tyuiopasdfghjklzxcvbnmqwertyui opasdfghjklzxcvbnmqwertyuiopa sdfghjklzxcvbnmqwertyuiopasdfg hjklzxcvbnmqwertyuiopasdfghjkl FINANCIAL MANAGEMENT zxcvbnmqwertyuiopasdfghjklzxc For MBA & PGDM vbnmrtyuiopasdfghjklzxcvbnmqw ertyuiopasdfghjklzxcvbnmqwerty uiopasdfghjklzxcvbnmqwertyuiop asdfghjklzxcvbnmqwertyuiopasdf ghjklzxcvbnmqwertyuiopasdfghjk lzxcvbnmqwertyuiopasdfghjklzxc vbnmqwertyuiopasdfghjklzxcvbn mqwertyuiopasdfghjklzxcvbnmq wertyuiopasdfghjklzxcvbnmqwer tyuiopasdfghjklzxcvbnmqwertyui opasdfghjklzxcvbnmqwertyuiopa sdfghjklzxcvbnmrtyuiopasdfghjkl zxcvbnmqwertyuiopasdfghjklzxc vbnmqwertyuiopasdfghjklzxcvbn mqwertyuiopasdfghjklzxcvbnmq6/4/2012 SAUMYA RANJAN BISWAL

FINANCIAL MANAGEMENT Financial management is an academic discipline which is concerned with decision-making. This decision is concerned with the size and composition of assets and the level and structure of financing. In order to make right decision, it is necessary to have a clear understanding of the objectives. Such an objective provides a framework for right kind of financial decision making. The objectives are concerned with designing a method of operating the Internal Investment and financing of a firm. There are two widely applied approaches, viz. (a) Profit maximization and (b) Wealth maximization. The term 'objective' is used in the sense of an object, a goal or decision criterion. The three decisions Investment decision, financing decision and dividend policy decision are guided by the objective. Therefore, what is relevant - is not the over-all objective but an operationally useful criterion: It should also be noted that the term objective provides a normative framework. Therefore, a firm should try to achieve and on policies which should be followed so that certain goals are to be achieved. It should be noted that the firms do not necessarily follow them. Profit Maximization as a Decision Criterion Profit maximization is considered as the goal of financial management. In this approach, actions that Increase profits should be undertaken and the actions that decrease the profits are avoided. Thus, the Investment, financing and dividend also be noted that the term objective provides a normative framework decisions should be oriented to the maximization of profits. The term 'profit' is used in two senses. In one sense it is used as an owner-oriented. In this concept it refers to the amount and share of national Income that is paid to the owners of business. The second way is an operational concept i.e. profitability. This concept signifies economic efficiency. It means profitability refers to a situation where output exceeds Input. It means, the value created by the use of resources is greater that the Input resources. Thus in all the decisions, one test is used I.e. select asset, projects and decisions that are profitable and reject those which are not profitable.

The profit maximization criterion is criticized on several grounds. Firstly, the reasons for the opposition that are based on misapprehensions about the workability and fairness of the private enterprise itself. Secondly, profit maximization suffers from the difficulty of applying this criterion in the actual real-world situations. The term 'objective' refers to an explicit operational guide for the internal investment and financing of a firm and not the overall business operations. We shall now discuss the limitations of profit maximization objective of financial management.

1) Ambiguity: The term 'profit maximization' as a criterion for financial decision is vague and ambiguous concept. It lacks precise connotation. The term 'profit' is amenable to different interpretations by different people. For example, profit may be long-term or short-term. It may be total profit or rate of profit. It may be net profit before tax or net profit after tax. It may be return on total capital employed or total assets or shareholders equity and so on. 2) Timing of Benefits: Another technical objection to the profit maximization criterion is that It Ignores the differences in the time pattern of the benefits received from Investment proposals or courses of action. When the profitability is worked out the bigger the better principle is adopted as the decision is based on the total benefits received over the

working life of the asset, Irrespective of when they were received. The following table can be considered to explain this limitation. 3) Quality of Benefits Another Important technical limitation of profit maximization criterion is that it ignores the quality aspects of benefits which are associated with the financial course of action. The term 'quality' means the degree of certainty associated with which benefits can be expected. Therefore, the more certain the expected return, the higher the quality of benefits. As against this, the more uncertain or fluctuating the expected benefits, the lower the quality of benefits.

The profit maximization criterion is not appropriate and suitable as an operational objective. It is unsuitable and inappropriate as an operational objective of Investment financing and dividend decisions of a firm. It is vague and ambiguous. It ignores important dimensions of financial analysis viz. risk and time value of money. An appropriate operational decision criterion for financial management should possess the following quality. a) It should be precise and exact.

b) It should be based on bigger the better principle. c) It should consider both quantity and quality dimensions of benefits. d) It should recognize time value of money. Wealth Maximization Decision Criterion Wealth maximization decision criterion is also known as Value Maximization or Net Present-Worth maximization. In the current academic literature value maximization is widely accepted as an appropriate operational decision criterion for financial management decision. It removes the technical limitations of the profit maximization criterion. It posses the three requirements of a suitable operational objective of financial courses of action. These three features are exactness, quality of benefits and the time value of money. i) Exactness: The value of an asset should be determined In terms of returns it can produce. Thus, the worth of a course of action should be valued In terms of the returns less the cost of undertaking the particular course of action. Important element in computing the value of a financial course of action is the exactness in computing the benefits associated with the course of action. The wealth maximization criterion is based on cash flows generated and not on accounting profit. The computation of cash inflows and cash outflows is precise. As against this the computation of accounting is not exact. ii) Quality and Quantity and Benefit and Time Value of Money: The second feature of wealth maximization criterion is that. It considers both the quality and quantity dimensions of benefits. Moreover, it also incorporates the time value of money. As stated earlier the quality of benefits refers to certainty with which benefits are received In future. The more certain the expected cash inflows the better the quality of benefits and higher the value. On the contrary the less certain the flows the lower the quality and hence, value of benefits. It should also be noted that money has time value. It should also be noted that benefits received in earlier years should be valued highly than benefits received later. The operational implication of the uncertainty and timing dimensions of the benefits associated with a financial decision is that adjustments need to be made in the cash flow pattern. It should be made to incorporate risk and to make an allowance for differences in the timing of benefits. Net present value maximization is superior to the profit maximization as an operational objective. It involves a comparison of value of cost. The action that has a discounted value reflecting both time and risk that exceeds cost is said to create value. Such actions are to be undertaken. Contrary to this actions with less value than cost, reduce wealth should be rejected. It is for these reasons that the Net Present Value Maximization is superior to the profit maximization as an operational objective.

PROFIT MAXIMIZATION VS WEALTH MAXIMIZATION PROFIT MAXIMISATION - It is one of the basic objectives of financial management. Profit maximization aims at improving profitability, maintaining the stability and reducing losses and inefficiencies. Profit in this context can be seen in 2 senses. 1. Profit maximization for the owner. 2. Profit maximization is for others. Normally profit is linked with efficiency and so it is the test of efficiency. However this concept has certain limitations like ambiguity i.e. the term is not clear as it is nowhere defined, it changes from person to person. Quality of profit - normally profit is counted in terms of rupees. Normally amt earned is called as profit but it ignores certain basic ideas like wastage, efficiency, employee skill, employees turnover, product mix, manufacturing process, administrative setup. Timing of benefit / time value of profit - in inflationary conditions the value of profit will decrease and hence the profits may not be comparable over a longer period span. Some economists argue that profit maximization is sometimes leads to unhealthy trends and is harmful to the society and may result into exploitation, unhealthy competition and taking undue advantage of the position. WEALTH MAXIMISATION - One of the traditional approaches of financial management , by wealth maximization we mean the accumulation and creation of wealth , property and assets over a period of time thus if profit maximization is aimed after taking care , of its limitations it will lead to wealth maximization in real sense, it is a long term concept based on the cash flows rather than profits an hence there can be a situation where a business makes losses every year but there are cash profits because of heavy depreciation which indirectly suggests heavy investment in fixed assets and that is the real wealth and it takes into account the time value of money and so is universally accepted. IMPORTANT FUNCTIONS OF THE FINANCIAL MANAGER: The important function of the financial manager in a modern business consists of the following: 1. Provision of capital: To establish and execute programs for the provision of capital required by the business. 2. Investor relations: to establish and maintain an adequate market for the company securities and to maintain adequate liaison with investment bankers, financial analysis and share holders. 3. Short term financing: To maintain adequate sources for companys current borrowing from commercial banks and other lending institutions. 4. 5. Banking and Custody: To maintain banking arrangement, to receive, has custody of accounts. Credit and collections: to direct the granting of credit and the collection of accounts due to the company including the supervision of required arrangements for financing sales such as time payment and leasing plans. 6. Investments: to achieve the companys funds as required and to establish and co-ordinate policies for investment in pension and other similar trusts. 7. Insurance: to provide insurance coverage as required.

8.

Planning for control: To establish, co-ordinate and administer an adequate plan for the control of operations.

9.

Reporting and interpreting: To compare information with operating plans and standards and to report and interpret the results of operations to all levels of management and to the owners of the business.

