hedge is common used in risk management to keep the value of the portfolio neutral due to changes in the share price. It is achieved from a long position in a share and a short position in a call option. The mathematical formula to determine the number of options is as follows:

(56)

Thus, if the investment bank has bought 30,000 shares of Vodafone and the delta of the call option of the same company is 0.50, then the number of call options that are needed to purchase to form a delta-neutral hedge are as follows:

Delta hedge = 30,000 / 0.50 = 60,000 options or 600 option contracts.

Weighted mean price of a portfolio

Let’s assume that we have a portfolio of four options with their market prices and the number of shares bought. It is required to calculate the weighted mean price of the portfolio.

Options Price expressed in $

Number of shares

Weight Weight x Price

A 14.00 300 0.4 5.6B 12.00 200 0.3 3.6C 8.00 100 0.1 0.8

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D 5.00 150 0.2 1Total 750 1

Source: author’s calculation

The mathematical formula is as followed:

By substituting the numbers from the Table into the equation we have the following:

0.8 + 1 = 11.

Exercise

Let’s assume that we have a portfolio of four futures with their market prices and the number of shares bought. It is required to calculate the weighted mean price of the portfolio.

Options Price expressed in $

Number of shares

Weights Weights x Price

A 14.00 300B 12.00 200C 8.00 100D 5.00 150

Total 750Source: author’s calculation

Please calculate first the weights, then the product or multiplication of the weights with the price and then apply the equation to calculate the weighted mean price of the portfolio.

Equally weighted portfolio risk

The portfolio risk or variance of the weighted portfolio is very important component as it is affected by the number of assets, the average variance and the covariance of the assets that are included in the portfolio. As the number of assets gets larger the variance of the portfolio gets closer to the average covariance. The mathematical formula is as follows:

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Exercise

Let’s assume two portfolios of options. The first portfolio has 4 call options and the second portfolio has 10 put options. The average asset variance is 0.20 and the average covariance is 0.05. Calculate the variance of each portfolio.

By substituting the numbers in the above equation we have the following:

Variance of the first portfolio = [(1 / 4) * 0.20] + [(3/4) *0.05] = ……………

Please complete the calculation……………

Variance of the second portfolio =

Please complete the equation and the calculation……….

Active return, active risk and information ratio

Active return is the difference in returns between a portfolio and the index or benchmark that is measured.

Active return = rp - rb (59)

Where: rp is the portfolio return. rb is the benchmark or index return.

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If the portfolio return is 0.80 and the benchmark return of the index is 0.70 then, the active return is………


Active risk or tracking error is the standard deviation of the difference of returns between a portfolio and the benchmark or index.

If the portfolio return is 0.80, the number of assets is 10 and the benchmark return of the index is 0.40 then, the active risk is………


Information ratio shows the consistency of the fund manager towards the active return. The mathematical formula is as follows:

It could be calculated very easily in Excel software. I will illustrate a simple table with the relevant calculations.

Day rp rb rp - rb

1 0.03 0.02 0.012 0.02 0.014 0.0063 -0.04 0.034 -0.0744 0.05 0.067 -0.017

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5 0.08 0.012 0.0686 -0.01 -0.056 0.0467 0.07 0.031 0.0398 0.034 0.023 0.0119 -0.021 0.015 -0.03610 0.045 0.001 0.044

Average 0.0258 0.0161Standard deviation

0.043

Source: author’s calculation

By substituting the values that we have found in terms of rp =0.0258, rb = 0.0161 and standard deviation = 0.043 in the following equation we have:

But what is the interpretation of the information ratio of 0.23. It means that the fund manager gained around 23 basis points of active return per unit of active risk. The higher is this number, the better the manager is performing in relation to active risk.

Clearinghouse and margin payments

The clearinghouse in standardized futures exchange is used to guarantee that the money settlement between two parties is done at the specified date. The margins that are maintained in the clearinghouse are initial margin, maintenance margin, daily settlement, and margin calls. When there is a loss that is greater than the initial margin, then, further deposits are required to compensate the losses. Every time that there is a mismatch between payments, the clearinghouse imposes a margin call to compensate the missing amounts. If the trader fails to cover the amount, then, the clearinghouse will close his/her position. During the period of the contract one party could experience substantial losses instead of gains.

Example of margin payments in the clearinghouse

An investor open a margin account with a minimum initial margin of 5,200 dollars per contract. The maintenance margin is 1,500 dollars per contract. He/she buys 7 July wheat futures contracts with a standard contract size of 200 bushels priced at 230 dollars per bushel. The July contract size in the next 2 days recorded the prices of 220 and 210 dollars per bushel. Show the cash flows, gains and losses for the buyer and the seller?