10. Evaluating and consulting: To consult with all the segments of management responsible for policy or action concerning any phase of the operation of the business as it relates to the attainment of objectives and the effectiveness of policies, organization structure and procedures. 11. Tax administration: to establish and administer tax policies and procedures. 12. Government reporting: To supervise or co-ordinate the preparation of reports to government agencies. 13. Protection of assets: To ensure protection of assets for the business through internal control, internal auditing and proper insurance coverage. Chapter 2 Time Value of Money Introduction Time Value of Money (TVM) is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. TVM is based on the concept that a dollar that you have today is worth more than the promise or expectation that you will receive a dollar in the future. Money that you hold today is worth more because you can invest it and earn interest. After all, you should receive some compensation for foregoing spending. For instance, you can invest your dollar for one year at a 6% annual interest rate and accumulate $1.06 at the end of the year. You can say that the future value of the dollar is $1.06 given a 6% interest rate and a one-year period. It follows that the present value of the $1.06 you expect to receive in one year is only $1. A key concept of TVM is that a single sum of money or a series of equal, evenly-spaced payments or receipts promised in the future can be converted to an equivalent value today. Conversely, you can determine the value to which a single sum or a series of future payments will grow to at some future date. You can calculate the fifth value if you are given any four of: Interest Rate, Number of Periods, Payments, Present Value, and Future Value. Each of these factors is very briefly defined in the right-hand column below.

PART I: Single Sum. Time Value of Money: Know this terminology and notation FV PV i t Future Value Present Value Rate per period # of time periods (1+i)t Future Value Interest Factor [FVIF] 1/(1+i)t Present Value Interest Factor [PVIF]

Question: Why are (1+i) and (1+i)t called interest factors? Answer: 1. Start with simple arithmetic problem on interest: How much will $10,000 placed in a bank account paying 5% per year be worth compounded annually?

Answer:

Principal +

Interest

$10,000 + $10,000 x .05 = $10,500 2. Factor out the $10,000. 10,000 x (1.05) = $10,500 3. This leaves (1.05) as the factor.

1. Find the value of $10,000 earning 5% interest per year after two years. Start with the amount after one year and multiply by the factor for each year. [Amount after one year] x (1.05) = = = [$10,000 $11,025. . x (1.05)]2

x (1.05)

$10,000 x (1.05)

So (1+i)t = (1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i) (1+i) for t timesFuture Value Find the value of $10,000 in 10 years. The investment earns 5% per year. FV = $10,000(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i) FV = $10,000(1.05)(1.05)(1.05)(1.05)(1.05)(1.05)(1.05)(1.05)(1.05)(1.05) FV = $10,000 x (1.05)10 = $10,000 x 1.62889 = $16,289 Find the value of $10,000 in 10 years. The investment earns 8% for four years and then earns 4% for the remaining six years. FV = $10,000(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i) FV = $10,000(1.08)(1.08)(1.08)(1.08)(1.04)(1.04)(1.04)(1.04)(1.04)(1.04) FV = $10,000 x (1.08)4 x (1.04)6 FV = $17,214.53 Present Value: Same idea, but begin at the end. Rearrange the Future value equation to look like this: PV = FV [(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)(1+i)]

PV = FV (1+i)t

[2]

Example: How much do I need to invest at 8% per year, in order to have $10,000 in__. a. One year: b. Two years: c. Ten years PV =10,000 (1.08) = $9,259.26 PV = $10,000 (1.08) (1.08) OR $10,000 (1.08)2 = $8,573 PV = $10,000 (1.08)10 = $10,000 2.1589 = $4,632

Rate of Return START WITH SAME RELATIONHSIP: FV = PV x (1+i)t Solve for i. (1+i)t =FV/PV. 1+i = (FV/PV)1/t i = (FV/PV)1/t-1. Question: Solution: $17,910 (1+i)10 = $17,910/10,000 = 1.7910 (1+i) = (1.7910)1/10

An investor deposits $10,000. Ten years later it is worth $17,910. What rate of return did the investor earn on the investment? = $10,000 x (1+i)10

= 1.060

i = .060 = 6.0% Finding the Future Value Find the value of $10,000 today at the end of 10 periods at 5% per period.

KEY RELATIONHSIP:

1. Scientific Calculator: Use [yx] y = (1+i) = 1.05 and x =t= 10. 1. Enter 1.05. 2. Press [y ].x

3. Enter the exponent.

FV = PV x (1+i)t

4. Enter [=]. 5. Multiply result by $10,000.

2. Spreadsheet:

3. Financial calculator. You may need to input something like this. Specific functions vary. Be sure to consult the calculators manual!!!!!! n [N] 10 i [I/YR] 5 PV 10,000 PMT 0 FV ?

NOTE: The future value will be negative, indicate an opposite direction of cash flow.

1. Set the calculator frequency to once per period. 2. Enter negative numbers using the [+/-] key, not the subtraction key. 3. Be sure the calculator is set in the END mode. Fundamental Idea. Question: What is the value of any financial asset? Answer: Finding the Present Value Find the present value of $10,000 to be received at the end of 10 periods at 8% per period. Scientific Calculator Scientific Calculator: Use [yx ] where y = 1.08 and x = -1,-2, or -10. 1. Enter 1.08. 2. Press [yx] 3. Enter the exponent as a negative number 4. Enter [=]. 5. Multiply result by $10,000. Spreadsheet The present value of its expected cash flows.

KEY RELATIONHSIP:

PV = FV (1+i)t

Financial calculator. You may need to input something like this. Specific functions vary. Be sure to consult the calculators manual!!!!!! n [N] c. 10 i [I/YR] 8 PV 10,000 PMT 0 FV ?

The present value will be negative, to indicate the opposite direction of cash flow. Finding the [geometric average] rate of return: Scientific Calculator To find i, use [yx ] and [1/x]. 1. Enter 1.7910, 2. Press [yx] 3. Enter the exponent 10 then press [1/x] 4. Press [=]. 5. Subtract 1

KEY RELATIONHSIP:

(1+i)t=FVPV (1+i) = (FVPV)1/t

2. Spreadsheet

3. Financial Calculator. (Your financial calculator may differ. Consult your manual.)

n [N] 10

i [I/YR] ? Answer i = 6%

PV -10,000

PMT 0

FV 17,910

Question: Today your stock is worth $50,000. You invested $5,000 in the stock 18 years ago. What average annual rate of return [i] did you earn on your investment? 13.646%.

Answer:

Question: The total percentage return was 45,0005000=900%. Why doesnt the average rate of return equal 50%, since 900%18 = 50%?

FUTURE VALUE WHEN RATES OF INTEREST CHANGE.

FV = PV x (1+i1) x (1+i2) x (1+i3) x x (1+it).Example: You invest $10,000. During the first year the investment earned 20% for the year. During the second year, you earned only 4% for that year. the end of the two years? FV = PV x (1+i1) x (1+i 2) = $10,000 x (1.20`) x (1.04) = $12,480. Question: The arithmetric average rate of return is 12%, what is the geometric average rate of return? Answer: An average rate of return is a geometric average since it is a rate of growth. The 12% is the arithmetic average. The geometric average rate of return on the investment was 11.7%. i = (FV/PV)1/t-1 = (12,480/10000)1/2-1 = .1171 OR How much is your original deposit worth at

i = (1.20) (1.04) 1 = 0.1171Although 20% and 4% average to 12%, the $10,000 not grow by 12%.

Important:

[$10,000 x (1.12)2= 12,544 NOT $12,480]. COMPOUNDING PERIODS Up to this point, we have used years as the only time period. Actually, all the previous examples could have been quarters, months, or days. The interest rate and time period must correspond. Example: Problem 1. Find the value of $10,000 earning 5% interest per year after two years. Problem 2. Find the value of $10,000 earning 5% interest per quarter after two quarters. Both problems have same answer

$10,000 x (1.05)2 = $11,025. However: In the first problem t refers to years and i refers to interest rate per year. In the second problem t refer to quarters and i to interest rate per quarter.

FVt = PV x (1+i)t. t = number of periods i = interest for the period.

Alternatively, FVtm = PV x (1+i/m) t m. m= periods per year, t= number of years, i = the interest per year [APR].

Example: What will $1,000 be worth at the end of one year when the annual interest rate is 12% [This is the APR.] when interest is compounded: Annually: Monthly: Daily: t=1 t=12 i =12% FV1 = PV x (1+i)1 = $1,000 x (1.12)1 i = 3% FV4 = PV x (1+i)4 = $1,000 x (1.03)412

= $1,120. = $1,125.51.

Quarterly: t=4

i =1% FV12 = $1,000 x (1.01) = $1,000 x (1.126825) = $1,126.825.

t=365 i = (12%365) = 0.032877% FV365 = $1,000 x (1.00032877)365= $1,000 x (1.12747) = $1,127.47.

n [N] 1 4 12 365

i [I/YR] 12 3 1 .032877

PV 1,000 1,000 1,000 1,000

PMT 0 0 0 0

FV ? ? ? ?

How about compounding at every instant? E. CONTINUOUS COMPOUNDING: [Used in Black Scholes option pricing model.] tm limm

1 + __i__ m

=

e

i

t

Example: What is $1,000 worth in one year if compounded at 12% continuously. FV = $1,000 x e.12

= This is $.03

$1,000 more

x

1.127497 than

= daily

$1,127.50 compounding.

Try this on your calculator. Find the ex button. e.12 = 1.12749 Present Value-.10 x 3

Interest

Factor

=

[e

-i

t

]

Problem: What is the present value of $10,000 to be received 3 years from today compounded continuously at 10%?PV = $10,000 x e = $10,000 x 0.74082=$7,408 Try this on your calculator. Find the ex button. e-0.3 = 0.74082 Review Fundamentals of Valuation part II Multiple Periods: Uneven and Even (Annuities) Periodic Uneven Cash Flows What is the value of the following set of cash flows today? Year and Cash Flow 1: $ 300 2: $ 500 3: $ 700 4: $ 1000 The interest rate is 8% for all cash flows.

Solution: Find Each Present Value and Add

300 500 700 1000 + + + = 1 2 3 1.08 1.08 1.08 1.08 4277.78 428.67 555.68 735.03 = 1997.16

Periodic Cash Flow: Even Payments An annuity is a level series of payments. For example, four annual payments, with the first payment occurring exactly one period in the future is an example of an ordinary annuity.

$1,0000 1

$1,0002

$1,0003

$1,0004

A. Present value of an annuity: The present value of each of the cash flows is the value of the annuity. This could be done one at a time, but this might be tedious.

Annuity Present Value Interest Factor PVIFA = [1/(1+i) + 1/(1+i)2 + ... + 1/(1+i)t]

PI A VF PI A VF

=

1 /(1 + ij =1

t

)

j

1 /( + i ) 1 1 = . it

Example: What is the present value of a 4-year annuity, if the annual interest is 5%, and the annual payment is $1,000? i = PV 5%; = 1,000 PMT /(1.05) = + $1,000; 1,000/(1.05)2 t + =4; PV = ?4

1,000/(1.05)3+ Long

1,000/(1.05) way.

Factor out the single sum interest rate factors: PV = 1,000 x [1/(1.05) + 1/(1.05)2+1/(1.05)3+ 1/(1.05)4] =

Short WayPV = 1,000 x [PVIFA (4,5%)] = Calculate: PVIFA(4,5%) = 1-1/(1+i)t = 1- PVIF4,5% i PV = 1,000 x [3.5460] = $3,546. 5% .05 1- 0.8227 = 3.54595.

Finding the Future Value of an annuity on a: 1. Scientific Calculator. To calculate PVIFA using scientific calculator: FIRST FIND: PVIF4,5% = 1/(1+i)t = 1/(1.05)4 = 0.82270 THEN FIND: PVIFA(4,5%) = 1-1/(1+i)t i = 1,000 x [3.5460] 2. Using a spreadsheet. = 1i PVIF .05 = $3,546. 10.8227 = 3.54595.

3. Using a financial calculator, the Present Value of an annuity.

n [N] 4

i [I/YR] 5

PV ? PV= $3,546.

PMT -1000

FV 0

Note:

Most financial calculators require i [I/YR] to be a percentage.

That is enter a 5, not .05.

However, Excel requires .05 or 5%. B. Future value of an annuity:

Annuity Future Value Interest Factor FVIFA = [1+ (1+i) + (1+i) + ... + (1+i) ].2 t-1

FVIFA =

(1 + i )j=0

t 1

t

(1 + i )t 1 FVIFA = ipayment is $1,000? i = 5%; PMT = $1,000; t =4; FV = ? $1,000x $1,000 x [FVIFA (4,5%)] = $1,000 x [4.3101] = $4,310.1 Finding FVIFA 1. Using scientific calculator: FIRST FIND: FVIF = (1+i)t [1+

.

Note: Last Payment earns no interest in ordinary annuity. The interest factor on that payment is 1. The first payment earns interest for t-1 periods, not t periods.

Example: What is the future value of a 4-year annuity, if the annual interest is 5%, and the annual

(1.05)

+

(1.05)2

+

(1.05)3]

=

=

(1.05)4

=

1.2155

THEN:

FVIFA(t,i) = FVIFA(t,i) =

(1+i)t -1 i FVIF4,5%- 1 5%

=

FVIF- 1 i 1.2155-1= 4.3101

Use Short Cut Formula.

.05

2. Using a Spreadsheet

3. Value of an annuity:

Using a financial calculator, the Future

n [N] 4 FV = $4,310

i [I/YR] 5

PV 0

PMT -1000

FV ?

Question: How much would you need to deposit every month in an account paying 6% a year to accumulate by $1,000,000 by age 65 beginning at age 20?

Data: FV = $1,000,000 i = 6%12 = 0.5% per month n = (65-20) x 12 = 45 x 12 = 540 months. Answer: PMT = $362.85

PMT = ?

C. RATE OF RETURN OF AN ANNUITY You borrow $60,000 and repay in 8 equal annual installments of $12,935 with the first payment made exactly 1 year later. To the nearest percent, what rate of interest are you paying on your loan? Difficult without financial calculator. Can use table to find answer to the nearest percent. Data: i=? PV = $60,000 PMT=$12,935 t = 8 years

Relationship: PV = PMT x PVIFA(t, i) 1. Solution: (Trial and Error with Table) PVIFA(t, i) = PV/PMT= $60,000/12,935 = 4.6386Table ..... 14%.... : 8 .. 4.6389 .. :

Therefore: PVIFA = 4.6386. So> i = 14% 2. (Trial and Error using a spreadsheet program)

3. calculator)

(Trial and Error using a financial

n [N] 8

i [I/YR] ? i = 14%

PV 60000

PMT -12935

FV 0

D. Example of Annuity with quarterly compounding: An investment of $3000 per quarter for 6 years at annual interest rate of 8%, compounded quarterly, will accumulate by the end of year 6 to: Solution: FV = ? PMT = $3,000 FV = FV = t = 24 i = 2% PMT x FVIFA (t, i). $3,000 x [30.422] = $91,266.

n [N] 24

i [I/YR] 2

PV 0

PMT -3000

FV ? $91,266

Review Problems with solutions. 1. This one: is a typical mortgage problem. You borrow $80,000 to be repaid in equal monthly installments for 30 years. The APR is 9%. What is the monthly payment? PV = $80,000 i t=360 PMT = ? $80,000 PMT = = PMT x 124.282 $643.70 =0.75%,

n [N] 360

i [I/YR] .75

PV -80000

PMT ?

FV 0

2. Try this one. You make equal $400 monthly payments on a loan. The interest rate equals 15% APR, compounded monthly. The loan is for 12 years. What is the amount of the loan? Answer: PV = $26,651

3. Retire with a million: How much would must you deposit monthly in an account paying 6% a year [APR], compounded monthly, to accumulate $1,000,000 by age 65 beginning at age 30?

Answer:

PMT

=

$701.90

n [N] 420 4.

i [I/YR] 0.50

PV 0

PMT ?

FV 1000000

Using a financial calculator for annuity calculations: Calculate the future value of $60.00 per year at 7% per year for eight years.

n [N] 8

FV = 607

i [I/YR]

(1 +0.07PVj=0

7

)

j

PMT -60 FV = $615.50 5.

FV ?

(1.07 )8 1 FV = 60 .07 FV = $615 .5n[N] 24 FV = $1,217.60 i [I/YR] 0.5 PV 0

Calculate the future value of

$50.00 per

month at 6% APR for 24 months PMT -50 FV ?

6. Calculate the present value of $500 per year at 6% per year for 5 years (monthly compounding).

n[N] 5 PV=$2,106 7.

i [I/YR] 6

PV ?

PMT -500

FV 0

You borrow $5,000 and repay the loan with 12 equal monthly payments of $500? Calculate the interest rate per month and the APR.

n[N] 12

i [I/YR] ?

PV 5,000

PMT -500

FV 0

i = 2.92% per month. APR = i x 12 APR = 2.92% x 12 = 35.04 8. Problem on inflation. You will receive $100,000 dollars when you retire, forty years from today. If inflation averages 3% per year for the next forty years, how much would that amount be worth measured in today's dollars? (Note, this is not a time value of money problem, but it solved with a similar calculation. Such adjustments are necessary to overcome money illusion] Solution: $100,000 (1.03)40 =100,000 3.26204 = $ 30,655 D. Annuity Due

$1,000 $1,0000 1

$1,0002

$1,0003 4

Question:

Compare the payments of the annuity due, above, with those of the ordinary annuity earlier.

What is the difference? How does this difference affect its value? Answer: Each payment in an annuity due occurs one period earlier than it would in ordinary annuity. Both present value and future value of each payment in an annuity due if (1+i) times greater than it would be for an ordinary annuity. Question: What is the present value of the above four-year annuity due? $1,000 x [1 + 1/(1+i) + 1/(1+i)2 + 1/(1+i)3] = = $1,000 x (1+i) x [1/(1+i) + 1/(1+i)2 + 1/(1+i)3+1/(1+i)4] $1,000 x (1+i) x PVIFA i,4

PV interest factor of an annuity due is: (1+i)PVIFA FV interest factor of an annuity due is: (1+i)FVIFA

Problem.

What is the present value of an annuity due of five $800 annual payments discounted at 10%? 800 x (1.10)xPVIVA 10%,5 = 800 x(1.10)x 3.79079 x = 800 x 4.16987 = $3,335.9

Note:

Financial calculators have a BEGIN and END mode. The above assumes the END mode. If the calculator is set in the BEGIN mode, it calculates an annuity due.

Problem.

What

is

the

present

value

of

an

annuity

of

five

annual

$800

payments

discounted at 10%?