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Solution

Initial margin = 7 x 5,200 = 36,400 dollars

Maintenance margin = 7 x 1,500 = 10,500 dollars

The cash flows, gains and losses for the next two days will be as follows:

Day 1

Cash flows for the buyer’s: 36,400 + 14,000 = 50,400 dollars. The investor’s recorded a gain.

Cash flows for the seller’s: 36,400 – 14,000 = 22,400 dollars. The investor’s recorded a loss.

Helpful hint: the amount of 14,000 is calculated from the difference of the bushel prices, (f0-f) x number of contracts x standard contract size. Thus, we have: (230-220) x 7 x 200 = 14,000 dollars. The same principle applies for the second day but with different bushel price.

Day 2

Please do the calculations for the second day.

This is why I am stressing the importance that the investors should buy or sell ONLY when the market is aggressively increasing or falling. If he/she gets trapped in a market that is not strong bull or bear, then, he/she will have to compensate regularly for the losses or he/she will experience a very small profit. If the amounts as the days passes is below the maintenance margin, then, the investor’s will receive a margin call and he/she should add the capital required to proceed with the contract. If the investor’s is short of money, then, the position is closed with the incurred losses.

Example of calculating a margin call due to changes of price futures

An investor has opened a short position of 20 Soybean futures contract. The initial margin was 500 Pounds and the maintenance margin was 430 Pounds per contract. The price change that will create a margin call is as follows:

Solution


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Exercise

Calculate the balance at the end of the 5th day from changes in the futures prices from 90 to 89, 91, 95, 97, 99. The trader has bought 50 futures contract for settlement in May. The initial margin is $8.

Day Beginning balance

Futures price Gain or loss Ending balance

0 400 90 0 4001 400 89 (50)2 350 91 1003 450 95 2004 650 97 1005 750 99 100


Beginning balance = initial margin x number of contracts.Beginning balance = 8 x 50 = $400

Please complete the values of the column ending balance.

The Christian Orthodox approach will help the investors to balance his/her thoughts and to eliminate the greed fear or anger and at the same time protect his/her capital. The Orthodox approach is a safe route to strengthen the investors’ patience and to teach him/her to reject his/her personal will by increasing the spiritual integrity.

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Case study based on capital investment appraisal methods

Introduction

Capital investment appraisal is a fundamental strategic process for every organisation, which want to invest in new projects. The strategic direction taken will depend on the organisations existing position and the current level of success at meeting the organisations key goals. The process includes planning the capital expenditure, evaluating and selecting projects and finally controlling capital expenditures.

On the other hand, capital budgeting involves a process of allocating the financial resources of a firm in a manner that best achieves its overall goals. Typically, the results of capital budgeting decisions affect the operations of a company for many years in the future. Therefore, selecting the appropriate project among a combination of projects is crucial as large sums of finance are often involved.

Consequently, a long-term financial investment decision needs to be financially justified by evaluating all the relevant costs and benefits associated with the project. A number of factors need to be taken into account including the size of the investment, the economic life of the project, the certainty of the returns, and the strategic importance to the company. In addition, the project selected must yield maximum returns with a minimum level of risk.

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The purpose of this report is to analyse different types of appraisal techniques and to evaluate the viability of the proposed projects. Detailed explanations will be given in order that the shareholders have a clear picture of the proposed project. Finally, we will discuss the problems associated to calculate the rate of discount rate.

The proprietors of X Co company can evaluate the viability and success of the two proposal projects through a range of investment appraisal techniques. They include:

1) The payback period2) The Net Present Value (NPV)3) The Internal Rate of Return (IRR)4) Profitability index5) Accounting rate of return (ARR)

By calculating the above methods (see appendix 1), we find the following results:

Project A Project BPayback period 1. 52 years 2 yearsNPV £ 4376 £ (1627)IRR 30.23 % 10.67%Profitability index 1.17 times 0.93 timesARR 83.3% 56.6%

According to the results, the proposed project A is viable and project B must be rejected. In more details, the positive NPV, £ 4376, of project A, means that the cash inflows from a capital investment will yield a return in excess of the cost of capital, and so the project should undertaken. In contrast, in project B, the negative NPV

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(£1627), means that cash inflow yield a return below the cost of capital, and so the project must be rejected.