The first payment is due in one-half year from today. 800 x (1.10)1/2 xPVIVA10%,5 = 800 x(1.04881)x 3.79079 x = 800 x 3.97581 = 3,180.7

Chapter 3

Introduction to risk & return The nature of risk Risk is associated with uncertainty (about the future), as opposed to variability (so the margin note on page 237 of the text is potentially misleading). There are very few aspects about the future of which one can be 100% certain. The solar system and mortality are candidates, but the uncertain timing of the latter leaves only the solar system. There is nothing in the future in the world of commerce and financial management that is 100% certain. Rates of return Rates of return on a personal investment have 3 elements of compensation. Compensation for: Forgoing current consumption; Inflation; Risk. Market rates of interest (designated i) are calculated from cash flows received (or expected to be received) as a result of making an investment. Mkt rates of return are nominal in the sense that they make no allowance for declines in the general purchasing power of money due to inflation (designated r). When rates of inflation are positive, nominal rates of return are higher than real rates of return (designated R). Real rates of return measure investment returns in terms of purchasing power rather than cash, and may be calculated as follows: R = (i r) / (1 + r) Note that this equation and associated symbols are adopted from page 239 of the text. Later in the chapter, R is used to indicate nominal rates of return. A risk-free rate of return (Rf) is identified as the rate of return offered on a short-dated govt security (issued by a credit-worthy govt). Whilst an individual may receive less than the risk-free rate of return on say a bank deposit; in the commercial world all investments that are not risk-free are required to earn a risk premium. A risk premium may be defined as the difference between the required or expected rate of return and the risk-free rate. The higher the risk, the higher the risk premium and required rate of return. A required rate of return may be defined as the minimum rate of return necessary to attract an investor to purchase or hold a security (page 256). Historically, the risk premium for the share market as a whole is about 7.7%.

Measuring risk: In any risky situation, a range of outcomes may be possible. By assigning probabilities to each possible outcome, an expected outcome can be defined in the same way as an arithmetic mean. Risk may then be measured as the standard deviation of the expected outcome. When expected outcomes are measured as per cent per year, the standard deviation is measured in the same way (per cent per year) and needs no adjustment to allow for investments of different amounts. However, a coefficient of variation (CV = std deviation divided by expected outcome) can still be calculated as a relative measure of risk. [The CV can also be calculated using dollar values for expected outcomes and associated std deviations.] Calculators should be used to calculate std deviations. 2 types of risk: diversifiable risk & systematic (or systemic) risk In commerce, the total risk associated with an investment can be partitioned into

(1) Diversifiable (or unsystematic, firm-specific or idiosyncratic) risk, and (2) Systematic (or non-diversifiable or market) risk. Reducing risk through diversification: A firm that sells ice-cream can reduce risk by also selling umbrellas. This is the nature of diversification. That is not putting all ones eggs in one basket; an ancient and almost universal concept. If sales of ice-cream and umbrellas were always perfectly negatively correlated, it might be possible to eliminate all risk through diversification. However, this is not possible because sales of all goods are to some extent influenced by general economic (or market or systematic) conditions and are therefore assumed to be, to a greater or lesser extent, positively correlated. [Note that if one places all ones eggs in different baskets, all of which are then placed in the same wheelbarrow, there is no reduction of risk. If the wheelbarrow suffers a mishap, all the eggs may be broken. That is, the security of all baskets is perfectly positively correlated and so there has been no risk reduction through diversification.] Because returns on different investments, although positively correlated, are rarely perfectly positively correlated, it is possible to reduce risk through diversification. For example, if $32 is invested in a single throw of one dice paying $10 per dot, the expected rate of return is 9.375% with a std deviation of 53.37%. If the investment is divided between two dice paying $5 per dot, the expected return is still 9.375%, but the std deviation falls to 37.74%. [Note that: (1) 37.74% = 53.37%

2 . (2) We assume zero correlation between

the two dice, whereas different real world investments are assumed to be positively correlated.]

Reducing portfolio risk through diversification An investment portfolio is a collection of different investments held by a single investor. If the investments are stocks of shares (actively traded in a share-market), most diversifiable risk can be eliminated by holding a balanced portfolio of at least 20 stocks (see Figure 9.5 on page 249). The remaining risk is systematic risk, which cannot be reduced through diversification (although further risk reduction may be achieved by investing offshore). Risk & return Because diversifiable risk can be almost eliminated, the risk premium required from a particular investment, held as part of a diversified portfolio, will depend on its systematic risk, rather than its total risk. Systematic risk is measured in terms of the response of an investments returns to changing mkt conditions. Beta (the Greek letter for b) is the unit used for measuring systematic risk. The beta value of the mkt as a whole is assumed to be 1. The beta value of a particular investment (j) is given by the following equation: j = j mj / m This indicates that the beta value of security j is the standard deviation of returns on security j, multiplied by the coefficient of correlation between the returns on security j and returns on the mkt, divided by the std deviation of returns on the mkt.

The beta value of a security (j) can be calculated through linear regression. That is, the returns on security j (the dependent variable) are plotted against corresponding mkt returns (the independent variable). Beta is then the slope of the line of best fit. See Figures 9.7, 9.8 & 9.9 on pages 254 & 256. Beta values may be calculated in this way using a calculator. [On the Sharp calculator, beta is designated b: 2nd function of the minus key.] The required rate of return on security j (Rj) is then given by the following equation: Rj = Rf + j(Rm Rf) Where Rm indicates the expected return on the mkt as a whole and (Rm Rf) is the expected mkt risk premium. This is the Capital Asset Pricing Model (CAPM). It indicates that the required rate of return on security j is the risk-free rate + the beta value of security j the mkt risk premium.

Remember that historically the risk premium offered by the Australian share-market as a whole has averaged about 7.7%.

Interest rates Interest rates reflect (i) risk and (ii) term to maturity. The relationship between risk and required rates of return is always positive: the higher the risk, the higher the required rate of return. The relationship between term to maturity and required rates of return is referred to as the term structure of interest rates or the yield curve. Yield curves are typically upwards sloping, but can assume a variety of shapes, including downwards sloping. An upwards sloping yield curve can be explained in terms of three different theories. 1. The unbiased expectations theory which postulates that a rising yield curve indicates that the market expects short-term interest rates to rise. 2. The liquidity preference theory which postulates that investors require a liquidity premium to induce them to hold longer-dated, less liquid, securities. The liquidity premium is the difference between forward rates implied by the yield curve and expected future spot rates, and is typically positive. The liquidity premium is typically positive because investors tend to have a preference for shorter-dated securities. 3. The market segmentation theory which postulates that the market is partitioned into segments for which different investors will have preferences. If the market preference for short-dated securities is stronger than for longer-dated securities, yields on the former will be lower than yields on the latter. This could be the case because financial intermediaries such as banks use short-dated securities for liquidity management purposes.

Calculating beta values The appendix to Chapter 9 of the text demonstrates how to calculate a securitys beta value using a calculator. Any calculator with a statistical function can be used it does not have to be a financial calculator. The minimum input data requirement is two observed rates of return for the security and coincidental mkt returns. The calculator is set into its statistical mode and each pair of coincidental returns entered. Mkt returns are entered through the RM key and the coinciding securitys return through the M+ key. After at least two pairs of data have been entered, the line of best fit can be determined in accordance with the linear regression equation: y = a + bx

Where y

= rates of return on the security x a b = mkt rates of return = the value of the y intercept when x = 0 = the slope of the line of best fit = beta.

The Sharp calculator displays beta as the 2nd function of the minus key. Example Coincidental rates of return on security j and the market are as follows: Market 14% 12% 10% Security j 18% 11% 6%

What is the beta value of security j? Note: 1. Returns on security j are more volatile than mkt returns. We should therefore expect security js beta value to be higher than 1 (the beta value of the mkt). 2. Mkt returns are the independent variable and must be entered through the RM key before the value of the dependent variable (return on the security) is entered through the M+ key. Keystrokes: 14 RM 2ndF 2ndF 18 M+ 3 0.9954 12 RM j mj 11 M+ 10 RM 6 M+

beta value of security j coefficient of correlation between returns on security j & the mkt

2ndF 9 2ndF 6 j

4.9216 1.6330

j m

std deviation of returns on security j std deviation of mkt returns

= j mj / m = (4.9216 0.9954) / 1.633 = 3

Required rates of return If the risk-free rate is 5% and the expected mkt return 12.5%, what would be the required rate of return on security j? Answer: Rj = Rf + j(Rm - Rf) = 0.05 + 3 0.075 = 0.275 = 27.5% See if you can draw a graph of this example.

The security mkt line defines required rates of return as a linear function of an investments beta value. Note that it is the required rate of return, rather than the expected rate of return Chapter 4 Sources of finanace 1.0 Introduction This is an informative and analytical report on Sources of finance. The report is written as an assignment of Managing financial resources and decision module of the first semester for the evaluation of our understanding and knowledge of the sources of finance to the lecturer Mr. Chamila. This assignment also tests our knowledge on choosing the appropriate source of finance and financial planning. The report also provides analysis of Singer (Sri Lanka) PLCs balance sheet for sources of finance. All of the information and research for this report is through the World Wide Web. 2.0 Sources of Finance Finance is essential for a businesss operation, development and expansion. Finance is the core limiting factor for most businesses and therefore it is crucial for businesses to manage their financial resources properly. Finance is available to a business from a variety of sources both internal and external. It is also crucial for businesses to choose the most appropriate source of finance for its several needs as different sources have its own benefits and costs. Sources of financed can be classified based on a number of factors. They can be classified as Internal and External, Short-term and Long-term or Equity and Debt. It would be uncomplicated to classify the sources as internal and external. 2.1 Internal sources of finance Internal sources of finance are the funds readily available within the organisation. Internal sources of finance consist of: Personal savings Retained profits Working capital Sale of fixed assets

2.1.1 Personal savings This is the amount of personal money an owner, partner or shareholder of a business has at his disposal to do whatever he wants. When a business seeks to borrow the personal money of a shareholder, partner or owner for a businesss financial needs the source of finance is known as personal savings. 2.1.2 Retained profits Retained profits are the undistributed profits of a company. Not all the profits made by a company are distributed as dividends to its shareholders. The remainder of the profits after all payments are made for a trading year is known as retained profits. This remainder of finance is saved by the business as a back-up in times of financial needs and maybe used later for a companys development or expansion. Retained profits are a very valuable no-cost source of finance. 2.1.3 Working capital Working capital refers to the sum of money that a business uses for its daily activities. Working capital is the difference of current assets and current liabilities (i.e. Working capital = Current assets Current liabilities). Proper working capital management is also vital as it is also a source of finance for a business. Current assets Current assets are also known as cash equivalents because they are easily convertible to cash. Current assets consist of Stock, Debtors, Prepayments, Bank and Cash. These assets are used up, sold or keep changing in the short run.

Stock this refers to the stock of goods available to the business for sale at a given time. It is very important to maintain the right amount of stock of goods for a business. If stock levels are too high it means that too much of money is being held up in the form of stock and if stock levels are too low the business will lose possible opportunities of higher sales. Debtors are a businesss customers owing money to the business having been bought the businesss goods or service on credit. If a business has cashflow problems it can maintain a low level of debtors by encouraging the debtors to pay as early as possible. Prepayments these are the expenses paid in advance. The payment being made even before the expense occurs is a prepayment. Bank and Cash Bank is the cash held in banks and cash is money held by the business in the form of cash. Having too much of money in the form of cash is also not good for a business since it can use that money to invest and earn a return but however a business should have healthy current ratio (current assets : current liabilities) of 2:1. Current liabilities Current liabilities are short-term debts that are in immediate need of settlement. Some examples of current liabilities are creditors, accruals, proposed dividends and tax owing. These obligations have to be paid within a year. Creditors also known as trade creditors are suppliers from whom the business purchased goods on credit. Paying the creditors as late as possible will ease cash flow requirements for a business. Accruals are the expenses owed by the business. Dividends proposed are the dividends payable for the year that is not yet paid. Tax owing is the sum of money owing as tax. 2.1.4 Sale of fixed assets Fixed assets are the assets a company that do not get consumed in the process of production. Some examples of fixed assets are land and building, machinery, vehicles, fixtures and fittings and equipment. Sometimes where the fixed asset is a surplus and is abandoned, it can be sold to raise finance in demanding times for the business. Otherwise businesses may choose to stop offering certain products and sell its fixed assets to raise finance. Selling fixed assets reduces the production capacity of a business affecting a businesss return. 2.2 External sources of finance Sources of finance that are not internal sources of finance are external sources of finance. External sources of finance are from sources that are outside the business. External sources of finance can either be: Ownership capital or Non-ownership capital

2.2.1 Ownership capital Ownership capital is the money invested in the business by the owners themselves. are mainly two main types of shares. They are: o o Ordinary shares Preference shares It can be the capital funding by owners and partners or it can also be share bought by the shareholders of a company. There

2.2.1.1 Ordinary shares Ordinary shares also known as equity shares are a unit of investment in a company. Ordinary shareholders have the privilege of receiving a part of company profits via dividends which is based on the value of shares held by the shareholder and the profit made for the year by the company. They also have the right to

vote at general meetings of the company. Companies can issue ordinary shares in order to raise finance for longterm financial needs. 2.2.1.2 Preference shares Preference shares are another type of shares. Preference shareholders receive a fixed rate of dividends before the ordinary shareholders are paid. Preference shareholders do not have the right to vote at general meetings of the company. Preference shares are also an ownership capital source of finance. There are several types of preference shares. Some of them are Cumulative preference share, Redeemable preference share, Participating preference share and Convertible preference share. Cumulative preference shares if a company is in a loss making situation and is unable to pay dividends for one year then the dividend for that year will be paid the next year along with next years dividends. Redeemable preference shares these preference shares can be bought back by the company at a later date. Normally the date of redemption is usually agreed. Participating preference shares give the benefit of additional dividends to its shareholders above the fixed rate of dividends they receive. The additional dividend is usually paid in proportion to ordinary dividends declared. Convertible preference shares convertible preference shareholders have the option of converting their preference shares to ordinary shares. 2.2.2 Non-ownership capital Unlike ownership capital, non-ownership capital does not allow the lender to participate in profit-sharing or to influence how the business is run. The main obligations of non-ownership capital are to pay back the borrowed sum of money and interest. Different types of non-ownership capital: o o o o o o o o o Debentures Bank overdraft Loan Hire-purchase Lease Grant Venture capital Factoring Invoice discounting

2.2.2.1 Debentures Debentures are issued in order to raise debt capital. Debenture holders are not owners but long-term creditors of the company. Debenture holders receive a fixed rate of interest annually whether the company makes a profit or loss. Debentures are issued only for a time period and thus the company must pay the amount back to the debenture holders at the end of the agreed period. Debentures can be secured, unsecured, fixed or floating. Secured debentures are debentures that are secured against an asset. They are also called mortgage debentures. Unsecured debentures these debentures do not have an asset as collateral. Fixed debentures have a fixed rate of interest. Floating debentures do not have fixed rate of interest and are not tied to any specific asset.

Bearer debentures these debentures are easily transferable. Registered debentures are not easily transferable and legal procedures have to be followed in case of a transfer. Convertible debentures can be converted to stock at the end of the debenture repayment date. 2.2.2.2 Bank overdraft Bank overdraft is a short term credit facility provided by banks for its current account holders. This facility allows businesses to withdraw more money than their bank account balances hold. Interest has to be paid on the amount overdrawn. Bank overdraft is the ideal source of finance for short-term cash flow problems. 2.2.2.3 Loan Loans are amounts of money borrowed from banks or other financial institutions for large and long-term business projects such as the development or expansion of the business. However loans can be substituted by other alternative sources of finance which are more suitable. 2.2.2.4 Hire purchase Hire purchase allows a business to use an asset without paying the full amount to purchase the asset. The hire purchase firm buys the asset on behalf of the business and gives the business the sole usage of the asset. The business on its part must pay monthly payments to the hire purchase firm amounting to the total value of the asset and charges of the hire purchase firm. At the end of the payment period the business has the option of purchasing the asset for a nominal value. 2.2.2.5 Lease In a lease the leasing company buys the asset on behalf of the business and the asset is then provided for the business to its use. Unlike a hire purchase the ownership of the asset remains with the leasing company. The business pays a rent throughout the leasing period. The leasing firm is known as the lessor and the customer as lessee. Leasing is of two types, namely Finance lease and Operating lease. Finance Lease this is where the lessees monthly payments add up to at least 90% of the total value of the asset. Operating Lease this lease does not run for the full life of the asset and the lessee is not liable for the full value of the asset. The residual risk is taken up by the lesser. 2.2.2.6 Grant Grants are funding given to businesses for programs or services that benefit the community or public at large. Grants can be given by the government or private firms. For example a grant may be given to open a new factory where unemployment is high. 2.2.2.7 Venture capital Venture capital is the capital that is contributed at the initial stages of an uncertain business. The chance of failure of the business is great while there is also a possibility of providing higher than average return for the investor. The investor expects to have some influence over the business. 2.2.2.8 Factoring This is where the factoring company pays a proportion of the sales invoice of the business within a short timeframe to the business. The remainder of the money is paid to the business when the factoring company receives the money from the businesss debtor. The remainder of the money will be paid only after deducting the factoring companys service charges. Some factoring companies even offer to maintain the sales ledger of the business. Factoring is of two types: Recourse factoring and Non-recourse factoring. Recourse factoring In this type of factoring the client company is liable for bad debts. Non-recourse factoring is where the factor takes responsibility for the payment of the debtors. The client company is not liable if debtors do not pay back. Non-recourse factoring is usually more expensive because of the high risks experienced by the factor. 2.2.2.9 Invoice discounting