Furthermore, IRR, which when applied to project cash flows, produces a net present value of zero must exceeds the WACC, in order that the project worth undertaking. In our case, IRR (30.23%) of project A is high enough to cover the WACC, and therefore the project is worth to consider. In contrast the low IRR of project B is an obvious sign that the project must be rejected.

Moreover, the shortest payback period, which measures the length of time taken to recoup the original investment, must be selected. In our case, project A (1.52 year) is more appropriate than project B (2 years).

On the other hand, profitability index is very crucial factor in capital investment, particularly, if we assume that the company is in a capital rationing situation. Projects with profitability index higher than 1 must be selected. In our case project A with profitability index (1.17 times) is more appropriate than project B( 0.93 times), as it can generate enough revenues to cover the initial investment.

Finally, the ARR is very subjective method as the benchmark used to select the appropriate method can be misleading. In our case if we assume a target rate of 70%, then it is clearly that project A (83.3%) is more favourable than project B (56.6%), which shows a low profitability for the investors and shareholder’s.

Theoretical arguments for the choice of NPV, and why in practice other methods are preferred

As it was mentioned earlier the NPV and IRR are closely related methods of selecting capital investment proposals as they take into consideration the time value of the money. Although, if in our case we assume that the projects are mutually exclusive, then the NPV is theoretical superior from the IRR for a variety of reasons.

Specifically, according to (Levy et al, 1986,p.64), by examining and comparing the incremental cash flows against the cost of capital, the NPV method ensures that the firm will reach the optimal scale of investment. In contrast, the IRR, which is expressed in terms of percent, rather than in terms of absolute dollar or pounds return ignores this important element of an investment decision. In other words, the NPV represents the absolute magnitude of the project while the IRR, being a pure number, does not. The reason behind the above argument is that the firm is concerned with absolute profits and not only with the rate of profit.

Furthermore, NPV is more superior than IRR because as both methods take the time element into account, the time adjustment made in the IRR method is incorrect (Levy et al, 1986,p.68). The above can be substantiated through the ‘reinvestment’ of interim cash flows. In more details, the NPV method assumes that the cash flows can

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be reinvested at the firm opportunity cost of capital. In contrast, the IRR assumes that the cash flows can be reinvested at the project internal rate of return. This has no economic basis. On the other hand, through NPV, projects that earn more than their opportunity cost would be accepted immediately.

On the other hand, the reinvestment assumption becomes crucial if we assume a changing cost of capital in the future years. In this case, the IRR becomes irrelevant as the single-valued rate of return can not be compared with the different rates of theWACC (Levy et al, 1986,p.70). For example, if the IRR is 24% and we have the following cost of capital. K1 = 19.76%, K2 = 24% K3 = 17.2% It is obvious from the above that the IRR can not lead to a clear accept or reject decision. On the other hand, the NPV does not face this problem as it uses the different WACC in reinvested decisions.

Finally, NPV is not only theoretically superior to the IRR but it shows technical advantages. Specifically, if the company use non-conventional cash flow, then IRR solution may not exist or more than one IRR may be found (Levy et al, 1986,p.90).

Despite of the advantages of the NPV method over the IRR, the IRR is widely used in practice as it shows the result as a %, which is popular for comparison with money market rates. Financial managers seem to prefer it, as it can then be compared to a hurdle rate, rather than the comparison of cash values for choosing between projects. Specifically, according to Collier and Gregory (1994), NPV method used in the hotel industry is the least popular in comparison with the IRR. The explanation of this phenomenon is based on the fact that IRR provides a ranking of projects of different size and time scale without the need for a predetermined discount rate, as it is required by the NPV method. In addition, the availability of computer software greatly assists in the calculation of this method and this has also probably lead to an increase in its usage. Despite of the above, the IRR can give misleading results in certain circumstances.

On the other hand, the payback period is widely used in practice than NPV for a variety of reasons. Specifically, it is a particularly useful approach for ranking projects where a firm faces liquidity problems and requires a fast repayment of investments. In addition, it is appropriate when managers make risky investments in uncertain market that are subject to fast planning or where future cash flows are difficult to predict due to inflation.

Furthermore, payback period is an easy screening device, which does not require a lot of time in order that to be calculated. On the other hand, it is attractive by managers as it is easily understood, assists fast communication, and signals good investment decisions at the earliest opportunity. Specifically, a survey conducted by Pike & Neale (1993)(see appendix 2), suggested that the payback method is used in the great majority (94%) by 100 large UK companies. Although it remains a traditional ‘rule-of-thumb method’ with limited theoretical justification because it ignores the timing of cash flows and the time value of money, it provide in practice a fair approximation to the NPV. In addition, it does not take any account of the size of the project, and does not give any indication of the rate of return.