In invoice discounting the client company send out a copy of the invoice to the invoice discounting firm. The client then receives a portion of the invoice value. In contrast to factoring, the client company collects the money from its debtors. Once the payment is received it is deposited in a bank account controlled by the invoice discounter. The invoice discounter will then pay the remainder of the invoice less any charges to the client. 3.0 The financial costs of the different sources of finance Personal savings have low costs since they are provided by an owner, partner or shareholder. The owner may charge a rate of interest for the loan provided. Retained profits have opportunity cost, that is the money could have been used elsewhere for some other purpose. Otherwise there arent any other costs for this source of finance. Working capital they do not have any costs other than opportunity cost. Sale of assets by selling fixed assets it uses then the firms production capacity will diminish. If it sells unused or abandoned fixed assets then only the potential production capacity reduces. Sometimes firms will have to stop offering certain products or services in order to sell its asset and raise finance. The asset may cost much more than what it sold for if it wants to replace it. Ordinary and Preference shares dividends has to be paid out of profits to shareholders as a return for their investment in the business. There are administrative costs occurring from issuing shares like stock exchange listing fee, printing and distribution fee and advertising fee. Debentures have to be paid a fixed or floating interest depending on the type of debenture that is issued. Bank overdraft interest is a little higher than for bank loans and interest is calculated on a daily basis. Loans Interest is usually fixed for short term loans, and long-term loans usually have a variable rate of interest. Interest rates are lower than for bank overdrafts. Hire-purchase the business ends up paying more than the original value of the asset for its purchase. Lease the ownership of the asset remains with the leasing company even after the business pays more than 90% of the assets value but however some leasing firms provide the option of purchase of the asset a nominal value. Grants are free and have no financial costs. Venture capital the venture capitalist will have some influence over the business and the business will have to share profits with the investor. The investor will want the capital back at a later date. Factoring Factors charge a rate of interest of about 1.5% to 3% of the invoice value as finance charges. Interest is calculated on a daily basis. Credit management and administrative fee are also charged and ranges from about 0.75% to 2.5% of turnover. Invoice discounting Invoice discounting also charges a rate of interest of about the same but its credit management and administrative charges are lower than a factors because only finance is provided and sales ledger is not maintained by an invoice discounting firm. Chapter 5 Leverage Firms can raise money through a variety of means. Usually, money is raised through the issuance of different types of securities (such as stocks and bonds). The capital structure of a firm is the proportion of each type of security that the firm has used. Most firms have both debt and equity in their capital structure. In general, debt is referred to as leverage and firms with debt in their capital structure are levered. Because firms have debt, we can divide the risk of owning a stock into two parts: 1) Business (or Operating) Risk: This is the risk associated with the assets of the company. In other words, it is the risk involved in the business activities of the firm. If the firm were 100% equity financed, this would be the only risk in the companys stock. 2) Financial Risk: When a firm is levered, its stock will have more risk. This derives from the fact that holders of the debt of the firm must be paid their interest before the stockholders can receive anything (i.e. dividends). Because of financial risk, the beta of a stock of a levered company will be greater than the stock of an identical, but unlevered, company.

Example: Consider two firms with identical operations. Each has raised $1,000,000 in financing. Firm A financed 100% with equity (sold 100,000 shares at $10 each). Firm B financed with $500,000 in debt (at 10% interest) and sold 50,000 shares at $10 each. Three possible outcomes for next year, depending on the economy: Firm A: Recession $50,000 0 50,000 20,000 $30,000 3% $0.30 Average $200,000 0 200,000 80,000 $120,000 12% $1.20 Boom $350,000 0 350,000 140,000 $210,000 21% $2.10

EBIT Interest Taxable Income Tax (@ 40%) Net Income Return on Equity EPS

Firm B: Recession $50,000 50,000 0 0 $0 0 $0 Average $200,000 50,000 150,000 60,000 $90,000 18% $1.80 Boom $350,000 50,000 300,000 120,000 $180,000 36% $3.60

EBIT Interest Taxable Income Tax (@ 40%) Net Income Return on Equity EPS

The variability in EBIT is the same for both firms (they have the same business risk), but EPS are much more variable for firm B. Firm B is leveraged, it has more financial risk. Note: Assume that the three possible outcomes are equally likely (each has 1/3 probability) Expected EPS for A = (1/3)(0.30) +(1/3)(1.20) + (1/3)(2.10) = $1.20 Expected EPS for B = (1/3)(0) +(1/3)(1.80) + (1/3)(3.60) = $1.80 Leverage increases the expected earnings per share (and the expected return on equity). Leverage increases the expected return to shareholders, but also the risk. Note that the numbers of interest to the shareholders of these firms, the Return on Equity and the Earnings per Share, are more variable for the levered firm than for the unlevered firm. Thus, the levered firm is more risky. This illustrates the point that, while people often think of leverage creating risk simply because it raises the possibility of bankruptcy, leverage increases the risk of the stock of a company even if that company is very healthy and there is very little chance of it going bankrupt.

The beta of a stock can be thought of as consisting of two parts, the part associated with business risk (which I will denote asset because it deals with the risk of the assets of the firm), and the part associated with the financial risk of the firm. If the firm is 100% equity financed, asset=equity where: equity is the beta of the stock of the firm (from CAPM). If the firm is levered: assetDFLA B has more financial leverage. Easier way to calculate DFL;

Consider a $1 change in EBIT. Percentage change in EBIT=1/EBIT Let I=interest, T= tax rate, S = number of shares

EPS =

( EBIT I )(1 T) S

$1 change in EBIT gives;

( EBIT + 1 I)(1 T) ( EBIT I)(1 T) S S Percentage change in EPS = ( EBIT I )(1 T) STo get DFL, divide the percentage change in EPS by the percentage change in EBIT, and with some simple algebra you will get:

DFL =

EBIT EBIT I

Degree of Operating Leverage Consider two firms which produce an identical product, but utilize different production technologies. Firm A uses a labour intensive process. It has fixed costs of $100,000 per year and its variable costs are $3 per unit produced. Firm B uses a more automated system. Its fixed costs are $150,000 per year and it has variable costs of $2 per unit produced. Both firms sell their at a price of $10 per unit. Sales next year depend on the state of the economy, which could be recession, average or expansion. Firm A: Unit sales Sales fixed cost variable costs EBIT Firm B: Unit sales Sales fixed cost variable costs EBIT 20,000 200,000 150,000 40,000 10,000 50,000 500,000 150,000 100,000 250,000 100,000 1,000,000 150,000 200,000 650,000 20,000 200,000 100,000 60,000 40,000 50,000 500,000 100,000 150,000 250,000 100,000 1,000,000 100,000 300,000 600,000

Both firms have the same degree of risk (variability) in their level of sales. However, firm B has higher variability in its EBIT. Hence, B has more business risk.

The greater risk in B is because of the higher operating leverage, a greater proportion of fixed costs. The degree of operating leverage (DOL) determines how risk in sales translates in to risk in EBIT (business risk). [The DFL then determines how risk in EBIT translates into risk in EPS.] How to measure DOL?

DOL =

percentage change in EBIT percentage change in sales

From the above numbers:

DOL A,500000

600000 250000 250000 = 1000000 500000 500000 1.4 = 1 = 1.4 650000 250000 250000 = 1000000 500000 500000 = 1.6

DOLB ,500000

As with DFL, there is an easier way to calculate DOL. By considering a $1 change in sales and doing some algebra one can show that:

DOL =

sales total VC EBIT

You should be able to use this formula to reconfirm the DOL numbers calculated for the example. Degree of Combined Leverage Recall that: - DOL translates risk in sales into risk in EBIT - DFL translates risk in EBIT into risk in EPS The degree of combined leverage (DCL) looks at how the two combine.

DCL =

percentage change in EPS percentage change in sales

Since the DCL is simply the effect of DFL and DOL combined: DCL = (DFL)(DOL) or

EBIT sales total VC DCL = EBIT I EBIT = sales total VC EBIT I

Note that there are two parts to the DCL, the DFL and the DOL. The implication is that managers can choose DOL and DFL to offset each other or to meet an overall goal for their total risk exposure. For example, if business risk is high naturally, the firm will probably choose lower leverage (lower DFL) to mitigate this. But, if the firm uses a production process with low FC (low DOL) then this may allow for higher DFL. Financial Distress What is Financial Distress? A situation where a firms operating cash flows are not sufficient to satisfy current obligations and the firm is forced to take corrective action. Financial distress may lead a firm to default on a contract, and it may involve financial restructuring between the firm, its creditors, and its equity investors. Definition of Terms Default Failure to meet an interest payment, or Violation of debt agreement Formal procedure for working out default Does not automatically follow from default.

Bankruptcy

Financial Distress Includes default and bankruptcy, but also Threat of default or bankruptcy and its effect on the company Defined to capture the costs and benefits of using large amounts of debt finance

Insolvency Stock-base insolvency; the value of the firms assets is less than the value of the debt. Flow-base insolvency occurs when the firms cash flows are insufficient to cover contractually required payments.

What Happens in Financial Distress? Financial distress does not usually result in the firms death. Firms deal with distress by Selling major assets. Merging with another firm. Reducing capital spending and research and development. Issuing new securities. Negotiating with banks and other creditors. Exchanging debt for equity. Filing for bankruptcy.

Responses to Financial Distress Think of the two sides of the balance sheet. Asset Restructuring: Selling major assets. Merging with another firm. Reducing capital spending and R&D spending.

Financial Restructuring: Issuing new securities. Negotiating with banks and other creditors. Exchanging debt for equity. Filing for bankruptcy

Chapter 6 The Cost of Capital

Cost of Capital, Discounts Rates, and the required Rate of Return

-

We know how to do capital budgeting problems, but what about the discount rate.

We also know that the discount rate will depend on the risk of the project:

-

Investors will require a higher required rate of return for riskier projects

Investors will look at projects as portfolios and therefore the systematic risk is the correct

measure of risk. Any unsystematic risk can be diversified away, and no compensation for this is necessary. Required rate of return, appropriate discount rate, and cost of capital are different names for the same concept. The cost of capital depends on the risk, and hence primarily on the use of the funds, not the source.

Firm's overall cost of capital reflects the required rate of return on the firm's assets as a whole. This overall cost of capital is called the weighted average cost of capital, and reflects the costs of debt, equity, and preferred stock.

Factors Affecting the Cost of Capital General Economic Conditions Affect interest rates Affect risk premiums Affect business risk Affect financial risk Affect flotation costs and market price of security Market Conditions Operating Decisions Financial Decisions Amount of Financing

Retained earnings is the cumulative net earnings (less losses) that is retained in the business (i.e., not distributed to shareholders) Retained earnings, opening balance + Net earnings (or - net loss) - Dividends = Retained earnings, ending balance The weighted average cost of capital (WACC)

-

Assume the firm has a target capital structure (mix of debt and equity)

Capital structure weights:

Value of the Firm = Value of Equity + Value of Preferred + Value of Debt

-

V=E+P+D

wE = E / (E +P + D) = E / V

wD = D / (E + P + D) = D / V

wP = P / (E + P + D) = P / V

Weighted Average Cost of Capital:

WACC = RWACC = wE RE + wP RP + wD RD (1 Tc)

Focus on before-tax or after-tax capital costs?

Shareholders are concerned with cash flows available to them

after corporate taxes have been paid

Therefore, use After-Tax WACC.

Only rD needs adjustment.

Why adjust rD ?

-

The cost of debt is tax deductible to the issuing firm.

Costs of preferred and common are not deductible.

What is marginal cost?

-

Decisions are being made regarding new capital investment.

Therefore, the cost of the next dollar of capital is the relevant question (marginal cost).

Market or Book Values?

-

Cost of capital measures marginal cost of issuing new securities to finance projects. These securities are issued at market value. Weights assigned to debt and equity in calculating WACC should be based on market value.

The Cost of Debt Example: Calculate the return on debt if you know the following information: Coupon = 10% semiannual; Face = $1,000 Price = $1,081.44; Maturity = 15 years

-

Example:

Pharmacia has bonds outstanding with the following specifications. These are 30-year, 7% annual coupon bonds, and selling at 96% of their face value ($1,000). What is the cost of debt for Pharmacia?

What if Debt isnt publicly traded? Note: Since the bond pays a coupon semi-annually, and earns 4.5% in six months, we could also calculate the effective annual rate (EAR).

-

EAR = (1.045)

2

- 1 = ________%

However, nominal rates are generally used for the cost of debt.

Reason: Flotation cost - Total costs of issuing and selling a security reduce the net proceeds from the sale These costs are typically small on public debt issues.

Most debt is privately placed directly with large investors. So flotation costs are almost nonexistent.

Flotation Cost Approaches

Incorporate into component costs of capital

bond price = par value = $1,000

flotation costs = 1% of issue = $10

net proceeds = $990

Treat flotation costs as investment outlay of new project

cost of capital theoretically depends on risk of use of funds, not source

-

increase initial cost to account for flotation costs

The Cost of Preferred Equity Example: Calculate the return on preferred stock if you know the following information: Price =$112.5; Dividend Yield = 9%; Par=$100;

-

Preferred Just rP.

dividends

are

not

tax

deductible,

so

no

tax

adjustment.

Nominal rP is used.

Preferred stock tends to be a small part of a firms capital structure, and in practice is often ignored.

Is Preferred stock more or less risky than debt? Corporations own most preferred stock, because 70% of preferred dividends are nontaxable to corporations.

-

Therefore, preferred often has a lower B-T yield than debt.

The A-T yield to an investor, and the A-T cost to the issuer, are higher on preferred than on debt.

The Cost of Equity Equity consists of two components: retained earnings and new equity issues Why is there a cost for retained earnings?

-

Earnings can be reinvested or paid out as dividends.

Investors could use dividends to buy other securities and earn a return.

Thus, there is an opportunity cost if earnings are retained.

Opportunity cost is the return stockholders could earn on alternative investments of equal risk.

They could buy similar stocks and earn RE, or the company could repurchase its own stock and earn RE. So RE is the cost of retained earnings.

Cost of Retained Earnings

-

Model I: The Security Market Line (SML) Approach

Remember, the required rate of return on a risky assets depends on:

the risk free rate, Rf

-

the market risk premium, E(RM) Rf

the systematic risk of the asset, relative to the average,

The SML, or CAPM tells us that the expected return on the firm's equity is

E(RE) = Rf + E [E(RM) Rf]

And, if we drop the expectations

RE = Rf + E [RM Rf]

Example: rRF = risk free rate = 7.0%

current rate on government security

RPM = (rM - rRF) = 5.0%

bS = 1.25

Example: Pharmacia has an equity beta of 1.6, the risk free rate for return is equal to 5%, and the return on a welldiversified market portfolio is 15%. What is the cost of equity capital for Pharmacia? The Risk-Free rate: T-bonds vs. T-bills

-

Embodies long-term inflation expectations.

Is influenced less by Federal Reserve actions, currency flows, etc.

Is the more logical investment alternative to stocks since they have similar investment horizons.

How do we calculate the risk premium on the market?

-

Ex e.g. Ibottson and

post Assoc. provides this

data on an annual

(Historical) basis :

RPM = 7.3% for 1926-1996. Future of market minus T-bond Model II: The Dividend Growth (or Discounted Cash Flow) Model estimates by financial analysts

-

P0 = (D0 [1 + g]) / (RE g) = D1 / (RE g)

RE = (D1 / P0)+ g

Example:

What is the DCF (discounted cash flow) cost of retained earnings?

Given: D0 = $5.00;P0 = $76; g = 6%?

Pharmacia has just paid a $9 dividend. The dividends are expected to grow at 12% per year. Pharmacia currently sells for $112 per share. What is the cost of equity capital for Pharmacia?

Disadvantages of Discounted Cash Flow Method

-

Model is simple to use, but there are many disadvantages and problems:

You need a firm that pays dividends

You need very constant growing dividends

You need a very accurate estimate of the growth rate

Can Discounted Cash Flow Method be used if g is not constant? New Common Stock versus Retained Earnings New Common stock incurs flotation costs

-

Some books suggest increasing the discount rate to reflect flotation costs.

End up with a cost of new equity greater than the cost of retained earnings

But required return should reflect risk of investment (use of funds, not source of funds)

Example:

The Weighted Average Cost of Capital Book value debt = $3 million Preferred stock is selling for $100/share and there are 10,000 shares out Common stock is selling for $20/share and there are 300,000 shares out Target capital structure (market value) B = 30% P = 10%

S = 60% Return on debt = 9% Return on Preferred = 8% Return on Equity = 13.1% Tax rate = 40%

-

Pharmacia has $200 million worth of equity and $600 million worth of debt on its balance sheet. The market value of the equity is $650 million, and the market value of the debt is $975 million. The corporate tax rate is 34%. What is the WACC for Pharmacia? We can use the WACC as the discount rate in capital budgeting only if the project has a similar risk as the firm as a whole. If the project has a risk that is different from the firm as a whole, the SML approach is needed.

Pure Play Approach: if there is no beta for the project available, use the WACC or beta from a company that has similar risk as the project. Example: Giant Eagle is considering an expansion in the pharmaceutical business. The problem that they are facing is that they do not have a beta for this project available, and they realize that the risk involved with the pharmaceutical business is quite different from being in the grocery store business. What discount rate could Giant Eagle use? Chapter 7 CAPITAL STRUCTURE DECISION

THEORY OF CAPITAL STRUCTURE Determination of an optimal capital structure has frustrated theoreticians for decades. The early work made numerous assumptions in order to simplify the problem and assumed that both the cost of debt and the cost of equity were independent of capital structure and that the relevant figure for consideration was the net income of the firm. Under these assumptions, the average cost of capital decreased with the use of leverage and the value of the firm (the value of the debt and equity combined) increased while the value of the equity remained constant.

%

Ks Ka Kd

Debt/Equity

Modigliani and Miller showed that this could not be the case. Their contention was that two identical firms, differing only in their capital structure, must have identical total values. If they did not, individuals would engage in arbitrage and create the market forces that would drive the two values to be equal. Their proof of this proposition was based upon several assumptions (many of which have subsequently been relaxed without changing the results): All investors have complete knowledge of what future returns will be All firms within an industry have the same risk regardless of capital structure No taxes (we will relax this assumption subsequently) No transactions costs Individuals can borrow as easily and at the same rate of interest as the corporation All earnings are paid out as dividends

FINANCING/CAPITAL STRUCTURE DECISIONS Financing decision of a firm deals with the determination of capital and financial structures of that firm. Here, the composition of the capital structure and financial structure is the vital one. Capital and financial structures of a firm may be composed of: (i) equity capital internal and external; (ii) preferred capital and (iii) debt capital short-term and long-term. Capital Structure Theory Concept of Capital Structure and its Differences with Financial Structure

The investment projects of a company can be financed either by: Increasing the owners claims(Equity); or Increasing the creditors claims(Debt) The owners claims increase when the firm raises funds by: Issuing common (or ordinary) shares Or Retaining the earnings

The creditors claims increase when the firm raises funds by: borrowing

The various means of financing represent financial structure of an enterprise. Balance Sheet Financial Structure Liabilities Current Liabilities Capital Structure Debt and Preferred Shareholders Equity Assets Current Assets

Fixed Assets

Capital structure is the permanent financing of a firm represented by long-term debts plus preferred stock and net worth. Net worth=Equity capital+ reserves and surplus+ retained earnings + other funds of the ordinary or equity shareholders or stockholders. Traditionally short-term borrowings are excluded from the list of methods of financing the firms capital expenditures, and therefore, long-term claims are said to form the capital structure of the enterprise. Capital structure is the composition of debt and equity securities that comprises a firms financing of its assets.- J.J.Hampton Capital structure is regarded as the proportion of debt and equity.-James C. Van Horne Capital structure is the mix of long-term sources of funds, such as debenture, long-term debt, preference share capital and equity capital including reserve and surplus (retained earnings).- I.M. Pandey The major distinctions between Capital Structure and Financial Structure are pointed out as under:

Bases Definition

Capital Structure Capital structure represents only the permanent (long-term) source of financing. Cost of capital is determined by it. Current liability is not included in it. Limited It is the part of total financing.