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Moreover, the ROCE (ARR) method in spite of its theoretical limitations, namely the lack to take into account the time value of money, it is proved to be very popular in practice. In more details, according to Pike & Neale (1993), ARR is used in half of the 100 UK companies surveyed. Its popularity is due to the fact that it is easily understood and that it uses profits rather than cash flows and hence it can be easily calculated from financial statements.

Problems associated with calculating the discount rate

The main difficulty in calculating the discount rate is to find the appropriate balance between the equity and debt capital. In more details, the cost of equity capital may not be the appropriate discount rate to use in NPV calculations if the project being appraised has not the same level of systematic risk as the systematic risk of the company’s existing cash flows.

On the other hand, both projects are not fully depreciated. The purpose of depreciation charge is to spread the cost of the asset, £ 25000, over its estimated two years life. Moreover, it depends what depreciation method the company will use, the straight line or sum-of-the years-digits method. The reason behind that is that different methods provide different yearly net income figures, which can affect the financing decision of the company and hence the discount rate calculations. For example, in our case there is a remaining £12000, which is not fully depreciated. The above can influence the net profits, cash flows calculations and therefore the discount rates in terms of seeking new sources of finance.

Moreover, the impact of working capital on investment decision is very important as it can influence substantially the stability of the discount rate. For example, additional cash may be needed to fund the higher levels of raw materials, finished goods, and amounts owing by customers and suppliers. The sources of financing to cover the above short-term liabilities can result to the issue of a new debenture or bank overdraft, which will affect negatively the pre-planned investment project and the already calculated discount rate. Therefore, it is essential that calculations of the acceptability of the investment must incorporate the cash flows associated with changes in working capital.

On the other hand, the way of calculating the cost of equity (Ke) can influence the accuracy of the discount rate. In more details, Ke can be calculated through the dividend growth model or the capital asset pricing model (CAPM). The first model can be illustrated as follows:

D1 (1+g) Ke = ----------------- + g P0 Where : Ke = cost of equity D1 = dividend next year Po = current price per share g. = expected annual growth in dividends

The above model provides a simple approach to finding the cost of capital but in practice, it is difficult to establish a value for g, the growth rate, with any certainty.

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Estimating the future on the basis of the past is never a reliable forecasting technique. This is obvious as, the sector of the economy that the firm operates can change from high-growth sector to low-growth sector. Other factors that can influence g is government economic policy, especially with regard to taxation. In addition, firm –specific factors such as the type of product, and managerial expertise( Pilbeam, 1998, p. 179)

Furthermore, there are data input difficulties incorporated with this model such as taxation. Specifically, the major problem with the presence of taxation is that it can interfere with the value equivalence between dividends and retained earnings. As a result, some shareholders may prefer dividends generated through selling part of their shareholding because the rate of capital gains tax may be lower than their marginal income tax rate, which would be imposed upon company-distributed dividends. In contrast, other shareholders may prefer company distributed dividends because their marginal tax rate results in less tax being paid than the combined effect of capital gains tax and transactions costs generated through selling part of their shareholding( Lumby.St, 1991.p.480). Therefore, it is obvious that in case of taxation regime changes it will arise a conflict between the two parties if they have to change their dividend policy or not. The above can lead to inaccurate estimation of the cost, and therefore influence negatively the discount rate.

Furthermore, the calculation of the Ke through the CAPM model can create difficulties in calculating the WACC. This model can be illustrated as following:

Ke = rf + (rm – rf)

Where: Ke is the cost of equity capital Rf is the return on a risk-free security Rm is the expected return on the market portfolio is the beta coefficient, which measures a stock’s sensitivity to market fluctuations

The above model apart from conceptual difficulties, it suffers from data input difficulties. In more details, the CAPM is a single-period model and therefore the rate obtained is the return expected over the next time period. In contrast NPV is a multi-period model. Moreover, there is a data input problem with the three of the CAPM variables. Specifically, according to (Lumby. St, 199, p.337), the risk free return is risk free in money terms, and it is not genuinely risk-free in consumption or purchasing power terms. In addition, it is sometimes difficult to select the appropriate risk free rate for the proposed investment. It can vary its calculation from the yield curve to the treasury or government stock.

Furthermore, the model is based on assumptions that do not hold in reality. For example, under a perfect market the required return is entirely determined by the company’s beta. In addition, as beta is a characteristic of an asset in relation to an index, then for every index there will be a beta for every asset. These betas may or may not be the same. (Roll’s critique 1977&1978).