Financial Structure Financial structure permanent

represents and

both

the

(long-term)

temporary

Cost of capital Current liability Scope Total/part financing

(short-term) source of financing. Cost of capital is not determined by it. Current liability is included in it. Wide It is the total or whole financing.

Features of Capital Structure (i) (ii) (iii) (iv) It is the mixture of both debt and equity It is the composition of retained earnings, debenture, preferred share, and ordinary shares. Long-term capital is included in it. The company changes the capital structure whenever it is required. Cost of capital affects capital structure.

(v)

Optimum Capital Structure

Optimum capital structure may be defined as the capital structure or combination of debt and equity which maximizes the value of the firms equity stock. It lies at the minimum cost of capital (cost of debt +cost of equity). Project 1 Debt capital ratio 2 Equity capital ratio 3 Cost of debt at 12% 4=2 @12% Cost of equity At 18% 5=3@18% Overall cost of capital 6=4+5

A B C

.60 .50 .70 The capital structure of

.40 .072 .50 .060 .30 .084 project C is optimum.

.072 .09 .054

.144 or 14.4% .15 or 15% .138 or 13.8%

Features/Characteristics of a Sound/Appropriate/Optimum Capital Structure

The features of an optimal capital structure differ from firm to firm, depending on the nature, size, products and markets, environments, specific and general etc. However, the following may be the general features of an optimal capital structure:

Profitability: It should be most advantageous. Within the constraints, maximum use of leverage at a minimum cost should be made. Solvency: The excessive use of debt threatens the solvency of the company. If the cost of debt is relatively high, then the debt should be avoided. Flexibility: It should be flexible so that the company can change it to finance its profitable activities or to meet the changing conditions. Debt Capacity/Conservatism: It should be conservative i.e. within the debt capacity of the company. The debt capacity of a company depends on its ability to generate future cash flows to repay the interest and principal amount in time. Control: The ordinary, not the debenture or preferred, shareholders usually control the company. The capital structure should involve minimum risk of loss of control of the company. The owners of closely held companies are particularly concerned about dilution of control.

Factors Affecting Capital Structure Decisions

A. Quantitative/ Financial Factors i) Profitability Aspect This determinant is the top-most one while determining capital structure of the enterprises. This signifies that the enterprises with higher profitability will prefer debt capital as compared to equity capital. This is because of the fact that interests on debt get exemption from tax burden and also because of comparatively cheaper source of capital and lower floatation costs involved in obtaining debt. On the other hand, enterprises with lower or negative profitability, having no other alternative, will take resort to equity capital. ii) Growth Rate The enterprises with higher growth rate will prefer debt capital as compared to equity capital. This is because of comparatively lower floatation cost involved in obtaining debt capital than issuing common stock and comparatively cheaper source of capital. On the other hand, the enterprises with lower, no or negative growth rate, having no other alternative, will take resort to equity capital. iii) Liquidity Aspect The enterprises with reasonable liquidity, nor too lower neither too higher will prefer debt capital to equity capital because of the advantages of debt capital of the enterprises mentioned earlier. On the other hand, the enterprises with either too lower or too higher liquidity, having no other alternative will go for equity capital. iv) Relative Costs of Sources of Fund

Since the authors of corporate finance hold the view that the effective cost of debt capital is comparatively cheaper; the enterprises should prefer debt capital rather than equity capital; other conditions like availability of fund, reasonable liquidity and higher profitability and growth rate remaining the same. v) Stability of Sales/ Investments The enterprises with more stable sales/ investments will prefer debt capital to equity capital because of the benefits attached to debt capital. On the other hand, the enterprises with less or unstable sales/ investments, having no other alternative will go for equity capital. VI) Financial Risk Financial risk is another important determinant while designing the capital structure of the enterprises. The enterprises with higher financial risk should use lower debt capital and higher equity capital. On the other hand, the enterprises with lower financial risk should use higher debt capital and lower equity capital. (vii) Corporate Tax The advantage of the presence of debt in capital structure in world of corporate taxes is that interest payments on debt are deductible as an expense. They elude taxation at the corporate level, whereas dividends on equity or retained earnings are not deductible for the tax purposes. Consequently, the total amount of payments available for debt holders and equity holders is greater if debt is employed in capital structure. Corporate taxes create an incentive for the debt holders through the deduction of interests as an expense. Therefore, one of the main reasons of using debt in capital structure of a firm is that interest on debt is deductible from calculation of taxable income, which lowers the effective cost of debt. viii) Operating Risk Operating risk or business risk, emanating from operating/ business leverage is influenced, among other things, largely by fixed costs. The more the fixed costs, the more will be the operating risk and vice-versa. The firms with higher operating risk should use lower debt and higher equity and vice-versa. B. Qualitative/ Non-financial factors i) Availability of Fund The determination of capital structure of corporate industrial firm is largely influenced by the availability of fund, both home and abroad. If requisite fund is easily available in capital market on reasonable terms and conditions; the management of a firm may design its capital structure in targeted manner. On the other hand, if fund is not easily available in capital market with reasonable terms and conditions; the management will not be in a position to design its capital structure in a desired way. Funds may be procured from two main sources viz., internal sources and external sources. Internal sources include retained earnings/ accumulated profits, reserves and surplus and accumulated depreciation. The availability of such internal sources mainly depends on profits earned and policies relating to dividend and retention and reserves and surplus. External sources include: equity share capital, preference share capital and long-term debts. The availability of such sources mainly depends on the efficient capital market of the country, which is examined under the sub-point state of capital market. ii) Proper Timing Closely related to flexibility in determining issue of securities is the factor of timing. Proper timing of security issue often brings substantial savings. Since it is known that securities market is dynamic, management has to make fair expectation regarding its future trends. After considering the factors of risk, income and control regarding the choice of a financing alternative; management may still pause in its decision if it feels that by waiting for a certain period the debenture or share issues can be made at a favorable price. The question of timing is equally relevant in case of issue of preference share and debentures. The enterprises which can follow

proper timing while procuring their requisite fund are in a better position to employ debt capital with comparatively less cost of capital in their capital structure. On the other hand, in the enterprises where proper timing cannot be followed in the procurement of requisite fund; the use of debt capital may become comparatively costly to these enterprises. iii) State of Capital Market Capital markets are integral part of developed and industrialized economy. It augments the process of economic development by a number of ways namely : i) encouraging savings, ii) attracting more savers and users into investment process, iii) helping mobilization of non-financial resources, iv) attracting external resources and v) offering financial innovations to match the diverts and changing needs of savers and users etc. In fact, capital market supplies cash capital as a long-term basis to the industrial entrepreneurs who, in turn, use the same for procuring other factors of production. When more factors of production are in use, more production is created, and as such, by supplying capital, a capital market helps create more productive capacity in the economy. iv) Control of Business The issue of ordinary shares involves the problem of control since each new share adds one new vote. To the extent that the additional issue of ordinary share is made to new shareholders as against the existing shareholders, there is a dilution in the control of the existing shareholders. On the other hand, the debt or debenture issue and preference share do not affect the control of existing group. The preference shareholders may have a right to elect a minority of directors in the event of lapse in dividend payment but this does not involve a major upset in control.

The impact of debt capital versus equity capital on the managements control position can influence the determination of capital structure. If management has majority voting control but not in a position to issue any more common stock/ share; it chooses debt capital in capital structure. On the other hand, management may decide to employ equity capital in capital structure if the firms financial position is so weak that the use of debt might lead to serious risk of default. v) DFIs Recommendation Capital structure of a private sector corporate industrial firm is also influenced by DFIs recommendation. Therefore, DFIs recommendation plays the vital role in designing capital structure of the corporate firms. If any DFIs recommends favorably to any firm for any bank loan; it becomes easy for that firm to employ more debt capital in its capital structure. On the other hand, if any DFIs recommendation is not favorable to any firm; the firm, having no other alternative will use equity capital. vi) Regulatory Framework of SEC Regulatory framework of SEC also influences capital structure determination of the private sector corporate industrial firms if they are the members of DSE/ CSE. That is, the rules and regulations as framed by SEC will influence the capital structure determination. Hence, if these rules and regulations are not conducive to the enterprises; they prefer debt capital to equity capital. On the other hand, if these rules and regulations are favorable to the enterprises; they will prefer equity capital to debt capital. vi