The approach also assumes that the past is an accurate indicator of the future. This is not necessarily true as market is imperfect and therefore share prices may be

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influenced by other factors such as: interest rates, inflation, and exchange rates (Pari & Chen, 1984,p.121-130). Consequently, it is obvious that by taking into consideration all these problems that CAPM face, it becomes difficult to predict accurately the cost of equity and therefore the WACC.

On the other hand, the cost of debt (Kd) can create problems in calculating the discount rate. In more details, the first problem is taxation. It is often very difficult to estimate accurately the tax impacts on debt capital (Lumby. St, 1991.p338). For example, corporation taxes that are paid 12 months in arrears can be forgotten to be included in the discounting calculations. In addition, most debt capital in the real world is unquoted and is issued in highly complex, and exotic forms (Lumby. St, 1991.p338). For example, conversion of loan stock to equity with incorporation of taxes is a complicated procedure, which can result to a misleading Kd and therefore to a false discount rate.

Furthermore, many companies raise floating rate debt capital. With floating rate debt capital, the interest rate is variable, and is altered every three or six months. The Kd will therefore fluctuate as market conditions vary. Therefore, floating rate become difficult to incorporate into the WACC. The best solution to this problem is to replace the floating rate with an equivalent fixed interest debt capital.

On the other hand, every company faces two types of risks. Financial and business risk. Financial risk arises through gearing, which indicate the % of finance by equity and debt. According to the traditional view, the capital structures of the company influence the WACC based on the perception of risk. As a result, there is a point that increase gearing to a certain point reduces WACC, and is known as the optimum level of gearing. However, Miller and Modigliani (MM) (1958), have proposed that gearing make no difference to the cost of capital (see appendix 4). Despite of the above, the theories remain unproved, and therefore gearing influence the cost of capital.

Moreover, other problems associated with calculating the appropriate WACC is the risk factor such as operational, business, or financial. To eliminate this factor, companies can use different techniques such as sensitivity analysis, probabilities, expected values, and ‘best’, ‘most likely’, and ‘worst’ forecasts. The best method is sensitivity analysis, as it is used to evaluate any changes in the cost of capital, the length of the project, and sales volumes.

On the other hand, other factors that can change the WACC is taxation and capital allowances. These incremental tax cash flows should be included in the cash flow. When taxation is ignored in the DCF, the discount rate will reflect the pre-tax rate required on capital investments. Specifically, financial managers must pay particular attention to the time- lag between when the profit is earned on a project, when cash is received, and when tax will be payable as it can affect the profitability of the project.

Finally, inflation can affect substantially the calculation of the WACC. In more details, inflation may be general affecting prices of all kinds, or specific to particular prices. For example, specific wages or labour costs can be increased at different level of inflation from the general rate. In our case, if we assume that the project will take place in high inflation country, then prices must change almost daily in order to maintain sufficient cash to replace inventory and keep operating. Therefore, if future

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rate of inflation can not be predicted accurately, then the manager must plan to obtain extra finance or ‘contingency funds’ if inflation exceeds expectations. Consequently, it is obvious that as inflation affects financing needs, it also affect gearing, and so the cost of capital.

Conclusion & Recommendations

Consequently, it is obvious from the above calculation that project A is the best selection than project B. The combination of different appraisal methods can help the managers to verify and identify the best choice. In addition, it was proved that NPV is the best method in theory only. In practice widely used methods are the payback, the internal rate of return, and the accounting rate of return.

On the other hand, the monitoring and control of capital projects is as important as the initial evaluation. The general manager needs to be aware of the implications of inflation, taxation, and risk on the capital investment decision and how to assess the effect of these factors in practice.

Furthermore, the cost of capital is an important concept to be understood in all types of organisations. All sources of funds have a cost of servicing associated with them, either in the form of variable or fixed charges. Therefore, organisations must try to balance their gearing by issuing more equity than debt capital. For example, bank overdraft issued by proprietors of X Co is a risky decision as it is extended to two years and is not based on short-term finance. Consequently, accurate determination of the cost of debt and equity is very important as this figure represents the discount rate. An estimate which is too low means that unprofitable projects will be accepted. In contrast, if the figure is higher than the actual level, this may result in profitable projects being rejected.

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Finally, it is generally believed that increased gearing up to a certain level reduces WACC. However, Miller & Modigliani have rejected this hypothesis. The theories remain unproved and consequently the general consensus is that gearing does have some bearing on the resultant cost of capital.

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Documents

Introduction to Corporate Finance